06 Sep 2017

## More on Flood Statistics

In my previous post, there was still some confusion in the comments. And on Twitter, I got the sense that even trained economists didn’t understand what the big deal was.

So remember, the claim is that the phrase “100-year flood event” or “500-year flood event” is very misleading. When the government data agency gives such a designation, it is referring to the probability of an annual occurrence. For example, a “100-year flood event” is defined as “a flood event that has a 1% probability of occurring in any particular year.” People erroneously think that means the same thing as, “We expect a flood like this to happen once per century,” but no, that’s not really what it means.

Let’s imagine instead that we’re talking about a “4-year flood event.” In other words, there is a 25% chance each year that we’ll see a flood of this magnitude.

Now, over a given 4-year stretch, what is the expected number of such floods? More specifically, what is the mathematical expectation of the number of floods we’ll observe?

One way to calculate this is to say each year we have an expectation of 0.25 floods, times 4 total years, means an expectation of 1.0 floods over the course of 4 years.

However, is that the same thing as saying, “We expect to see 1 flood over a 4-year stretch?”

I don’t think so. First, let me ask a different question: “Do you expect it to rain tomorrow?”

How do you answer? Surely, if the person thinks there is less than a 50% chance of rain tomorrow, then he can’t possibly answer, “Yes I expect it to rain tomorrow.” Right?

So by the same token, if you think there is less than a 50% probability that we will see 1 flood during a 4-year stretch, then it is arguably incorrect to say, “I expect to see 1 flood during a 4-year stretch.”

Here’s the actual breakdown of possible outcomes:

As the chart shows, there is only a 42% chance that we will observe exactly 1 flood during any 4-year interval. So if someone asks me, “Do you expect 1 flood to occur in the next 4 years,” I could plausibly answer, “No, because there is a 58% chance that something besides 1 flood will occur.”

This isn’t just a matter of semantics. It can definitely mislead people in certain settings.

For example, when people learn that their house is located in a “100-year flood zone,” they think their house is only going to get hit with a flood “once per century,” and so they might not buy flood insurance.

However, since what this actually means is that there is a 1% chance each year of such a flood, we can tell such a homeowner that over the course of his 30-year mortgage, there is a 26% chance of being hit by such a flood at least once. That sounds a lot more deserving of flood insurance than, “You’ll get hit by a flood like this once a century.”

06 Sep 2017

## Amplifying Oren Cass on a Carbon Tax, Part 1 of 2

My latest post at IER amplifies some of the points Oren Cass made in a fantastic essay he wrote (two years ago) on the case for a US carbon tax. (I just came across the essay recently.) Here’s an excerpt:

Let me paraphrase Cass’s remarks to make sure the reader appreciates them. Cass was studying a very scholarly tome put out jointly by several organizations that support a carbon tax.

In order to demonstrate its potency, the book argued that a carbon tax had the power to reduce U.S. emissions in half by the year 2050. But in order to achieve that drastic result, the authors assumed a carbon tax that hit \$163 per ton in the year 2050.

In the next chapter of the book, the authors sought to reassure the reader that the “Macroeconomic Effects of Carbon Taxes” wouldn’t be so awful. Yet the figures showing the impacts on the economy assumed a carbon tax that maxed out in 2050 at less than \$90 per ton.

As Cass wryly observes, these are not the same carbon tax—it was much more aggressive in Chapter 4 when the authors wanted to showcase its ability to tackle climate change, but it became much weaker in Chapter 5 when the authors wanted to illustrate its benignity.

06 Sep 2017

## A Surplus of Articles on Price Gouging

I pile on. However, all modesty aside, I think I collected everybody’s good points into a one-stop-shop for you and your normal co-workers/relatives. I also hit an issue related to philanthropy that many standard “economistic” defenses of price gouging miss. Two excerpts:

In the path of an incoming storm, where thousands of people want to evacuate the coast, depending on refinery interruptions and other bottlenecks, it’s possible that some local stations will run out of gas if they don’t raise their prices significantly. The people who are lucky enough to get to the stations first will naturally fill the tank up, before getting on the interstate to get out of Dodge. Then the unlucky followers will see the gas station is empty, and may end up stalling on the interstate. The authorities then have a problem of dealing with stranded motorists who are stuck not because of flooding, but because they ran out of fuel during their escape.

