## Cheers to Sumproduct!

I teach macroeconomics, finance, and other things.

Often, I use Excel to complete repetitive calculations for my students. The version that I show them is different from the version that I use. They see a lot more mathematical steps displayed in different cells, usually with a label describing what it is. But when I create an answer calculator or work on my own, I usually try to be as concise as possible, squeezing what I can into a single cell or many fewer cells. That’s what brings me to to the sumproduct excel function that I recently learned. It’s super useful I’ll illustrate it with two examples.

Example 1) NGDP

One way to calculate NGDP is to sum all of the expenditures on the different products during a time period. The expenditures on a good is simply the price of the good times the quantity that was purchased during the time period. The below image illustrates an example with the values on the left, and the equations that I used on the right. That’s the student version. There is an equation for each good which calculates the total expenditure on the individual goods. Then, there is a final equation which sums the spending to get total expenditures, or NGDP.

## In Praise of the FRED Excel Add-in

Sometimes, large entities have enough money to throw at a problem that by sheer magnitude they produce something great (albeit at too high a cost). The iPhone app from the FRED is not that thing. But the Excel add-in is something that every macroeconomics professor should consider adding to their toolkit.

Personally, I include links to FRED content in the lecture notes that I provide to students. But FRED makes it easy to do so much more. They now have an add-in that makes accessing data *much* faster. With it, professors can demonstrate in excel their transformations that students can easily replicate. The advantage is that students can learn to access and transform their own data rather than relying on links that I provide them.

The tool is easy enough to find – FRED wants you to use it. After that, the installation is largely automatic.

Installed in excel you will see the below new ribbon option. It’s very user friendly.

## Hyperinflationary Efficiency?

I’m advising a senior thesis for a student who is examining the strength of Purchasing Power Parity in hyper-inflationary countries. Beautifully, the results are consistent with another author* who uses a more sophisticated method.

For those who don’t know, absolute purchasing power parity (PPP) depends on arbitrage among traders to cause a unit of currency to have the same ability to acquire goods in two different countries. If after converting your currency you can afford more stuff in foreign country, then there is a profit opportunity to purchase there and even to re-sell it in your home country.

Essentially, when you make that decision, you are reducing demand for the good in your home country and increasing demand in the foreign country (re-selling affects the domestic supply too). Eventually, the changes in demand cause the prices to converge and the arbitrage opportunities disappear. At this point the two currencies are said to have purchasing power parity – it doesn’t matter where you purchase the good.

So does PPP hold? One way that economists measure the strength of PPP is by measuring the time that it takes for a typical purchasing power difference to be arbitraged away by 50% – its ‘half-life’.  The more time that is required, the less efficient the markets are said to be.

The ex-ante question is: Is PPP be stronger or weaker during hyperinflationary periods?

## Good Old Lemons

This post doesn’t have a darn thing to do with economics, statistics, or finance. This is a post about citrus storage.

There are problems with buying citrus.

• If you get a big Sam’s Club size bag of limes, then they start going hard and thin-skinned by the end of a week.
• A bag of grapefruit? There’s usually one in the bag that’s goes moldy almost immediately and you know what they say about one bad grapefruit spoiling the bunch.
• Mandarins shrink and get hard to peel.
• Lemons – even if you refrigerate them – get soft and un-zest-worthy.

There is a solution. Now, our lemons and limes last upwards of 6-8 weeks with hardly a symptom of age. Mandarins don’t shrivel and grapefruits remain edible. No, silly goose, the answer isn’t free markets and the price system.

Maybe it’s all of the additional vitamin C that I’m getting. Maybe it’s the warm and fuzzy feeling of money well spent. But I’m now excited each time that we purchase citrus. And I get a cozy feeling of satisfaction whenever I see a nice lemon that definitely should not still be any good.

The answer is really simple. You too can achieve such amazing results. All you have to do is:

• Rinse your citrus under water, rubbing gently to remove any invisible bad-guy germs. In reality, you’re probably getting rid of mold spores.
• Place the wet citrus into a ziploc bag, seal, and refrigerate. The refrigeration further retards the growth of any unwanted spores. The sealed bag prevents too much air flow and drying.( I don’t bother refrigerating grapefruit and oranges because I eat them quickly enough).

That’s it. You too can have 8 week old limes and lemons that you bought on sale or in bulk that are nearly as fresh as the day that you purchased them.

Enjoy!