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MICRO ECONOMICS ANALYSIS
4: BASIC DEMAND ESTIMATION ANDFORECASTING

Table of Content
1
...
Introduction
3
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The functional Form of Empirical Demand Function
A Linear Empirical Demand Function
A Non-Linear Empirical Demand Function
Selection of a Demand Specification
5
...
Forecasting
Linear Trend Forecasting
Presence of Cyclical/Seasonal Variation
Use of Dummy Variables to Correct Seasonal Variation
7
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1: MICRO ECONOMICS ANALYSIS
MODULE No
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Learning Outcomes
After studying this module, you shall be able to understand clearly
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The direct methods of estimating demand function
Specification of the empirical demand function
Linear and non-linear empirical demand function
Method to estimate the parameters
Forecasting methods
Linear trend forecasting technique
Forecasting in the presence of seasonal variations
Use of dummy variables to correct seasonal variation

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Information about demand is also essential for making production and pricing decisions
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Big corporations use empirical
demand functions and econometric price forecasts while taking pricing decisions as it is really
important to set an optimal price
...
The statistical
forecasting does not fully eliminate the uncertainty prevailing with the pricing decisions but
nevertheless it definitely provides better insights thus helping in better pricing decisions
...

The fundamental integrant of this statistical analysis is the empirical demand estimation
...
In this chapter,
we will discuss methods of demand estimation, firstly the direct method and secondly by using
regression analysis
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This method can be used for a wide variety of forecasting needs of a business
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METHODS OF DEMAND ESTIMATION
There are direct techniques of demand estimation that do not involve regression analysis
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They include a) Market Experiments; and b) Consumer Interviews
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Market Experiments
This is quite an expensive and somewhat difficult technique of estimating demand functions
...
There are laboratory experiments as well as field experiments, where in the former,
volunteers are used to simulate actual buying conditions; and in the latter, firms display their
products in different showrooms at different locations with different characteristics and
population over a period of time and observe consumer’s behavior and choices
...
In these lab experiments, firms look for suitable volunteers and pay them to simulate
actual buying conditions but without going through the real markets
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With numerous shopping trips by various consumers, an approximation of demand is obtained
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In the second method i
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field experiments/field study, when firms display their products in the
actual markets, they make certain that there are enough units available at the showroom at each
price in order to satisfy demand
...
The researchers
want to change the price of goods and actually observe the behavior of the consumers
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With this, it is possible to remove influence of other things and a realistic
approximation of the actual demand is made possible
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This straightforward method simply involves asking the potential buyers how much
of the good they would buy at different prices
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The interviewer has to be careful while selecting the right
representative sample
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A random selection of members from the population has to be made
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In real life, it is difficult to get a perfect sample and true representation of the population
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The sample would consist of
relatively well-off people and it would be upwardly biased and will not represent the true
population where most population is middle class
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Yet another problem is that the interviewee is unable to answer accurately
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However, though the method has some problems, it is still a very valuable method to know the
actual needs of the people and quantifying the demand on the basis of their responses
...


4
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It can have both, a linear or a
non-linear form, and both will be discussed below
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e
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For example, we need to define the
physical boundaries of the market in which the product is to be sold
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Similarly, we need to look at the available substitutes and should include their prices
because they affect sales of the product
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Hence overall, careful consideration is required
while collecting information for estimating the demand function
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In this equation, β measures the change in quantity demanded that would result from one unit
change in price
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Also, γ measures the change in
quantity demanded where there is one unit change in income M
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Similarly, δ measures the change in quantity demanded with one unit
change in price of related good
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If the
related good is a substitute (complement), then the relation would be positive (negative)
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This
linear equation is estimated by using linear regression techniques and significance of the
parameters are checked using t tests or examining p values
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This means
price elasticity of demand is given by
Ep = β*(Px/X)

(2)

Similarly, income elasticity of demand is given by
Ei = γ*(M/X)

(3)

Epr = δ*(Pr/X)

(4)

And cross price elasticity is given by

A Non-Linear Empirical Demand Function
The most commonly used non-linear empirical demand function is a function in log linear form,
which can be written as:
X = α*Pxβ*Mγ*Prδ*bλ

(5)

This functional form provides direct estimation of the elasticities
...
e
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Selection of a demand specification
It is important to carefully choose the exact functional form between linear and non-linear but
unfortunately the researcher does not know the exact functional form of the demand function
...
Final selection of
the demand function is based on mainly judgment and experience
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He/she can check the
validity of the functional form by observing the signs and significance of the parameters
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The question is, which of the two – linear and non-linear demand
equations are more appropriate in different situations
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Whereas, if the sample is clustered around a narrow range of values, the log-linear
form is more appropriate
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ESTIMATING THE PARAMETERS
A firm needs to set price for its product and for that purpose, firm needs to estimate demand
which is done in the following steps:
a) Specify the firm’s demand function: this is done by choosing an exact functional form of
the demand function as discussed in the previous section
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c) Estimating the firm’s demand: Generally, linear regression method is used to estimate the
parameters of the demand function, from which respective elasticities can also be
computed
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An upcoming fast food delivery chain ‘Burger House’, which delivers burgers in area Y and
has one competitor in the neighborhood, namely ‘Big Burger’
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Hence the manager decides to collect prices in the last 12 months of its own product
as well as the price charged by the competitor
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Then the price and income data is deflated by using the price
indices
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It turns out
that number of residents did not change in the last 12 months, so the variable can be dropped

from the specification
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X = α + βPx + γM + δPr
Where
X = Sales of burgers at Burger House
Px = Price of a burger at Burger House
M = Average annual household income
Pr= Price of a burger at Big Burger
The least square regression gives the following results:

