Pooling cross sectional:

There are a number of ways to  study the relationship between energy demand and value of output.  First, we can  run  the  following  times series regression  for each sector separately:  

for agricultural sector

for industrial sector and so on.

where,  Y_i  -  energy consumption

X_i =  sectoral value of output

Using the dummy variable technique as discussed earlier or the chow test one can find out if the parameters of these demand functions  are  the same or not.

The second way  is to estimate for each of the year the cross-sectional regression. In such a case there would be one regression  for each of the  18 years giving a total of 18 regressions to be estimated.

The third way  is to pool  all the 54 observations  (18 times series observations for the three sectors) and estimate the following regression

where,  i stands for i-th sector and t for  the  t-&h  time perk i.

we have assumed that only the  'intercept  terms differ across the sector but not  the slope terms.  Readers can  assume both  the slope coeficients and intercept terms  to be different across sectors and  test of their significance  themselves).