【Econometrics】Econometric Questions

Econometric Questions

In the last post, I laid out a broad overview of what consists an econometric analysis. As a start, this post cites a couple of examples of econometric studies and demonstrate what kind of questions and information are included and important.

2020/06/05 - [Studies/Econometrics] - Econometrics (0) :: What is Econometrics?

---

Example 1. Breastfeeding and IQ.

"Based on data collected from 1,312 mothers and their babies, the study finds that infants who breast-fed for a longer duration through the first year of life scored higher on measures of language recognition at age 3 and on verbal non-verbal IQ measures at age 7."  - USA Today

In this single sentence, USA Today reports the following information:

- Sample: 1,312 Mothers and their Babies

- Study Goal: Impact of length of breast-feeding through the first year of infant life on (1) Language recognition metrics at age 3 and (2) Non-verbal IQ at age 7

We could infer that:

1. Mothers and their babies were studied/tracked over time

2. Certain measures or tests were performed at two different points in time (age 3 and age 7)

3. Study hypothesized a positive relationship (increase in A to be associated with increase in B) between length of breast-feeding and IQ in the future.

Potential problems from making a definitive conclusion could include reasons such as:

1. Mothers are related to each other 

2. Mothers are exposed a common environment

3. Some mothers are falsely reporting the length of breast-feed

4. Some mothers and babies are exposed to environment that could significantly impact IQ, such as economic stability, nutrition, pollution, age of mother, divorce, etc.

5. Some mothers and babies are exposed to time periods that could significantly impact IQ, such as war, natural disaster, financial crisis, etc.

---

Example 2. Drinking during Pregnancy

An economist gets pregnant: "Several times-with alcohol and coffee, certainly, but also things like weight gain-I came to disagree somewhat with the official recommendations. This is where another part of my training as an economist came in: I knew enough to read the data correctly. Pregnancy suffers from a lot of misinformation. One or two weak studies can rapidly become conventional wisdom. At some point, I came across a well-cited study that indicated that light drinking in pregnancy-perhaps a drink a day, causes aggressive behavior in children. The study wasn't randomized; they just compared women who drank to women who did not. When I looked at a little closer, I found that the woman who drank were also much, much more likely to use cocaine."

Instead of positing a result of study, this statement notes on an important question, not different than the number 1 in the potential problems we identified above: Was the Study Randomized?  We will discuss further on the reason why randomization is so important in an econometric analysis. But to get to the point, we would want to draw out the most, if possible, clean and filtered relationship between two factors, which in this example is "drinking during pregnancy" and "child aggressiveness". 

---

Example 3. Ice Cream Sales and Temperature

John noticed a long line in front of an ice cream truck on sunny days. John acquired the sales statistics from the ice cream truck and temperature over the last few months to run some analysis. Based on the analysis, John concluded that higher  temperature causes higher ice cream sales. 

John's conclusion, "higher temperature causes higher ice cream sales" is a very strong statement, at least in this field that is entirely devoted to sufficiently prove that A actually "causes" B. Yes, it is very likely that higher temperature may induce more people to purchase ice creams compared to when not; and yes, there may in fact be a causal relationship. However, given John in only incorporating A. Temperature and B. Ice cream sales data to determine the relationship, there is insufficient evidence to support the statement that "A causes B". 

"Correlation does not imply Causal Relationship"

John's analysis rather portrays what we consider as a "positive relationship" or "higher temperature is associated with higher ice cream sales". 

This is more evident in cases associated with spurious correlation, a relationship that is apparent but is not valid. If interested, please open the section below for your information.

Example 3.1. Sunspot and Stock Market Cycle

By Robert R. Prechter, Jr. and Peter Kendall, originally published in the September 2000

According to the study <The Sunspot Cycle and Stocks>, stock market tended to hit the bottom and rebounded shortly before a sunspot cycle. Based on the research, sunspot cycle was 10.3 years, and stock market had a very close cycle. While this was a very interesting finding, there was little evidence to support a causal relationship between stock market and sunspot, as there is theoretically no possible explanation to how stock market could impact sunspot and sunspot impacting stock market. Yet, it did suggest that both stock market and sunspot cycle shared an approximately 10-year cycle that serendipitously (spuriously) lined up.

This study is a great illustration of how a hasty judgement on causal relationship could be dangerous if made without consideration of context and factors.

Econometric Questions

As we saw in the examples above, an econometrician seeks to ask and answer:

What is the relationship between A and B?

How can we quantify A and B?

What are potential limitations?

How can we control for the limitations or interference?