# Sales and advertising with spillovers at the firm level: estimation of a dynamic structural model on panel data

Emmanuel Duguet, Nicolas Iung

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Emmanuel Duguet, Nicolas Iung. Sales and advertising with spillovers at the firm level: estimation of a dynamic structural model on panel data. 1998. halshs-04660405

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CAHIERS ECO & MATHS

98.17

SALES AND ADVERTISING WITH SPILLOVERS AT THE FIRM LEVEL :
ESTIMATION OF A DYNAMIC STRUCTURAL MODEL ON PANEL DATA

Emmanuel DUGUET

Nicolas IUNG

CEME
# Sales and advertising with spillovers at the firm level:
estimation of a dynamic structural model on panel data

EMMANUEL DUGUET*

NICOLAS IUNG**

Revised, March 1998

We thank D. Encaoua, D. Fougère, F. Kramarz, G. Laroque, J. Mairesse, J.-M. Robin and B. Salanié for helpful suggestions and comments. We are also indebted to the participants at the CREST, CEME-University of Paris 1 and INSEE-DESE seminars.

*Centre d'Economie Mathématique et d'Econométrie (CEME CNRS URA 924) - Université de Paris I - Panthéon - Sorbonne and Institut National de la Statistique et des Etudes Economiques (INSEE) - Division Marchés et Stratégies d'Entreprises.

** Institut National de la Statistique et des Etudes Economiques (INSEE) - Division Marchés et Stratégies d'Entreprises.
Résumé

Chiffre d'affaires et publicité avec externalités:
estimation d'un modèle structurel dynamique sur données de panel

L'objet de cet article est d'étudier la relation entre les dépenses de publicité et les ventes des entreprises de l'industrie manufacturière française. Dans un premier temps nous proposons un modèle théorique simple compatible avec les modèles empiriques estimés par le passé, puis son extension au cas dynamique. Nous montrons que les modèles qui ne tiennent pas compte du caractère dynamique de la publicité surestiment son impact sur les ventes. Dans un second temps, nous estimons notre modèle en tenant compte des principaux problèmes rencontrés par la littérature antérieure, simultanéité et effets fixes individuels, en recourant à la méthode des moments généralisés. Pour cela nous disposons des dépenses de publicité de 4882 entreprises industrielles sur la période 1988-1994. Nous trouvons que la publicité permet bien de différencier les produits dans quelques industries et faiblement dans la plupart, que les effets externes sont toujours positifs ou nuls et que la dépréciation du capital de publicité est plus élevée que ne le suggèrent les études antérieures.

Mots-Clef : chiffre d'affaires, publicité, effets externes, capital immatériel, équation d'Euler, méthode des moments généralisés, données de panel, industrie manufacturière.

Classement J.E.L. : C23, D43, D62, D92, L60

Abstract

The aim of this paper is to study the relationship between advertising and sales of French
manufacturing firms. First, we use a simple theoretical model compatible with past
econometric studies of sales and advertising, and extend it to dynamics. We show that
the models that do not account for the dynamic features of advertising lead to overstate
the impact that advertising has on sales. Second, we estimate our model while
accounting for the main problems encountered in the previous econometric studies:
simultaneity between sales and advertising and fixed effects, using the generalized
method of moments. We use new data on advertising expenditures for 4882 firms over
1988-1994. We find that advertising allows for product differentiation in some industries,
that advertising by competitors always has a non-negative effect on own sales and that
the depreciation of advertising is higher than suggested in previous studies, always above
60%.

**Keywords:** sales, advertising, spillovers, goodwill capital, Euler equation, generalized method of moments, panel data, manufacturing.