Table 1: Results of the regression
Variable
Coefficient value
Px
-115
...
09
Pr
10
...
43

P value
0
...
0005
0
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3890

All the three parameters are tested for statistical significance at 5% level of significance with the
degrees of freedom 9 (n-k=12-3)
...
The values are: PX=9, M= 20000, Pr=10
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43 + (-115
...
09)*20000 + (10
...
54
The elasticities are calculated as follows:
Price elasticity of demand is given by
Ep = β*(Px/X)

= (-115
...
54) = -0
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09*(20000/2047
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879
And cross price elasticity is given by
Epr = δ*(Pr/X) = 10
...
54) = 0
...
Correspondingly, the coefficient of cross price elasticity of 0
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5 per cent
increase in quantity demanded of burgers of Burger House
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FORECASTING
In this chapter we will focus on the quantitative methods of forecasting
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Forecasting requires a time series model
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We confine our discussion to time series model
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It describes the process by which past data is generated
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Linear Trend Forecasting
This is the simplest time series forecasting technique
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Suppose data for sales is
given for the period 2000-01 to2011-12 (i
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12 data points)
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The firm can
assume that the trend continues in the future and forecast the future sales by extending the line
and extrapolating for the desired period, say 2013-14 to 2016-17
...
We can
generalize this linear relation between time and sales of the product X as follows:
Xt = a + b*t
Where
Xt = Total sales of the good in period t
t = 2000-01, 2001-02, 2002-03 …
...
We get
̂t
̂=𝒂
𝑿
̂+ 𝒃
If the value of b is positive and significant, then we get an upward trend; if b is negative and
significant, we get a downward sloping trend line and if b = 0, then sales are constant over time
...

̂ *(2016-17)
X20016-17 = 𝒂
̂+𝒃

BUSINESS
ECONOMICS

Presence of Cyclical Variation/Seasonal Variation
Time series data my exhibit regular variation and we need to account for this kind of variation as
it would bias the forecast while estimating the forecasting equation
...
Hence we need to
incorporate such variations while forecasting a trend
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Use of Dummy Variables to Correct Seasonal Variation
Dummy variables are independent variables which take the value of either 0 or 1
...

A relatively straightforward approach to modeling and forecasting seasonality is through the use
of dummy variables in multiple regressions to represent the seasons
...
For example, we can represent
quarterly time series with three dummy variables and monthly series by eleven dummy variables
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For example, the complete
model for a monthly time series can be specified as follows:
Xt = a0 + a1*t + b1*M1+ b2*M2+ b3*M3+ b4*M4+ b5*M5+ b6*M6+ b7*M7+ b8*M8+ b9*M9+
b10*M10+ b11*M11
where:
• a0 is the intercept
• a1 is the coefficient for the time trend component
• b1, b2… b11 are the coefficients that indicate how much each month differs from the reference
month
...
Hence, Xt represents the sales figure in the tth period
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One in which dummy = 0 and one where dummy = 1
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For the month of January, the intercept would
be 𝒂̂𝒂̂+ 𝒂̂and for rest of the months the intercept would be 𝒂̂𝒂̂
...

Perhaps the best way to explain the use of dummy variables can be used to account for seasonal
variation is through an example
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It has trend overtime and also is subject to seasonal variation
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The data has 16 observations
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e
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The
equation to be estimated is:
Xt = a0 + a1*t + b1*D1 + b2*D2 + b3*D3
Where D1,D2 and D3 are dummy variables for quarter 1, 2 and 3 respectively
...
1
0
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34
0
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59
0
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21
0
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22
0
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The above low P
values indicate that the prediction of the sales for next two years will be higher
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Intercept for
First Quarter (q1)
Second Quarter (q2)
Third Quarter (q3)

Estimate for
Intercept
̂𝟏
𝒂
̂𝟎 + 𝒃
̂𝟐
𝒂
̂𝟎 + 𝒃
̂𝟑
𝒂
̂𝟎 + 𝒃

Value of the Intercept
1599
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59 = 898
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1-672
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88
1599
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21 = 940
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The manager checks
̂ are significantly lower than 𝒂
for the significance of these intercepts i
...
if ̂𝟎 + 𝒃
̂𝟎 , then it is
̂
necessary that 𝒃is significantly less than 0
...
The
intercepts in all the three quarters come out to be significant, which gives evidence that sales are
significantly lower in the three quarters
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Figure2: Sales with
Seasonal Variation

The next step is to forecast sales for first quarter of 2014 for which t=17, D 1=1, D2=0 and D3=0
...
1 + 271
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59 = 5511
...

The linear trend model discussed above is one of the simplest models from among many different
types of time series models that can be used to forecast economic variables
...


Activity
Calculate the future sales for the above example for the second, third and fourth quarters of
2014
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7
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There are two specifications for demand, Linear and Non-linear;
When the demand is specified in the linear form, the coefficients measure the rate of change
in the quantity demanded holding all other explanatory variables constant;
When the demand is specified in non-linear form, we convert it to log –linear form and the
coefficients measure the relevant elasticities;
Time series forecasts use the time ordered sequence of historical observations on a variable to
develop a model for predicting future values of that variable;
When data exhibits seasonal variations, dummy variables can be added to the time series
model to account for the seasonality;
If there are ‘n’ seasonal time periods, then n-1 dummies are to be added to the demand
equation;

Precautions to be taken: Incorrect specification of the demand equation can undermine the quality
of the forecast; Also, further is the future to be predicted, wider is the confidence interval and
hence greater the uncertainty

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