A Micro Modeling Approach To Investigate The Advertising - Sales

Relationship

Introduction:

� Purpose- To derive the model of advertising effects on the sales.� To develop more optimal advertising budgets.� Many lag models were used, none gave satisfactory results.� Advertisers focus on 2 aspects- i. % of buyers reached by an ad.

ii. Effect of an ad on future behavior of the buyer.� A micro model will be used to derive the aggregate sales relationship.� Topics in this presentation:1. The Consumer Model2. General form of consumer model equation3. Special case of model4. Evaluation of the model5. Application and comparison the model6. Conclusions

1.The Consumer Model

� Assumption1:

1. Let ‘q’ be the probability of the consumer to be exposed to any ad.

2. For total of ‘n’ insertions, the probability of a consumer being exposed to ‘x’ ads is assumed to have a bernoulli’s distribution with probability ‘q’:

[n!/x!(n-x)!]qx(1-q)1-x

3. To account for the homogeneity of the population it is assumed to have Beta-bernoulli’s distribution.

� Assumption2:

1. Exponential decay of effectiveness function: p(t)=e-α(t-ti)….(1)

2. Decay between t1 and t2 is : f(t) = qe- αt.3. After t2 ,(1-q) proportion of 1st group won’t see the ad.

4. Therefore, f(t)= q(1-q)e- αt +qe- α(t-t2

) …for the second insertion

5. For t= 0,1,2,3….

q + q(1-q)e- α + q(1-q)2e-2α +…= q/[1-(1-q)e-α]6.For computing sales over an interval, we integrate:

For kth period of length τ,

s(k)= c1τ + c2∫k τ

(k-1) τ f(t) dt…(2)Where c1 and c2 are constants.

7. This model assumes competitive environment is stable.

8. Therefore some error could be incorporated as competitive effects:s(k)= c1τ + c2∫

k τ(k-1) τ f(t) dt + Єk

2.General form of the consumer model equation:

Where ti is the time of the most recent insertion and ti-1 the time of the insertion preceding it.

Assumption: Insertions occur at constant rate.

For nk insertions in any period k of time ‘τ’ time interval between insertions is: τk= τ/nk.

Using (2) and (3) i.e. integrating, sales-advertising eq. becomes:

…(3)

…(4)

Where: and

It is assumed that the insertions are equally spaced.

3.Special Case of the Model:

� Assumption: q is very small.

� The previously discussed model becomes:

where ….(5)

Rewriting the equation(5) as :

Simplifying:

The variables, c1, β’ , Xk , β” and Yk can be obtained by obtaining α.

4.Evaluation of the model:

In this section we will discuss:

i. Effect of advertising on sales.ii. The carryover effect.

iii. Koyck’s Modeliv. The Bass-Clarke result

i. Effect of advertising on sales:

� The effect of advertising on sales in non-linear:

1. Is not of the form: sk=ln(nk) or ln(sk)=ln(nk).2. As α increases sk declines at decreasing rate.3. As q increases sk increases at decreasing rate.

ii. Carryover Effect:

� Definition: Effect of present period advertising on next period’s sales divided by effect of present period advertising on presentperiod sales.

• As alpha, q or nk+1 increases, the carryover effect decreases.

•Is not constant over time.

•It is non-linear with the frequency nk.

One period carryover effect:

iii.Koyck ’s Model:

� Model:

Sk=a + bAk + λSk-1

• Effect of the insertion pattern and carryover effect on λ.• Two cases: 1. When the insertions are random and 2. When the

insertions are at regular intervals.• λ is calculated using the linear model with q=0.1, c1=50,000,

c2=532,000 and α=1, for random and regular insertions as:

Effect of time aggregation on the model:

� Marketers using this model found λ to increase with increased duration of time.

� Values of λ were calculated for monthly and quarterly data, following result was found:

� Monthly data acts as random insertions and the quarterly data asregular insertions.

If we control insertion pattern we can control λ.

iv. Bass -Clarke Result:

This section is based on the observation made by Bass-Clarke and by using the approximate form of the previously obtained linear model.

The Model used:

Results:

� Effect decays with time and has maximum impact immediately afterthe ad is seen.

� The decay depends on the value of α.

� The results obtained in the above table requires low value of q.

� The model is less sensitive to time aggregation.

5.Application and comparison of the model:

� The models are applied to the 3 yrs advertising and sales data.

� 90% duration and the of the ad and variance is calculated using the model, for the values of alpha=1 and 1.5.

� As compared to the Koyck model the derived model has more variance and is less sensitive to the time aggregation.

6.Conclusions:

1. A macro model was generated from the micro model, using the assumptions on the reach and the decay.

2. The micro and the aggregate models work on different principles.

3. The model is non-linear and has diminishing returns to the advertising.

4. Carryover effect depends on present and past spending levels.

Thank You.