JEL Classification: C23, D43, D62, D92, L60
# 1. Introduction

A first approach to advertising considers it as a mean to provide information to consumers who otherwise would ignore the existence of a product. In this case, advertising is a way to increase the social surplus (for a survey, see Tirole, 1988). But it is more widely accepted that advertising is a way to build barriers to entry (Comanor and Wilson, 1967, Sutton, 1991). Here advertising is a sunk cost with no resale value. Following Brown (1978), we can distinguish three ways through which advertising creates additional sunk costs for potential entrants. First, high levels of advertising from incumbents imply higher levels of expenditures for potential entrants; second, there could be scale economies so that the entrants would have to pay a higher average amount of advertising. Third, the incumbents would benefit from lower fares than newcomers. Overall, advertising would result in a reduction of output and in higher prices. But this approach has the following limitation: it implicitly assumes an incumbent monopoly and bypasses the advertising competition that takes place between the incumbents themselves. In the latter case, advertising expenditures of one firm can well be canceled by the expenditures of its competitors, or on the contrary a firm can benefit from the advertising of its competitors. This problem has been studied in Netter (1982) and Kelton and Kelton (1982). When firms compete, advertising is a way to reallocate market shares between incumbents. In fact, this depends on the homogeneity of the products. When firms compete on a homogenous good, advertising would have a short-run effect only, and could be considered as useless expenditures that cannot even protect the preexisting market power. On the long run, advertising would benefit neither to producers nor to consumers.

In order to assess the effect of advertising, we build a structural dynamic model and show that past static models lead to overstate the effect of advertising on prices. Then we estimate the dynamic model on a panel of 4882 French manufacturing firms over 1988-1994. We account for both simultaneity and unobservable fixed effects, through the use of the generalized method of moments (GMM).

The questions are: what is the effect of advertising on equilibrium prices? Does
advertising spill over to competitors? And does advertising accumulate in a « goodwill » capital?

The first section of this paper presents a brief survey of past studies of advertising. Then, a simple theoretical foundation for these empirical models and its dynamic extension are developed. The data are presented in section 3, which leads to the discussion of the econometric method in section 4. The results are presented in section 5 and our conclusions in the last section.

## 2. Previous econometric studies of advertising

A number of empirical studies have tried to evaluate the effects of advertising on market structure and performance. In this section, we review briefly some representative studies. More precisely, we are interested mostly in firm level studies and in the response of sales and market shares to advertising expenditures.

These studies were conducted at the product level, at the firm level or at the industry level. Brown (1978) raises this problem: should we work at the product level or at the firm level? On the one hand, firm level data aggregate several kinds of products that could have different degrees of homogeneity but, on the other hand, what matters for consumers could well be the overall image of the firm. Then, looking at the problem by product could underestimate the return on advertising. A second problem faced by empirical studies is the choice of the performance variable that advertising is supposed to affect. Most studies use sales, and we follow this approach in this paper, but other variables have been studied, such as market value, mark-ups and market shares. Finally, some studies (Hirschey, 1982) consider advertising as one part only of immaterial capital that includes research and development expenditures as well. We briefly recall their main results in this section.

### 2.1 Models with rivalry

Both own and rivals' advertising affect own sales. Then, there could be excessive
advertising: a first ad campaign would be canceled by a second one, etc. There would be
a short-run effect of advertising but, on the medium run, the equilibrium market shares
would be the same if advertising had never taken place. The paper of Netter (1982)
addresses this issue at the firm level. A first relationship explains sales by both own
advertising and industry advertising expenditures. The finding is that advertising has a
positive effect on sales. Conversely, for industry advertising, the effect depends on the
type of good sold. For non-durable goods, industry advertising would have a negative
effect on sales, which does not contradict excessive advertising. For durable goods, there
would be no effect of industry advertising. This first regression analysis is followed by a
profit rate equation. The same results are found for non-durable goods but no effect of
advertising at all is found for durable goods.

Two problems gave rise to new studies. A first one, well known in the literature, is simultaneity. It is clear that the lag between advertising and sales is lower than a year. Therefore, advertising and sales are simultaneously determined due to temporal aggregation (Mundlak, 1961; Rao, 1986). But another argument can be used to justify simultaneity: the sales equation can be derived directly from an equilibrium relationship where both sales and advertising are endogenous. This problem seems to have been accounted for in the industry level studies only.

The second problem, stressed by Landes and Rosenfield (1994), is that there are unobservable and permanent components that affect sales, like product quality. It is the well-known fixed effect model in the econometric literature (Mundlak, 1978). Other arguments for this fixed effect are the innovation level of the firm, products' durability, or a permanent deviation from profit maximization<fnref n="1" />.

