# Using estimated parameters as dependent variables

I'm doing a project on gold mining firms. I've taken the daily prices of the stocks of the 10 biggest gold mining companies in the last 15 years (I'm using the returns in order to make the data stationary) as a dependent variable and I'm trying to see if there is a contemporaneous relationship with the daily returns of gold, the s&p500 index, the strength of the dollar and the returns of the firms' stock. I'm using OLS to estimate my parameters: the daily return of the firms' stock as a dependendent variables, and the returns of gold/copper/s&p index/usd(trade weighted index) as independent variables. (r means return)

This is the equation of my OLS regression for firm $i$ the year t

$$r_{i} = \beta_{0} +\beta_{1}rgold_{i}+\beta_{2}rcopper_{i}+\beta_{3}rs\&p_{i}+\beta_{4}rusd_{i}$$

I have splitted my data in 15 periods of 1 year and I ran an OLS regression for each year. Obviously, I've found a positive significant relationship between the returns made by the firms, and the returns of the gold. ( the s&p and dollar index were also strongly significant).

I've observed that the evolution of the gold coefficient followed a similar trend for the firms. The gold exposure of gold firms seems to rise in period of crisis (year 2008-2009).

Now, since I have 10 firms, and 15 regression, (1 for each year) I was thinking of taking the $\beta_{1}$ coefficient as a dependent variable and do a new regression to try to explain this evolution.(For example, using different ratios of the firms as explanatory variables, such as the log(market capitalization) or the ROE etc...). However I'm asking the question to myself whether I can use estimated parameters as dependent variables? Is it "right" to do it? I think that the OLS might not be the best way to estimate this, but these are the tools that I have. What are your opinion on my idea?

As the RHS variables are generated by OLS, they are actually "generated regressors". It is perfectly fine to estimate the model by OLS, but you have to adjust standard errors. The classic paper by Pagan addresses this: "Econometric issues in the analysis of regressions with generated regressors." International Economic Review

• Thanks for your input. Yes I've corrected my standard errors for Heteroskedasticity. Still, the coefficients remains significant. So, in your opinion, it is fine to use the $\beta_{1}$ as new dependent variables? – Aurel Dec 5 '15 at 17:44
• Heteroskedasticity is a different issue. Using coefficients as dependent variables needs the "generated regressor" correction that I mentioned above. – ChinG Dec 5 '15 at 17:46
• Unfortunately, I was not able to access the paper you linked since it is quite expensive, could you give me a brief insight of it? Also I thank you for the rapidity of your answer. – Aurel Dec 5 '15 at 17:57