In contrast, if the few relevant station owners charge \$15 per gallon, then people who had (say) a half-tank in their car when the storm hit, will say, “That’s outrageous!” and get back on the highway, to see if prices are any better in another 50 miles. At a price of \$15, only people who are about to run out of gas will buy any, and even they will only purchase enough to give them some breathing room. They too will probably take their chances and hope that gas is cheaper if they move away from the storm.

and

Suppose instead, however, that the owner charges the full \$14, but then donates his \$1,000 windfall to a local relief effort that is handing out free packets of food and dry clothes to families who were flooded out of their homes and have literally nothing (including wallets). Or to make the point even more clearly, suppose he donates the \$1,000 windfall to a local organization that uses the money to buy bottled water and hand it out to desperate people?

Once we go down this path, we see that the insistence on charging only \$4 for the cases of water really just means that our hypothetical store owner is concentrating his \$1,000 worth of charity on the particular Houstonians who happen to walk into his store and pull out their credit card to make a big purchase. What are the odds that these people are the ones in Houston most in need of his implicit \$1,000 charitable donation that day?

05 Sep 2017

## “100 Year Flood Event”

Gene’s post on media reporting of the flooding is typical: Gene makes a confident claim, rob chimes in to meekly disagree, Gene bites rob’s head off, and we all end up wiser.

First and probably most important: The “100 year flood event” stuff is defined for a specific region. So over the country as a whole, we’d expect a bunch of “100 year flood events” every year.

(The odds of someone picking the winning lotto numbers make it way way less than a “once in a lifetime” event. And yet every couple of months, somebody wins the lotto. Thing must be rigged!)

But more interesting are the following distinctions:

==> A “100 year flood event” is defined as an event that has a 1% probability of happening in a given year.

==> This is NOT THE SAME THING as saying that we expect a flood of such magnitude to occur one time per century.

==> It IS equivalent to saying that the expected number of times of such a flood occurring per century is 1.

To understand the above statements, consider someone rolling a fair die. If we ask, “What’s the expected value of the roll?” we can calculate it by doing the probability of an outcome times the value of that outcome, and summing over all possible outcomes. So for our fair die, the expected value is 3.5.

Thus, the “expected value of the die roll” is 3.5.

But suppose I ask you, “Hey, do you expect the next die roll to turn up as 3.5?” then the answer is clearly no, since that is literally impossible. We can be quite sure the next die roll will NOT be 3.5.

The expected value of the die roll is 3.5, even though we do not expect the value of the die roll to be 3.5.

05 Sep 2017

## The Fun Stuff on Liberty Classroom

I was checking the Student Dashboard for my History of Economic Thought classes on Tom Woods’ Liberty Classroom, and came across a fun question prompted by my lecture on utility and welfare theory. Just to show you the romping good time, I’ll reproduce the question and answer below. Sign up today and join the fun!

Q: OK, I give up. How do you move from Pareto suboptimality to Pareto optimality, and still make some people worse off? I keep trying to figure this out and it just makes my head spin.

A: Heh it’s a fun one, isn’t it? It’s easier to do on a blackboard, but here goes:

Picture a 2-person, 2-good economy. It’s Xavier and Yolinda, and they have apples and bananas. There is no production, just a total of 10 apples and 10 bananas, that can be split between them.

Assume their preferences are such that each person always wants more of either good, but also prefers variety.

Now suppose Xavier has 10 apples and 10 bananas, while Yolinda has 0 apples and 0 bananas. This is Pareto optimal. You can’t make Xavier happier because he has all the goods already. And if you make Yolinda happier, you necessarily hurt Xavier. So since it’s impossible to make one person better off without hurting the other, the original allocation is Pareto optimal.

Now consider a different allocation, where Xavier start with 9 apples and 1 banana, while Yolinda has 1 apple and 9 bananas. It’s plausible that this is *not* Pareto optimal, because I said they like variety. E.g. we can imagine their preferences are such that if Xavier trades away 4 of his starting apples in exchange for 4 bananas from Yolinda, that they are both getting more utility (or end up with a preferable combination of goods).

So, I hope you find it plausible that this 2nd allocation I’ve described–where Xavier starts with 9 apples and 1 banana, while Yolinda starts with 1 apple and 9 bananas–is Pareto suboptimal.

Now, imagine we move from this 2nd allocation to the 1st allocation (the one where Xavier has everything). We’ve moved from a Pareto suboptimal to a Pareto optimal allocation, and yet in doing so we made Yolinda worse off, because now she has nothing.