## 2.2 Industry studies

The simultaneous equations models have been used essentially on industry level
data. Following the previous works like Comanor and Wilson (1967), several authors

<footnote n="1">¹ See section 3.2 of this paper.</footnote>
study the relationship between advertising, concentration and the markup of price over
marginal cost (e.g. Martin, 1979). This last author improves on the previous models and
distinguishes consumer goods from the other goods. It is found that, in consumer goods
industries, concentration increases the advertising rate which itself increases the markup.
The markup then increases advertising. But no significant effect of advertising on
concentration is found. The latter result is reinforced by the analysis of the other
industries. The only relationship that remains is between markups and advertising.

These results are interesting since they indicate that advertising could be a weak
barrier to entry, at least in some industries. In fact, this last study also accounts for other
types of barrier to entry, like the minimum efficient scale, which could explain why the
effect of advertising is weak. It remains that the positive relationship between advertising
and profits is not incompatible with the theory of advertising as information.

2.2.1 *Advertising as a capital*

Following the critics by Weiss (1969) advertising should not be considered as a
simple expenditure but as an investment that accumulates in a « goodwill » capital. Two
empirical approaches are possible: using yearly expenditures and strong assumptions<fnref n="2" />
(Hirshey, 1982) or using a distributed lag model with more data (Brown, 1978).

Hirshey (1982) includes both R&D and advertising capital in a Tobin's q equation.
Overall, both types of immaterial capital have a positive effect on the market value of the
firm. However, a more detailed analysis shows that television advertising only would
have a significant effect on market value.

But the estimation method suffers from several limitations: simultaneity and the
lack of fixed effects. Landes and Rosenfield (1994) use a fixed effects model. The
authors find no significant effect of advertising (table IV, p. 274) on Tobin's q. But this
could be a downward bias associated to simultaneity. Other studies find a significant

<footnote n="2">² The steady state assumption of asset models, which has been tested and rejected by Landes and Rosenfield (1994).</footnote>
effect of advertising at the brand or at the firm level (Kelton and Kelton, 1982; Nakao, 1993).

### 2.2.2 *Contribution of this study*

Our aim is to solve the five following problems associated with previous studies

*Structural model.* A common criticism valid for nearly all the previous studies is that there is no clear structural model behind the estimation. The authors mostly quote several papers addressing one point and then directly introduce a proxy variable in the equation to account for the argument. Sometimes, a theoretical model is provided but is not used in the estimation. Therefore, our first goal is to propose a bridge between the empirical and the theoretical papers. We estimate a model that allows for the identification of the three following structural parameters: the elasticity of the inverse demand to advertising, the spillover effect of competitors' advertising and the depreciation rate of goodwill capital. Our theoretical work is made of two parts: first, to provide a theoretical justification for the sales equations that have been used in the past and, second, to propose a new model that accounts for the intertemporal features of advertising capital (Euler equation). We show that studies that do not account for the dynamic features of advertising *overstate* the effect of advertising.

*Simultaneity at the firm level.* We have observed that while industry studies account for the simultaneity issue, the firm level studies do not. Then, we will account for simultaneity using the GMM approach under weak exogeneity.

*Firm level and time fixed effects.* Most studies do not account for fixed effects, which may give biased estimations. We allow for both firm level and time fixed effects, and use panel data on seven years (estimation on first differences with time dummies). This was made possible by the availability of new data on French manufacturing: advertising expenditures at the firm level over seven years (1988-1994).

*Coverage.* Most studies suffered from the lack of data. We are luckier: advertising
expenditures are included in the French manufacturing Industry Census every year since 1988. Our sample includes 4882 firms in all manufacturing industries, and not only in one line-of-business or at a highly aggregated group of products (like durable or non-durable). Firm level data is available for the 7 years 1988-1994.

*Separate regressions for eighteen industries.* Data availability allows for the estimation of different structural parameters in each industry. Up to now, no such detailed regression analysis seems to have been performed.

### 3. A simple theoretical background and its extension to dynamics

#### 3.1 Static models of advertising

The model we consider is close to the R&D literature with spillovers (especially Katz, 1986; Levin and Reiss, 1988; Kamien, Muller and Zang, 1990). We consider an industry composed of N firms that engage expenses in advertising to increase their profit. The model is not symmetric and the inverse demand function addressed to firm i is:

$$p_i = P(Q, A_i), i = 1, \dots, N \text{ with } P'_i < 0, P''_i > 0$$

where $p_i$ is the price of firm i's product, $Q$ is the quantity produced by the entire industry and $A_i$ is the pool of advertising that firm i is enjoying. Advertising plays the role of a differentiation parameter which relaxes the price competition that would take place if the products where homogeneous ($A_i = 0, \forall i$).

