Aggregation Test Procedure

In my last post I mentioned that I was undertaking an aggregation test on the production inputs of software capital, hardware capital and non-IT capital to see if they can be combined into a single measure. I had performed this test but Dr. Poon had asked me to slightly adjust the model which I was using in the test which is based on Stiroh and McGukin (2002) aggregation paper. I am testing for two effects which are:

1. If software and hardware capital can be aggregated into a single measure called IT capital
2. If software, hardware and non-IT capital can be aggregated into a single capital measure

In either situation these separate capital items can be aggregated if they are perfect substitutes for each other and i.e. implies that the composition of these different capital measures are not important as the different components can be perfectly replaced by another component. E.g. if software capital and hardware capital can be aggregated into IT capital, IT capital would give the same result if it was 100% software capital, 50% hardware capital and 50% software capital etc. The first aggregation test, tests to see if the concepts of hardware and software capital are different. The second aggregation test tests to see if the concept of IT capital is different from the standard definition of ordinary capital.

The models to estimate are as follows:

Where:

KS is software capital

KH is hardware capital

L is labour

K1 is KS+KH, i.e. IT capital

K0 is non-IT capital

K is K0+KS+KH, aggregate capital

T, I control for time and sector effects

Initially I had used a restricted F-test on both models in accordance with Aizcorbe (1990) who proposed the aggregation test to see if these variables can be aggregate. A rejection of the null hypothesis of the restricted f-test means they are not aggregates and I rejected the null in both cases. However, Dr. Poon has asked me to calculate the implied gamma and delta values in addition to each variables p-value. Whilst it is simple to calculate the implied values by dividing b₂ or b₃ by b₀ the p-value is more difficult since we don’t know the standard error of the implied value obtained by division. Dr. Poon said that we will work on this tomorrow in our meeting using some of the inbuilt functions in shazam as I have not found a function in R that will assist in calculating the p-value.

However, I might be able to determine the p-value of the implied coefficient via the following procedure. First I will run a regression of the proportional variable on the dependent variable:

Second, I will then use the fitted value obtained as a replacement for the regressor of the original model and re-run the regression.

Now not only will I have and estimate of the delta value as well as its standard error and will now be able to calculate the p-vale. However, I am not too sure if this will be valid as the implied value of delta should be obtained by the procedure I mentioned earlier. Nevertheless I will ask Dr.Poon if this procedure can be used in tomorrows meeting. After my meeting I will post up the details of which procedure was used to obtain the p-values of the implied delta and gamma values.