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Hi guys,

I'm in my final year studying economics and I'm writing my final paper around price and income elasticities of fuel prices, and how their changing etc. However I'm having some problems with my model specification, especially as this is the side of economics I'm not too comfortable with. I'll outline where I am at the moment:

I plan on using the following (simple, but straightforward) model to estimate the elasticities, I've adapted from a previous paper on the topic.

ln(Q) = ln(a) + b ln(p) + c ln(y) + d ln(Q{t - 1}) + v

where Q = vol of fuel consumed; p = price of fuel; y = level of household income; v = catchall variable; Q{t - 1} = fuel consumed in previous period. b & c will be used to calculate price and income elasticity.

Could anyone please advise on the following:
How to control to endogeneity of price and income

The parameter d captures a lagged effect on the model - notably that changes in fuel consumption may not happen immediately. The author included this in his model, but I was wondering what exactly to do with it or what purpose it serves in the model... :?

Appreciate your help in advance, and I realise all this must seem fairly basic !!

Cheers

Hi there,

I'll start with the easier question: interpreting coefficient d

First of all I'm assuming you are studying household demand for transport fuel.

There are both economic and econometric reasons why you would include an autoregressive element in your model, especially if you are using data which is of relatively high frequency (such as monthly or to a lesser extent quarterly). Economic interpretations (which are very much related) are habit persistence and lack of substitutability, at least in the short run. The price of fuel might increase at time t but you might not suddenly stop using your car/buy another car which runs on different fuel/use your bicycle/etc. You might be used to the comfort of using your personal car, so a higher price doesn't neccessarily change your behaviour in the short run. The trip distance might also prohibit you from using your bike. This very much depends on the context of your data. The same can also occur for income; earning a higher wage might not neccessarily induce you to take longer trips to reach your destination!

On econometric terms, if the data you have really shows some form of habit persistence, then estimating the regression (I'm assuming you're using OLS) without the lagged term will result in autocorrelation in the residuals, which will lead to biased standard errors and hence an inability to use statistical significance tests on your estimated coefficients and the model as a whole. It could also be the case that a model without the lagged term is a mis-specified one, leading also to biased coefficient estimates altogether. Refer to your textbook for a discussion.

As regards endogeneity with regards to the price of fuel and income this is somewhat trickier. In my opinion it all depends on how important fuel is in the household's consumption basket. A low share would imply that the price of fuel does not really affect the household's real income, so the endogeneity problem is reduced or a trivial one. This is not the case if the share of fuel in the consumption basket is high. In any case the proper way to go about it is to use Two-Stage Least Squares. Search the forum on how to implement this.

Hope this helps

Thanks for your help! Really appreciate it.

Do I need to use the parameter 'd' at all in any of the elasticity calculations itself? Or does its presence merely reduce potential autocorrelation and model mis-specification?

I do remember doing a two-stage least squares procedure last year in one of my lectures, so I'll review that method and apply it.

Thanks again.

Whether you need to estimate your model with a lagged dependant variable depends on the data, you'd need to test for this. Also you have to start the analysis by ensuring that your variables are stationary, as if not your estimate for 'd' would be greater than or equal to 1, implying a unit root and making your model useless (not much sense in trying to fit a model to data which has a stochastic trend, i.e a random walk).

If your model is specified in logs then the coefficients are direct elasticities, so you don't need to use any algebra. Refer to a textbook in this regard.

Then again if you do not include the lagged variable, you are running the risk of obtaining biased standard errors (due to the possible presence of autocorrelation) or even biased coefficients (due to outright mis-specification). You need to test for these before being confident with your results.

Assuming your model is otherwise correctly specified, the short-run elasticities are b and c and the logn-run elasticities are b/(1-d) and c/(1-d).

Thanks for your help so far. I've got another question now regarding stationarity of my dependent variable.
When i do a unit-root test on my dependent variable, i'm unable to reject the null that it has a unit root (ive pasted the output in below). Im using the ADF test (hopefully correctly..), how can I go from here to correct and ensure stationarity? should I adjust the number of lags and/or test in 1st/2nd difference?

Null Hypothesis: LQ_PETROL has a unit root
Exogenous: Constant
Lag Length: 2 (Automatic - based on SIC, maxlag=9)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -0.890532 0.7801
Test critical values: 1% level -3.621023
5% level -2.943427
10% level -2.610263

*MacKinnon (1996) one-sided p-values.


Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LQ_PETROL)
Method: Least Squares
Date: 03/06/12 Time: 12:46
Sample (adjusted): 1973 2009
Included observations: 37 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

LQ_PETROL(-1) -0.031693 0.035589 -0.890532 0.3796
D(LQ_PETROL(-1)) 0.396864 0.166807 2.379180 0.0233
D(LQ_PETROL(-2)) 0.204454 0.170081 1.202095 0.2379
C 0.309544 0.349822 0.884859 0.3826

R-squared 0.324455 Mean dependent var 0.002066
Adjusted R-squared 0.263042 S.D. dependent var 0.032986
S.E. of regression 0.028317 Akaike info criterion -4.188870
Sum squared resid 0.026462 Schwarz criterion -4.014716
Log likelihood 81.49409 Hannan-Quinn criter. -4.127473
F-statistic 5.283158 Durbin-Watson stat 2.000670
Prob(F-statistic) 0.004362