I am a research student currently conducting a study to determent the price and income elasticity of demand for fuel products in Nigeria, using a Quadratic Almost Ideal Demand System. I am using a cross sectional data (Harmonized National Living Standard Survey, 2009) obtained from the statistical agency in Nigeria.
Currently, I face a challenge estimating the price elasticity of demand for fuel product because prices are constant across household units in the survey period (2009). The survey data contains information on expenditure of various fuel products, but no information is available on the price and quantities of fuel products purchased.
However, I obtained the price of each product in 2009, but it is constant across all households, as a uniform price is applicable in Nigeria. This poses a challenge in estimating the price elasticity of demand for fuel products. To circumvent this problem, some studies have used quantities of each product to divide expenditure of each product. This will create the needed variability in prices. This approach seems impossible to me since my data set has no quantity of fuel products purchased. I humbly write to seek for more clarification on how to obtain variability in prices of each product across various households units in the survey.
I'm afraid I can't offer any further insight to what you've already said. I don't do empirical work and as you said, you don't have the data do produce estimates here. It seems to me the best you can do is some survey on what others have found. After a quick search I found this paper by Boshoff. You are probably aware of it already. But in case not, on page 48 (page 6 of the pdf) there is a table with other estimates provided. And then, of course, there are his own estimates later in the paper. Those are for South Africa, not Nigeria. In the absence of data about your own country, however, you should find what else is known about gasoline demand elasticity elsewhere.