A Cointegration Analysis of Car Advertising and Sales Data in the Presence of Structural Change

Abstract

This paper examines whether there is a long‐run stable equilibrium relationship between advertising and sales across the market segments of the UK car industry over the period 1971–2001. In order to achieve this goal, we allow for structural breaks in the series using cointegration techniques. The results show the existence of long‐run equilibrium relationships in all six market segments, although in four of them the relationship is not stable. In general, one structural change is detected in the late 1970s and another in the early 1990s, coinciding with two economic recessions. When we do not account for structural changes, the estimated long‐run elasticities of advertising on sales are seen to be substantially downwardly biased. Finally, a noticeable increase is observed in long‐run elasticities in most car market segments during the nineties with respect to previous decades.

Key Words:

• Advertising
• Sales
• Cointegration
• Structural Break
• Car Industry
• JEL Classifications: C12, C22, L10

Notes

1. The optimal advertising/sales ratio can vary for other reasons. Different market structures may affect the optimal marketing mix strategy due to strategic interaction among players. For example, Lambin et al. (1975) extrapolate the Dorfman‐Steiner condition to the case of an oligopoly with multiple competitive reactions, that is, a competitor may react to a change in price by changing both price and advertising. In all the cases under study they find an optimal advertising/sales ratio which depends on own price and advertising elasticities as well as on cross‐price and cross‐advertising elasticities.

2. Dekimpe and Hanssens (2000) provide a survey of the marketing literature in the nineties on the long run relationship between sales and advertising. Of the 21 papers reviewed, 16 used a bivariate approach.

3. The data can be obtained from the authors on request.

4. The following code is used to identify market segments: (0) total market (excluding 4b × 4 and PC); (1) supermini/mini; (2) small; (3) medium; (4) large; (5) luxury; and (6) sport. The two segments excluded (4 × 4 and PC) emerge in the eighties so the number of observations is considerably reduced for cointegration analysis. In 2001, the 4b × 4 and PC segments represented around 9% of sales revenues in the UK car market.

5. See Ng and Perron (2001) and Perron and Ng (1996) for a detailed description of these tests.

6. In the case of the test, the unit root hypothesis is rejected in favour of stationarity when the estimated value is smaller than some appropiate critical value.

7. The null hypothesis of nonstationarity for the series in first differences [I(2) vs I(1)] was strongly rejected in all the cases.

8. See Monte Carlo simulations in Campos et al. (1996) and Perron (1997) for DF tests, and Perron and Rodríguez (2003) for and tests.

9. For more details, see Perron (1997).

10. Recent research has developed estimation techniques and tests of structural change at unknown break dates. See Andrews (1993) and Andrews and Ploberger (1994) for the case of a single structural change, and Andrews et al. (1996), Liu et al. (1997), and Bai and Perron (1998, 2003a, 2003b) for the case of multiple structural changes.

11. See the Appendix for technical details.

12. Notice that we found a deterministic rather than stochastic long term relationship, which implies a stronger cointegration between advertising and sales. Determistic cointegration implies that the same cointegrating vector eliminates deterministic trends as well as stochastic trends. But if the linear stationary combinations of I(1) variables have nonzero linear trends this corresponds to stochastic cointegration. For definitions of deterministic and stochastic cointegration, see Ogaki and Park (1997).

13. Another line of work using firm‐level data and unit root tests studies the volatility in temporal market shares as indicative of push‐and‐pull tacties of intense rivalry. See, for example, Gallet and List (2001).

14. Negative advertising elasticities are not uncommon in other studies. For example, Lariviere et al. (2000) report negative elasticities for alcoholic beverages.

Additional information

Notes on contributors

Vicente Esteve

The authors thank two anonymous referees for comments and suggestions that helped us to improve the paper greatly and James Walker for access to the advertising data. The authors acknowledge financial support from the Valencian Council of Education and Science, through the project GRUPOS03/151 as well as from the Spanish Ministry of Science and Technology, through the project SEC2002–03651 (V. Esteve) and the project SEC2005–05966 (F. Requena).