The advertising pool $A_i$ is a mix between firm's i and its competitors' advertising. More precisely, we assume that:

$$A_i = a_i + \theta \sum_{j \neq i} a_j, i = 1, \dots, N$$

where N is the number of firms in the industry under study, $a_i$ is advertising of
firm i and θ a spillover parameter analogous to the one of the research and development literature. However, there is a difference with models of research and development: the sign of θ is not necessarily positive. This sign is crucial to determine whether there is excessive investment in advertising or not. If θ is positive, firms can free ride on their competitors' expenditures. On the contrary, a negative value for θ implies that firms must offset the reduction of their advertising's efficiency by increasing their own investment, which triggers their rivals to do the same in return. So that, we can conclude with Netter (1982) that a negative value for the externality parameter would be likely to provoke a waste of resources.

The firm's profit function is given by:

$$ \Pi_i = (p_i - c_i)q_i - a_i, \quad i = 1, \dots, N $$

where cᵢ is the unit variable cost of production. Profit maximization according to advertising gives the first order condition<fnref n="3" />:

$$ \frac{\partial \Pi_i}{\partial a_i} (a_i^*, q_i^*) = \frac{\partial P_i}{\partial A_i} \times \frac{\partial A_i}{\partial a_i} \times q_i^* - 1 = 0, \quad i = 1, \dots, N $$

where the « * » denotes equilibrium quantities.

For our purpose, we do not need to derive the first order condition on the production level<fnref n="4" /> ($\partial\Pi_i/\partial q_i$), so that our estimates are robust to deviations from this condition. However we bear in mind that this condition implies that sales and advertising are *simultaneously* determined. We have to take this into account in our estimations

<footnote n="3">³ The second order condition is equivalent to $\alpha < 1$, where $\alpha$ is the elasticity of the inverse demand function to advertising. We will see later that this condition is empirically fulfilled.</footnote>

<footnote n="4">⁴ This first condition can be written as a relationship between the markup of price over marginal cost and the market share of the firm in volume. This market share is different from the *value* market share in our model since each firm has a different price. In our data, only *value* market share are available so that we cannot evaluate the elasticity of demand, due to the unavailability of firm-level prices.</footnote>
Further, we assume that price, represented by the inverse demand function, presents a constant elasticity to the total advertising the firm benefits from:

$$ \alpha = \frac{\partial P_i}{\partial A_i} \times \frac{A_i}{P_i}, i = 1, \dots, N $$

This expression can be rewritten as:

$$ \alpha = \frac{\partial P_i}{\partial A_i} \times \frac{a_i + \theta \sum_{j \neq i} a_j}{P_i} \Leftrightarrow \frac{\partial P_i}{\partial A_i} = \frac{\alpha P_i}{a_i + \theta \sum_{j \neq i} a_j}, i = 1, \dots, N $$

By substituting this quantity into the first order condition, we obtain:

$$ P_i^* q_i^* - \frac{1}{\alpha} \times a_i^* - \frac{\theta}{\alpha} \times \sum_{j \neq i} a_j^* = 0, \quad i = 1, \dots, N $$

This expression describes the relationship between firms' sales and advertising. *This relation is not causal* so that the endogeneity of both sales and advertising must be accounted for.

A weakness of this structural model is that sales are depending on advertising only. Many other variables do play a role. An answer to this critic is the use of the time dimension of our data, which enables us to include individual and time dummies into the equation. These dummies represent missing or unobservable variables in the equation as in the paper by Mundlak (1978). We develop a clear interpretation of these fixed effects in the econometrics section.

## 3.2 Empirical model with current expenditures

In order to estimate the previous equation, one has to assume that this relation holds at every date, except for fixed effects and a random disturbance. The panel data equation is then:
$$S_{it}^* - b_1 \times a_{it}^* - b_2 \times \sum_{j \neq i} a_{jt}^* = \mu_i + \delta_t + u_{it}$$

where $S_{it}^* = p_{it}^* q_{it}^*$ is equilibrium sales of firm i at time t, $b_1 = 1/\alpha$ and $b_2 = \theta/\alpha$.

