## Econometrics Summary

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*Econometrics* is an economics textbook by Japanese economist Fumio Hayashi. A fellow of the Econometric Society, Hayashi has taught at Northwestern University, the University of Tokyo, and Columbia University, among others. Econometrics is a way of applying statistical methods and other quantitative analyses to the field of economics.

Introducing the concept of econometrics, Hayashi starts with one of its most basic and commonly cited models: the multiple linear regression model, which is much more simple than it sounds. Say, for instance, that we want to determine the relationship between the rate of change of a country’s gross domestic product (GDP) and its unemployment rate. We would start by creating a simple X- and Y-axis chart with four quadrants. The two axes would intersect at zero. The Y-axis would represent one value and the X-axis would represent the other. For example, we might have the Y-axis represent the country’s GDP growth values while the X-axis would represent unemployment rates. We would then make a dot on the chart for each three-month period (or quarter) of a given time frame that measures both values. Therefore, if in October 2001, the GDP growth rate was zero but the unemployment rate was 13 percent, we would place a dot located at zero on Y-axis and thirteen on the X-axis. We would keep making these dots until we have a cluster of dots. Finally, we do a math equation to draw a line through these dots. When we are finished, the line will capture the general trend of the relationship between these two factors. If a dot is far away from the line, that dot represents a quarter in which the usual trends did not bear out. This would then cause the researcher to look deeper into what other factors may have caused this anomaly on the chart. The analysis discussed here is called Okun’s Law.

Another illustrative example cited by Hayashi is the relationship between a person’s wages and the years of education that person has. This relationship is generally considered to be linear: the higher a person’s wages are, the more education that person has probably had. Where this example gets interesting is when researchers use it to determine other factors that affect wages, such as place of birth or decade in which the person was born. If we know, for example, that the effect of education on wages is largely the same given all other variables are the same, we can then use those same models and apply them to people with different variables surrounding their place of birth or time of birth. This allows the researcher to determine just how much impact these other variables have on wages.

The work of econometrics also covers the use and discovery of “estimators.” Estimators are general rules for calculating an estimate based on observed data. For instance, to use some of the above examples, if we know a large GDP rate of growth coincides with a larger unemployment rate, and we see this relationship established time and time again with a great deal of consistency and very little bias, that is considered a strong estimator.

These estimators, along with the regression models cited above, are especially helpful in econometrics, Hayashi holds, because economists cannot as easily do “controlled experiments” like purveyors of other scientific fields can. For example, if a biologist wants to study the effects of a particular toxin on an organism, the biologist can set up a closed experiment in which that toxin is introduced to the tissue of the organism under controlled circumstances in a laboratory. However, if an economist wants to see if raising the GDP would lower the unemployment rate, the economist cannot just go out and raise the GDP. The GDP isn’t in a scientist’s or any one person’s control. It is subject to too many factors. And even if the economist *could* raise the GDP for experimental purposes, there would be no way to study its effect on the unemployment rate because there would be too many variables outside the economist’s control. That is why economists use econometrics to study these historical trends over time, establish estimators and models, and then use them to show how these relationships prevail or falter in the face of other variables.

With *Econometrics*, Hayashi illuminates the ways in which mathematics and observation can be used to study and predict outcomes in a field like economics where controlled experiments are virtually impossible.