Episode 20: What is Economics Useful For?

What is economics good for? I think there’s a lot of confusion as to what it can do and what its limitations are.

The problem us economists face is that we must always have answers, and they must always be accurate. Anything short of that means that the entire science is bogus.

But economics is only as good as the data it relies on, and data is always imperfect in some way.

The way I like to talk about economics to the general public is that it helps tell you where to look, and also if you’ve found what you’re searching for.

The first part is like advanced geology mapping equipment. Let’s pretend that you’re looking for gold in your back yard. Now you can stumble around blindly and just dig here or there, and depending on how much gold you have you might find some. But economics can point you to where the best spot to dig would be.

Economics achieves this by figuring out which way data are facing. That is to say, to maximize profit, should we decrease prices? Well if you do that you calculate  that you’ll sell more products, but make less money per sale. Is it worth it? Economics can give you your answer.

But it’s not perfect because your data isn’t perfect.  Maybe your sales estimation model is off. Maybe reducing your prices doesn’t lead to as many new sales as you thought. Just like how you can miss the gold vein, sometimes you can end up with the wrong result. But it helps you get close. And with more refinement you can often strike something.

The second way it can help is to verify what you’ve found. So you pull a strange rock out of the ground. Does it have gold in it?  Economics can help you test if the strategy you’ve discovered is indeed a winning one.

The way economics can tell you with certainty what it is that you have is with the magic of the p values. You’ll see this in most econ literature. The p stands for probability, and it’s the probability that the effect you are seeing is because of random chance. The lower the p-value, the more confident you can be that an effect is “real”. The higher the p-value, the more likely the result is just the randomness of data.

A quick example is the fastest way to illustrate the point. You’re flipping a coin, heads or tails. My hypothesis is that the coin is rigged to always land on heads.

You flip the coin and it lands on heads twice in a row. Well that’s data in the direction of my hypothesis, but you could get the same result with a normal coin easily. So the p-value would be maybe .5 or a 50% chance that the coin is rigged (yes economists, I know this isn’t how p-value is directly calculated but I’m trying to keep things simple to illustrate the point), but also a 50% chance that the flips of a coin are random.

The next two flips are tails. Wow. The chance that a rigged coin would “misfire” twice in a row is pretty unlikely. Our p-value jumps to maybe .99, or 99%. We’re almost certain it’s not a rigged coin based on the data that we have.

Then the next 10 flips are heads. Every single one; right in a row. That is statistically fairly unlikely, but not impossible (probability of about .01%). So our p-value jumps down to maybe .07. Then the next 10 are heads. 20 head flips in a row? That’s really very unlikely to be a “localized streak” (probability of about .0001%). There’s almost certainly some connection between the coin and these flips; it almost certainly can’t be random chance!

For our example let’s assume our p-value falls to .04, or 4%. It is generally accepted in the scientific community that a p-value under 5% is “statistically significant”. That is to say, we’ve crossed a magical threshold. I can tell you with reasonable certainty that the something with these flips is indeed rigged. It’s still possible that I’m wrong, but so unlikely, that I can say with reasonable certainty that the rigging of the toss is real.

Then we flip heads another 10 times in a row. Well now we’ve flipped 2 heads, 2 tails, and 30 heads in a row. The chances of a coin being flipped 30 times heads in a row are astronomically small. I mean like .0000001%. Another way to think about it is you can expect to have a run like this if you did a series of 10000000000 coin flips (I may have missed a zero or two it’s hard to keep track). We’re talking rare.

So our p-value now jumps below .01, maybe to .009, or .9% that the effect is due to chance (in reality it might be much lower with 30 flips but stay with my analogy). We can be almost positive that our results are in fact real. There is something rigged about the tosses. The chance that they are not connected is practically, but not entirely, zero. There is truth to the famous Mac (from IASIP) quote that “with God, all things are possible”. And that’s certainly true. But really our data suggests we have a fact. Under 1%, or <.01 p-value is the next generally accepted threshold for scientists. Usually when 5% gets a * (to mark it’s significant), 1% gets ** (two stars)!

Okay so let’s flip the coins some more, and let’s in fact say that you flip heads another 70 times.

That’s a run of 100 head flips in a row. The odds become… impossible on a near universal scale. Like. A .00000000000000000000000000007% chance. I mean it’s such a small number it’s insane. In the scientific community we’d just say your p-value is now <.001. This is generally regarded as the last stop and is given *** (3 stars) to denote its statistical significance. There’s generally no point in going smaller because at just a .1% chance of being due to a random streak of data we can say with confidence that this effect is real.

Certain applications of statistics will push for an even lower p-value, but it’s really just to make a point. At <.001 whatever you are trying to prove is a fact.

Here’s another way to think about it. Lavar Ball says his son Lonzo Ball is going to play for the Lakers at Lonzo’s birth.  The chances of someone playing in the NBA are amazingly tiny, and to play for a specific team are tinier still. If Lavar Ball’s statement had a p-value of <.001 however, then even if Lonzo’s birth existed in 1001 different universes, he would play for the Lakers in 1000 of them.

At that point you can just say it’s destiny that Lonzo is in fact going to play for the Los Angeles Lakers. There is a cosmic connection, or a rigged system. It’s not up to chance.

And the same can be said for our coin.

Economics and p-values are powerful tools. And I’m only scratching the surface. There’s R-values and T-values and regression analysis to tell you all sorts of fun stuff.

But for the general layperson out there, this is the basis of the power of economics. To give you a general map of what is really going on, and then to test to prove that the gold you found is really gold, and not fools gold.

Episode 21: Monkey (Unconsciously) See, Monkey (Unconsciously) Do
Episode 19: Subjective Probability (Part 2)

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