Demand function estimation

The model specification is:

$$D_{ij} = A + aP_{ij} + bY_{ij} + cN_{ij} + e_{ij}$$

where:

$i, j$ = $i$-th year, $j$-th month, $D$= demand (outgoing minutes) $P$ = average price of call, $Y$ = average income per capita, $N$ = number of base stations.

During the 5-year period under examination, a tax has been levied on telecom gross revenues for two years. Is it reasonable to include instrumental variable such as amount of revenue/profit which could have direct effect on price? If not, perhaps you have any other suggestions.

Any guidelines would be very appreciated.

• You have to enhance your question much more and describe your theoretical model and your econometric specification in some detail (and the title has nothing really to do with what you are asking, which is an econometrics question). Otherwise any answer would be just a gamble. – Alecos Papadopoulos Dec 19 '14 at 22:32
• @Alecos Papadopoulos I have revised my question. Hopefully, the question is less fuzzy now. – Quirik Dec 20 '14 at 12:13

It appears that you suspect that the regressor "price" is endogenous, i.e. correlated with the error term, and that you consider what kind of instrument to use in order to tackle endogeneity.

You think a possible instrument could be revenues or profits, because they are correlated with the price. Say, Revenues, denoted by $R$. But

$$R_{ij} = P_{ij}\cdot D_{ij} = P_{ij}\cdot(A + aP_{ij} + bY_{ij} + cN_{ij} + e_{ij})$$

and so Revenues are a function of the error term, therefore they will certainly be correlated with it, and same goes for profits (and this should be obvious since both depend on quantity and therefore on the error term).

In order to find an admissible instrument, you must first conclude about what are the variables that may be included in the error term, and are correlate with price. This will help you to search for admissible instruments.

PS: I cannot see the connection of the tax mentioned with the issue of instrumental variables estimation.

• @ Alecos Papadopoulos I am still in the self-learning process of econometrics... I wanted to connect the tax as a state of company's reduced revenues and price. As a newbie, I would really appreciate any advice/appropriate literature considering the fact that I didn't take any classes on the subject but I'm willing to learn... – Quirik Dec 21 '14 at 16:46
• Instrumental Variables estimation is not for beginners. Start from where everybody starts -there is a reason for it: Linear Regression and Ordinary Least Squares. There are many university-sponsored free on-line educational materials on the subject. And many good books available (some free), by well-known and respected scholars. Note that since this subject is old and mature, it is not really affected by current research. – Alecos Papadopoulos Dec 21 '14 at 17:01
• An instrument for demand function estimation is typically a variable which affects supply curve (and thus also equilibrium price), but not demand curve. Perhaps the corporate tax rate could be such instrument? – ivansml Dec 22 '14 at 0:43
• @ivansml The corporate tax rate is not expected to vary -so no variability, no explanatory power. Moreover, here we have monthly data, so one needs a variable recorded monthly. It is also of interest to learn the descriptive statistics on the price variable -does it vary sufficiently, month per month? – Alecos Papadopoulos Dec 22 '14 at 1:10