Chapter 17 Measurement Key Concept: If you want to estimate the demand curve, you need to find cases where the supply curve shifts.

Chapter 17 Measurement If we would like to estimate the demand and supply curves using statistical techniques, then we need to learn econometrics. When we analyze data we generally are interested with the following questions.

Summarize, estimate, test, forecast, predict.

Summarize. How can we describe the data succinctly Summarize. How can we describe the data succinctly? How many cups of coffee are consumed per person per day? Estimate. How can we estimate some unknown parameters? What is the elasticity of demand for coffee?

Test. How can we determine whether an unknown parameter satisfies some restriction? Do mean and women drink the same amount of coffee per day on average? Forecast. How can we forecast what the price of coffee will be next year?

Predict. How can we predict what would happen to some variable of interest if something changes? If the government imposed a 10% tax on coffee, what would happen to consumption?

Summarize: How can we describe our data succinctly? Data from an online survey of 1000 consumers on how many cups of coffee they drink per day. 1=2, 3=4.

Can also break down the information by category Can also break down the information by category. We could look at coffee consumption across men and women.

Simpson’s paradox is a paradox in probability and statistics, in which a trend appears in different groups of data but disappears or reverses when these groups are combined.

The application and admission statistics to graduate school at UC Berkeley in 1973.

If we look at the overall mean, men are more likely to get admitted than women. But if we break down the data by department, no department is significantly biased in favor of men.

The paradox arises because women tended to apply to departments with lower admission rates.

Coffee consumption increases as income increases for both men and women, but decreases as income increases overall.

Test: Men drank 1. 23 cups of coffee per day and women drank 1 Test: Men drank 1.23 cups of coffee per day and women drank 1.39 cups per day. How confident can we be that the mean consumption of coffee by women exceeds the mean consumption of coffee by men?

Suppose men and women actually drank the same amount of coffee per day. How likely would it be to observe one group drinking 0.16 (1.39-1.23) cups more than the other?

It turns out with a few additional assumptions the probability that we would see a difference at least this large is about 9.6%. So it is not that uncommon.

Estimate: Suppose you work for a company which sells coffee beans. Your coffee currently sells for 15 per pound, you are thinking to cut the price to 14. You hope to sell more at the lower price so that the profit could be increased. But how much more can you sell?

To figure that out, you could (1) Cut the price for a few weeks and observe whether the profit goes up. (2) Put your coffee beans for sale in a few cities, see what happens in these locations and infer what will happen if you do it full scale.

treatment group (the cities you reduce the price) vs. control group (the cities you leave the price constant)

Bear in mind that the coffee you sell in a given city may vary with the season of the year or the weather. So when you choose which cities are treated you want to use some random method such as a coin flip. Such randomized treatment may help eliminate systematic bias.

Or you have a good idea what to control. For instance data on weather may be thrown into your regressions to control for the observed variation in weather.

Effect of treatment One important lesson is people who choose to be treated may be different from the population. Suppose you send out coupons to a randomly chosen set of people and see how many people use the coupons to buy coffee.

It is likely that people who go through the trouble of using the coupons might be more price sensitive than those who don’t bother to use the coupons. Thus the inference based on this selective group may not be readily generalized to the population.

If you would like to infer the price sensitivities of the general population, sending out coupons may have this selection problem. However, if you are evaluating the effect of sending out coupons to the entire population and evaluate its effect, then sending out the coupons to a subset of population makes sense.

Suppose now you are interested in estimating how the nationwide demand for coffee changes as the price changes. There is no obvious way to do an experiment. You have to use observational data.

Suppose you decide to try the functional form ln(x)=lnc+bln(p)+dln(m)+e, ideally you want to estimate b, c, d and e is the error term. When you estimate b, you hope to have price variations while holding everything else constant and see how x changes.

To estimate a demand for a particular country, the price of coffee beans may vary exogenously since coffee beans are grown and sold on a world market. The supply of beans may vary a lot from year to year, depending on weather, political events, changes in transportation costs, and so on. These factors may not affect the demand for this particular country.

In this case, the supply facing this country is more or less flat and shifts from year to year. The resulting equilibria would trace out the demand curve.

However, if we are interested in the world demand of coffee, it does not make sense to assume that the price variation is exogenous.

When you estimate a demand, you want something that shifts the supply When you estimate a demand, you want something that shifts the supply. But if both curves are shifting, you can’t indentify what is driving the price changes.

We also have to distinguish correlation and causality We also have to distinguish correlation and causality. If we see more police in precincts with high crime rates, can we conclude that police cause crime? In fact, it is more likely that more police are assigned to high crime area. To get the causal effect of police on crime rates, we need an exogenous change in the assignment of the police and see the change in crime rate.

A natural experiment may be such a case. An example is that the police department in Washington, DC, increases the number of police on the street during periods when there are security alerts concerning elevated risk of terrorist activity. It is found that crime was substantially lower, particularly for auto theft.

Chapter 17 Measurement Key Concept: If you want to estimate the demand curve, you need to find cases where the supply curve shifts.