Applying Econometrics To The Law Of Demand

Following the general methodology used by econometricians, explain how you would proceed to determine if a good complies with the Law of Demand.

While analysing any economic theory, a step by step methodology is to be followed. Therefore, with reference to the question, a few essential steps need to be taken in order to proceed with determining whether or not a good complies with the Law of Demand which states that the quantity demanded of particular good or service decreases as the price of it rises.

There would be first of all a formulation of two competing hypothesis. For example, consider the good to be bread. The law of demand postulates that all thing held equal when price of a good falls quantity demanded would increase and in turn when price of a good rises quantity demanded would decrease and so therefore, Hypothesis a) Bread does complies with the law of demand Ho:

b) Bread does not comply with the law of demand

After the various testing techniques, we have to derive a decision rule to choose the correct hypothesis that has been confirmed through the tests carried out.

The next step would be to proceed to collect data. There are three types of data collection which includes: a) Time series data - this is a type of data or observation collected through time. This data can be continuous e.g. at every point in time or they can be discrete e.g. at spaced intervals like every hourly weekly, monthly, yearly etc

b) Cross section data - this refers to the observation of different individuals or subjects at a given point in time.

c) Pooled and panel data

2. Specifying the mathematical model would be the next essential step. At this stage, we would like to know how a good affects the law of demand. This can be represented as the equation (Y = B1+B2X) and so, through the data provided we can draw a scatter diagram showing how the dependent variable Y affects the independent variable X, and then we are able to tell its relationship and if there is any correlation. A positive correlation would be where there is an upward trend and the line of best fit which passes through most of the points while a negative correlation would be where there is a downward trend and the line of best fit goes passes most of the points but in a downward manner. Furthermore, B1 represents the intercept which tells us the value of Y when X is zero while B2 represents the slope which tells us the rate of change in the value of Y for a unit change in the value for the equation X on the right hand side.

3. Specifying the econometric model - As mentioned earlier that econometric data can be presented in a scatter diagram. However, the points in a scatter diagram are not perfect. There is no such line which is exact and no exact linear relationship can be drawn even though the variables are inversely related. Only a line that best fits can be drawn. This is because since Q = f (p, there might be other limitations affecting the law of demand e.g. advertising, consumer income, price of substitute and complimentary goods, and some external mathematical factors we might not know about and cannot see. These other limitations can be represented as a random error u. This represents all other forces affecting Y and so therefore the equation, Y=B1+B2X+u. This is an example of a linear regression model which in general explains the behaviour of the dependent variable (on the left hand side) in relation to the behavior of other variables (on the right hand side). However, it is important to know that Y=B1+B2X+u is a predictive relationship since X cannot be entirely responsible for the cause and effect relationship. Y and X are not always causally related and so regression or correlation does not always imply causation.

4. Estimating the parameters of the model is the next important step. This would imply estimating the parameters of B1 and B2. Ordinary Least Squares (OLS) method would be used to obtain these results since it gives the best estimates for b1 and b2 by minimizing the sum of squared residuals. Furthermore, the b1 and b2 parameters obtained are said to be BLUE (Best Linear Unbiased Estimates).

5. Checking for model adequacy; model specification testing - As mentioned earlier that other forces that can affect the law of demand includes; advertising, consumer income, price of substitute and complimentary goods and other external forces which we cannot see. However, Price is the main force that affects the law of demand whereby if price of a normal good rises consumers are less likely to buy that good and switch to alternative products. So price has to be considered bringing about the equation Y=B1+B2X+B3X1+u. This is an example of a multiple linear regression model. However, no matter how many independent variables being introduced in the equation, one cannot fully explain and nothing can be fully responsible for the behavior of the dependent variable Y. The regression equation above does not imply Causation.

6. Hypothesis testing is then carried out in order to find out whether the estimated model makes economic sense and if it matches the economic theory that normal good does in general comply with the law of demand. The results have to be interpreted in order to come to a conclusion and to see if the results found are in agreement.

7. Using this model now, econometricians are able to predict and forecast for the future.