The firm-specific effect $\mu_i$ represents missing or unobservable variables that are constant over the estimation period, and $\delta_t$ a time effect common to all firms. Here, we propose two interpretations for this fixed effect: a missing time-constant variable in the spillover function or a relaxation of the profit maximization hypothesis. We also account for a random effect with conditional mean $E(u_{it} | a_{1t}^*, ..., a_{Nt}^*) = 0$.

### 3.3 Justification of the fixed effects: missing variables and profit non-maximization

Other types of immaterial capital, summarized in the firm fixed effect can affect the spillover function:

$$A_{it} = a_{it} + \theta \times \sum_{j \neq i} a_{jt} + \mu_{1i}$$

A classic interpretation of the fixed effect $\mu_{1i}$ is that it represents missing variables like products quality, durability, or the innovation level. More generally it is all the other time constant variables that influence sales.

But a more interesting interpretation of the fixed effect is that firms do not maximize profit. It can be seen as a theoretical version of Mundlak's « quality of management ». We assume that firms systematically underinvest or overinvest in advertising, possibly because of informational problems. In this case, the marginal profit according to advertising will systematically be either negative (i.e., overinvestment) or positive (i.e., underinvestment). This is what captures the following fixed effect. From the basic model, we get:
$$ \frac{\partial \Pi_i}{\partial a_i}(a_i^*, q_i^*) = \mu_{2i} \text{ instead of } \frac{\partial \Pi_i}{\partial a_i}(a_i^*, q_i^*) = 0, i = 1, \dots, N $$

This gives an empirical equation similar to the previous case. Moreover, this interpretation can be extended to the time fixed effects, when all the firms in a *same* industry make the same optimization error at a given date, possibly due to industry-wide poor expectations.

We also add a random deviation to the first order condition, so as to allow for our relationship to hold « on average » conditional on the fixed effects and the variables. We finally get the specification:

$$ S_{it}^* - b_1 \times a_{it}^* - b_2 \times \sum_{j \neq i} a_{jt}^* = \mu_i + \delta_t + u_{it} $$

where $\mu_i = \mu_{1i} / \alpha + \mu_{2i}$ summarizes the two specification errors mentioned above, $\delta_t$ is the common systematic error and $u_{it}$ the usual disturbance. Overall, adding these fixed and random firm-level effects makes estimation more robust.

Moreover, we allow the coefficients to vary across industries and therefore we run separate regressions for each industry. It also implies that the firm and time dummies as well as the distribution of the disturbance are specific to each industry.

## 3.4 The dynamic model

The previous model implicitly assumes that the depreciation of advertising is perfect. But if advertising can accumulate in a goodwill capital, only a dynamic model is appropriate. In this section, we assume intertemporal optimization from the firm. More precisely, we consider a firm whose expected net present value at the start of period t is given by:

$$ V_t = E_t \left\{ \sum_{k=0}^{\infty} \frac{\Pi_{t+k}}{(1+r)^{t+k}} \right\} \quad \text{with } g_{it} = (1-\gamma)g_{it-1} + a_{it} \quad \forall i, t $$
where g<sub>it</sub> is the goodwill capital of firm i at the end of period t, γ the annual depreciation rate of advertising and E<sub>t</sub> the expectation operator conditional on the information available at the start of period t. Expectations are taken over the future competitors' decisions. The parameter r is the actualization rate common all firms and is assumed to be exogenous.

The value function verifies the Bellman equation:

$$
V_t[a_{it-1}] = \operatorname{Max}_{z_{it}, q_{it}} \left\{ \Pi \left[ (1-\gamma)g_{it-1} + a_{it}, q_{it}, a_{it} \right] + \frac{1}{1+r} E_t \left\{ V_{t+1} \left[ (1-\gamma)g_{it-1} + a_{it} \right] \right\} \right\}
$$

The first order condition, with respect to g, is:

$$
0 = \left(\frac{\partial \Pi}{\partial g}\right)_t + \left(\frac{\partial \Pi}{\partial a}\right)_t + \frac{1}{1+r} E_t \left[ \frac{\partial V_{t+1}}{\partial g_t} \right]
$$

