I am facing some problems regarding steps of OLS, In OLS regression model I have one dependent variable and six explanatory variables. these variables data on the basis of time series.
firstly I have run model without any changes in the variables data (original data) but residual diagnostic shows that serial correlation. After that I have change my dependent variables in lag 1. then again run OLS but here create another problem such as no statistical significant explanatory variables has been found in my OLS model (only 2 variables are statistical significant out of 6). Here I would like to know how to make significant and is it necessary to take a log entire model (means log for both DV and IV).
Suggest me how I run OLS appropriate and is it necessary converted into log and take T explanatory variables for the time trend.
2 things you might think about. 1. Variable coeffs are either significant or not. We can't make them significant. We model the data as best we can and see what the p-values tell us. 2. there are other ways to deal with serial correlation. I would start by looking at Neter, Wasserman & Kutner, Applied Linear Statistical Models 2nd ed. Chapt. 13, Autocorrelation in time series data. There are many other similar books that cover this topic. Look in the index for autocorrelation or serial correlation. As a start, have you done a Durbin Watson test? If so, what were the results.
Re-ruun the regression again. Do not lag the dependent variable. Take the lagged dependent variable and use it as an additional explanatory variable, like this:
Assume this your regression model
Y = X1+X2+X3+X4+X5+X6+ e
Re-run the regression like this:
Y = Yt-1 + X1+X2+X3+X4+X5+X6+e
(As you can see, the lagged dependent variable is now an explanatory variable. This should improve the statistical significance.)
You can also apply White's robust standard error correction. This works often by reducing overstated t-statistic/standard errors or increasing understated t-statistic/standard errors.
If this does not work, then, you may have to drop some variables (with p-values close to 1)
Caveat: In addition to Booth's comment, we cannot force a variable to be 'statistically' significant if the distribution of the data justify why it remain insignificant
Hope this helps!
Regards
Peterson.
Peterson makes a good suggestion however you have to be careful with inference because now you have a random variable on both sides of the equation. what to do in that case is difficult. I've attached the first paper on the topic by Albert Madansky. Best wishes.
Your use of levels or logs of variables should be determined by the economic or other theory of the system that you are trying to estimate rather than statistical tests. For example if a shock to a dependent variable causes a percentage increase in the variable you should take logs of the variable before estimation. a 4% increase in a variable at 100 causes an increase of 4, and at 1000, 40. If the variable is logged the increase is .04 in both cases. Do you expect the relationship between your variable and your independent variable to an elasticity or a semi-elasticity or an additive one.
As your variables are time series you also need to pay some attention to their stochastic properties. Have you checked if they are stationary or non-stationary. If they are . non stationary are they cointegrated. Some of the problems that you may encounter are to complex to solve in a forum such as this and you should consult an expert in time series. The coverage of time series in many introductory econometrics texts may not be sufficient in your case
There may be several reasons for this kind of results. Check your data for stationarity, outliers, multicollinearity and other assumptions of CLRM and then go ahead with data transformation like log/ square root etc.
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