## Inactive Week

So far this week all of my attempts to work on my project have been interrupted by homework for other classes. Hopefully progress will be made between now and the weekend. What I want to accomplish is a very broad outline of what I need to do, and what I am working towards. I’ll attempt to do this informally below, and then clean it up later.

What I have done so far is break the simplest form of the panel data model down into terms of x’s and y’s. What I’d like to do next is write out why the panel data model is awesome, and back it mathematically (in an informal way). Then I need to break down specific variations of the model, and explain them. Finally, I was told that I can prove that the variance in a panel data regression is less than that of an ordinary least squares regression, and I think that doing this may add necessary mathematical rigor. When I finally have what I plan on doing completely laid out, I’ll meet with Prof. Munson again to see if I need to make any changes.

## Capstone Update 2

Last weekend I participated in the Mathematical Competition in Modeling (MCM). This event took place over a 96-hour period starting on Thursday night at 5 Pm and ending Monday night at 5 PM. Having dedicated my entire weekend (and then some) to this endeavor, I was thus forced to spend the rest of the week playing catch up on my homework. Consequently, very little progress was made on my capstone project.

Over the next week I hope to finish constructing the basic forms of the panel data model at their simplest levels. I then will type them using LaTeX so they are easier to read and understand.

## Capstone Update

Over winter break and J-Term I thought of my capstone project seldom and worked on it even less. However, towards the end of J-Term I did make a trip to PLU’s library. I checked out three books on data analysis and panel data modeling, and began breaking the panel data model down to its simplest form. Ironically, its “simplest” form was too big to fit on a single piece of paper, and involved several matrices filled with summations.

One interesting thing that I learned was that the basic form of the panel data model actually has four variations, each based on its own set of assumptions. Needless to say I have a lot of work ahead of me.

I also met with Professor Munson last Wednesday to discuss the error term of the basic form(s) of the panel data model. We agreed we needed to do some more research and meet again at a later time.

## Random Effects

My last post was on the fixed effects model. I established that the fixed effects model assumes that variables not included in the regression are correlated with the variables included in the regression, and thus the results of the regression cannot be used to assess the effects of unobserved variables. The random effects model, on the other hand, assumes that unobserved variables are not correlated with observed variables, and allows the regression to be used to investigate the effects of variables not included in the regression.

In my past posts on the panel data model and its specific variations, I explained that the general form of the panel data model is $y_{it} = \alpha_i + \beta'x_{it} + \epsilon_{it}$, and the general form of the fixed effects model is $y_{it} = D \alpha_i + \beta'x_{it} + \epsilon_{it}$. With the random effects model, the general form is $y_{it} = \alpha + \beta'x_{it} + u_i + \epsilon_{it}$. In this model, $\alpha$ is taken to be constant, and $u_i$ is a measurement of random disturbance for each cross-sectional unit.

In choosing whether to use a fixed effects model or a random effects model, one must first test to see if individual effects exist. This is done using a Langrange Multiplier (LM) test. If they do indeed exist, then a Hausman test can be used. The Hausman test uses a hypothesis test to determine whether or not the fixed effects model and the random effects model have the same variance. If their variances are the same, then a random effects model may be used. If not, the more restricting fixed effects model must be used.