Econometrics 7960--Special Topics in Econometrics
This is a hands-on survey of econometric techniques used when ordinary least squares (OLS) linear regressions are not applicable. OLS linear regressions is the best technique when the dependent variable is a continuous outcome such as differences in wages, changes in the number of workers unemployed, or other such continuous variables and also the data are cross-sectional (namely you have many observations at one point in time). While this is common, often your problem or your data are constructed differently.
Non-OLS linear regression techniques are designed to address two basic problems: first, special forms of data, and second, outcomes that are not continuous such as categorical outcomes or count outcomes or time to event outcomes.
Data:
Time series data: if your data are observations of one individual or one country or one anything over many periods of time, even if your outcome is a continuous variable, the special problems associated with correlation in the error term across time periods means that OLS linear regressions have to be specially tested for autocorrelation in the error term and/or specially adapted to other time series issues.
Cross-sectional/time series data: here your data is a hybrid or cross-sectional and time series because you have observations for many individuals (or states or companies, etc.) at one point in time and observations for each individual (etc.) across several periods of time. Even if your outcome is continuous, a variety of specialized models called fixed and random effects models have been developed to exploit the added information embedded in data that permit both here-and-there variation (cross-sectional variation) and before-and-after variation (time series variation).
Panel data: these data are a special case of cross-sectional/time-series data where you are looking at many but precisely the same individuals (or other entity, like a company) over time. Where cross sectional-time series might involve (say) states from the decennial census, and you will not have precisely the same people in (say) California in 1980 as in 2000, in panel data you are following the exact same people over time. A key problem in panel data is the loss of individuals as the survey you are using gets older.
Another issue is censored data: an example is salary data that is "top coded" such as data that above (say) $100,000 does not give the precise income but simply says "more than $100,000." Tobit regressions are designed to deal with censored continuous data.
Outcomes:
A common non-continuous outcome often confronted by economists (and others using regression analysis) is a categorical outcome. Say you want to explain why someone is married, divorced or single--or you want to explain if someone is employed, unemployed or out of the labor market. These categorical outcomes require logistic or probit regressions. Categorical outcomes can be binomial (e.g. male-female) or multinomial (e.g. car, bus, truck). Categorical outcomes can be all on the same level (Canadian, US, UK) or they can be ordered (poor, fair, good, best). Related techniques are designed to deal with each of these outcomes.
A second common non-continuous outcome is time until an event takes place. This is often referred to as time to failure. How long until a car breaks down? How long until someone has a heart attack? How long until someone leaves a job? Survival or event-history models are exciting techniques increasingly being used by economists.
You may be interested in how things work differently in a continuous outcome depending on whether you are looking at the top or the bottom of the distribution of that outcome. Say, for instance, that you wanted to know how professional basketball players salaries are effected by game attendance and you suspect that it affects the better paid players but not the benchwarmers. Quantile regressions allow you to parse the dependent variable looking at the lower end of the distribution separately from the upper end.
A recently developed technique that promises to help with a bunch of questions is called stochastic frontiers regressions. This technique is designed to assess changes in production efficiency. Economic historians are applying this technique in the debate over the economic viability of slavery and I have used this technique in a recent publication on the effects of the Fair Wage law on public school construction in British Columbia.
So there are a lot of specialized techniques beyond OLS linear regression. We cannot study them all (and because my own research has not led me in the direction of time series analysis, I cannot go beyond an introductory discussion of what turns out to be a huge literature on time series). This will be a small class and we will choose techniques that fit our mutual interest and hopefully will be related to what you eventually do for your dissertation.
Required Books
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