1) Interpreting correlations
Suppose you observe a negative correlation between A) the amount of government debt in a country and B) the economic growth rate of that country.
Does this mean that a greater government debt causes slower economic growth?
Well, correlation does not necessarily imply causation. What else could be going on?
The causation could be the other way around. “Reverse causation“. Perhaps higher economic growth leads to lower debt.
For example, the government receives greater tax receipts as more is being produced. Hence the government can pay down its debt.
Also, consider the link between the number of years spent in school and wages later in life. Does a positive correlation between the two mean that spending more years in school boosts wages?
Not necessarily. In fact, it could be that an omitted third factor leads to changes in both years of school and average wages. This could be some sense of “natural” or innate ability.
We might expect those with higher innate ability to be able to handle more years in school and potentially be more productive in work later on, boosting wages.
In order to establish any sense of causation, we will need more than just a correlation…
2) Econometrics – normal distribution and similar distributions; hypothesis testing; regression, natural experiment.
Statisticians can “run regressions”. This means drawing a line of best fit for any correlation.
We can then conduct “hypothesis tests” to see if the correlation is significantly large or not.
Regression equations can be very useful, for example in:
- Estimating key “parameters”, like the price elasticity of demand for a good.
- Predicting / forecasting variables like stock prices or the rate of unemployment.
- Testing an economic theory, such as whether education boosts wages.
To help overcome the correlation problem, enter the idea of a “natural experiment“.
A natural experiment, using random events in the real world as a sort-of experiment, may allow us to conduct experiments in the real world on economic events.
This could include unexpected variations in the minimum wage or any other policy variation. An alternative is another event like a change in government or a natural disaster.
Natural experiments indeed won a recent Nobel Prize .
Question to discuss: can you think of natural experiments to measure the effect of changes in police numbers on crime rates?
3) Dealing with uncertainty
Suppose if a fair coin lands on heads, you receive £100. But if it lands on tails, you get nothing.
Would you choose to flip the coin, or to receive £40 for certain?
Does your answer change if the £100 becomes £100 million and the £40 becomes £40 million?
Many will choose to take the amount for certain. Even if this amount is less than what you “expect to get” from a flip of the coin.
On average, the coin toss will get you more money (£50) than the certain option of £40.
We call this “risk aversion“.
Analysing people’s risk preferences is important. It may affect government policy, for example people may avoid littering if there is a sufficient risk of being fined.
Alternatively, firms may use this to try to reassure consumers through refund policies for instance.
Risk-neutral or expected value methods may be used to value financial assets. This includes stocks and bonds. The “binomial pricing” model is one way to price financial assets, using a “probability tree”.
4) Mixed strategy Nash equilibrium
A “Nash equilibrium” in game theory occurs when there is no beneficial deviation for any agent, given the other agents’ actions.
For instance, in an oligopoly, price reduction by all firms is often the Nash equilbrium. Both firms raising their prices would increase total profits. But each firm prefers to price low while the other is pricing high. .
But what if the opponent “mixes” their actions? In the game rock-paper-scissors, someone could randomly pick each option with probability one-third for instance.
Using probabilities allows us to find “mixed strategy Nash equilibria“. These occur when there is no beneficial deviation to another mixed or non-mixed (“pure”) strategy, given other agents’ strategies.
The mixed strategy Nash equilibrium is an important result. It features in a lot of applications, including:
- Volunteer’s dilemma – When a crime occurs, witnesses may have a choice in whether to call the police or intervene. But many may not intervene – the bystander effect. Does the bystander effect get larger or smaller, the more people witness a crime?
- Attack and defence – suppose one corporation wants to challenge the dominant market position of another company. Which products should they compete on? Where should the incumbent firm allocate its marketing resources to defend its position? A mixed strategy Nash equilibrium may be the optimal outcome here. This can apply not just to companies but also governments in any kind of trade or military conflict.
5) Checking papers for mistakes
It is important to check the stats work of academic papers. Junior students often “replicate” the work of senior academics, just to make sure there are no mistakes.
However there is one famous instance of significant mistakes.
Reinhart and Rogoff wrote a paper showing a correlation between economic growth and debt-to-GDP. Above 90% debt-to-GDP ratios, countries appeared to head into negative economic growth on average.
Yet, a researcher found a mistake in Reinhart and Rogoff’s Excel spreadsheets. The accidental exclusion of five countries led to a significant overstating of the link between debt-to-GDP ratios and economic growth.
Since this incident, standards for what can be accepted by the top economics journals have broadly continued to rise.
Yet throughout economies and also several science subjects, there are concerns about the “replication crisis” and “p-hacking”. For instance, the replication crisis finds that many studies are very difficult to reproduce, which may undermine findings.
Improving the credibility of studies will continue to be a key research agenda going forward.
Question to discuss: how can researchers improve the credibility of their research and reduce the scale of the “replication crisis?”.
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