Go ahead, admit it. You thought you’d have to go to Steve Landsburg’s blog to get mathematical econ like this. You thought I’d just say, “GOVERNMENT BAD. APPLES GOOD.”

05 Sep 2017

## Contra Krugman on Hurricane Harvey

In episode 102 we talk about climate change and Houston zoning. Even though Krugman himself didn’t bring it up, Tom and I review the case against the case against (sic) “price gouging.”

In fact, I liked our exchange so much that I clipped it into a stand-alone YouTube segment, which you can share with all of your friends and co-workers:

04 Sep 2017

## “Pauly are you OK?”

Unfortunately these guys missed the deadline (which was mostly our fault because we should’ve given better guidance), but this was a very creative submission to our Contra Cruise contest.

04 Sep 2017

## Jesus, the Magnificent Leader of Men

(I am picking the title here as a reference to this.)

I believe I’ve mentioned this episode before, but for some reason I thought of it again over the weekend and decided to repeat it. Consider this famous passage that occurred after the Last Supper:

30 And when they had sung a hymn, they went out to the Mount of Olives. 31 Then Jesus said to them, “You will all fall away because of me this night. For it is written, ‘I will strike the shepherd, and the sheep of the flock will be scattered.’32 But after I am raised up, I will go before you to Galilee.” 33 Peter answered him, “Though they all fall away because of you, I will never fall away.” 34 Jesus said to him, “Truly, I tell you, this very night, before the rooster crows, you will deny me three times.” 35 Peter said to him, “Even if I must die with you, I will not deny you!” And all the disciples said the same.

Of course, Jesus’ prediction comes true. Even though Peter had the courage to follow (at a distance) Jesus after He had been taken into custody (while the other apostles fled), nonetheless Peter eventually denied knowing Jesus when he was confronted about it:

54 Then they seized him and led him away, bringing him into the high priest’s house, and Peter was following at a distance. 55 And when they had kindled a fire in the middle of the courtyard and sat down together, Peter sat down among them. 56 Then a servant girl, seeing him as he sat in the light and looking closely at him, said, “This man also was with him.” 57 But he denied it, saying, “Woman, I do not know him.” 58 And a little later someone else saw him and said, “You also are one of them.” But Peter said, “Man, I am not.” 59 And after an interval of about an hour still another insisted, saying, “Certainly this man also was with him, for he too is a Galilean.” 60 But Peter said, “Man, I do not know what you are talking about.” And immediately, while he was still speaking, the rooster crowed. 61 And the Lord turned and looked at Peter. And Peter remembered the saying of the Lord, how he had said to him, “Before the rooster crows today, you will deny me three times.”62 And he went out and wept bitterly.

For all of us who have remained silent when scoffers mocked things we hold dear–even in cases, Jesus–this should pierce our hearts.

But what I want to focus on is not Peter’s failure, but rather Jesus’ rehabilitation of him. For context, Jesus is making Peter the Rock upon which His church will rest. In just a short while, Peter is going to deliver a single sermon that wins thousands for Christ.

How is this possible? Peter is broken after his denial of His Lord. How can he possibly forgive himself for this failure and move on, serving the Lord?

Because Jesus fixes it, that’s how. After His resurrection but before His ascension, Jesus has this conversation with Peter:

15 When they had finished breakfast, Jesus said to Simon Peter, “Simon, son of John, do you love me more than these?” He said to him, “Yes, Lord; you know that I love you.” He said to him, “Feed my lambs.” 16 He said to him a second time,“Simon, son of John, do you love me?” He said to him, “Yes, Lord; you know that I love you.” He said to him, “Tend my sheep.” 17 He said to him the third time,“Simon, son of John, do you love me?” Peter was grieved because he said to him the third time, “Do you love me?” and he said to him, “Lord, you know everything; you know that I love you.” Jesus said to him, “Feed my sheep. 18 Truly, truly, I say to you, when you were young, you used to dress yourself and walk wherever you wanted, but when you are old, you will stretch out your hands, and another will dress you and carry you where you do not want to go.” 19 (This he said to show by what kind of death he was to glorify God.) And after saying this he said to him,“Follow me.”

In isolation, this passage seems odd, and no doubt a critic could say, “Aha! Yet again, the God of the Bible is really insecure and needs to be constantly adored by humans.”

But of course, what’s really happening here is that Jesus is giving Peter the opportunity to affirm Him three times, to make up for the triple denial. Obviously this conversation isn’t for Jesus’ ego, it’s for Peter’s rehabilitation.

After all, Jesus has a job for him to do.