The envelope theorem implies:

$$
\frac{\partial V_t}{\partial g_{t-1}} = (1-\gamma) \left(\frac{\partial \Pi}{\partial g}\right)_t + \frac{1-\gamma}{1+r} E_t \left[ \frac{\partial V_{t+1}}{\partial g_t} \right]
$$

From these two equations, we obtain the shadow value of advertising:

$$
\frac{\partial V_t}{\partial g_{t-1}} = -(1-\gamma) \left(\frac{\partial \Pi}{\partial a}\right)_t
$$

Substituting this expression into the first order condition, gives the Euler equation:

$$
\frac{1 - \gamma}{1 + r} E_t \left( \frac{\partial \Pi}{\partial a} \right)_{t+1} = \left( \frac{\partial \Pi}{\partial a} \right)_t + \left( \frac{\partial \Pi}{\partial g} \right)_t
$$

Assuming rational expectations, we can replace the expected values by the future
values. Rewriting the previous condition, we obtain the following empirical expression:

$$S_{it}^{*} - \frac{r+\gamma}{r+1} \frac{1}{\alpha} g_{it}^{*} - \frac{r+\gamma}{r+1} \frac{\theta}{\alpha} \sum_{j \neq i} g_{jt}^{*} = 0$$

The difference with the static model lies in the interpretation of the coefficients. We cannot estimate $\alpha$ independently of the depreciation rate. Consistently, when depreciation is perfect (i.e., $\gamma$ is equal to 1), we obtain the same model. Notice that the externality parameter can be computed exactly in the same way as in the static model. Then, an interesting finding of our model is that, provided the depreciation of advertising is large, the past studies of sales and advertising remain approximately valid<fnref n="5" />.

As before, we account for missing and unobservable variables by adding firm-specific effects and time dummies:

$$S_{it}^{*} - \frac{r+\gamma}{r+1} \frac{1}{\alpha} g_{it}^{*} - \frac{r+\gamma}{r+1} \frac{\theta}{\alpha} \sum_{j \neq i} g_{jt}^{*} = \mu_{i} + \delta_{t} + u_{it}$$

Using the previous relationship lagged once and taking the first difference, we obtain:

$$S_{it}^{*} - (1-\gamma)S_{it-1}^{*} - \frac{r+\gamma}{r+1} \frac{1}{\alpha} a_{it}^{*} - \frac{r+\gamma}{r+1} \frac{\theta}{\alpha} \sum_{j \neq i} a_{jt}^{*} = \gamma\mu_{i} + \delta_{t} - (1-\gamma)\delta_{t-1} + u_{it} - (1-\gamma)u_{it-1}$$

So that we have to estimate the relationship:

$$S_{it}^{*} - b_{0}S_{it-1}^{*} - b_{1}a_{it}^{*} - b_{2} \sum_{j \neq i} a_{jt}^{*} = v_{i} + \eta_{t} + v_{it}$$

<footnote n="5">⁵ If we were to study variables like R&D, this result would not hold since its depreciation rate is much lower than the one of advertising.</footnote>
where $b_0 = 1 - \gamma$, $b_1 = \frac{r + \gamma}{r + 1} \frac{1}{\alpha}$, $b_2 = \frac{r + \gamma}{r + 1} \frac{\theta}{\alpha}$, $v_{it} = u_{it} - (1 - \gamma)u_{it-1}$, $\eta_t = \delta_t - (1 - \gamma)\delta_{t-1}$, and $v_i = \gamma\mu_i$.

Notice that this model implies serial correlation among the disturbances $v_{it}$.

## 3.5 Previous models with goodwill capital overstate the effect of advertising

The previous models did not account for the intertemporal optimization features of advertising: goodwill capital was put directly into the equation and the static first order conditions were supposed to hold. The problem with this specification is that the first order conditions are not the same in a dynamic model.

Under these assumptions, that is if firms do not take intertemporal decisions, the static model remains unchanged and one can substitute the advertising capital for the current advertising expenditure in the sales equation. The slight change is the introduction of a new parameter $\gamma$, the depreciation rate of advertising.

The new relationship is:

$$S_{it}^* - b_1 \times g_{it}^* - b_2 \times \sum_{j \neq i} g_{jt}^* = \mu_i + \delta_t + u_{it}$$

where $g_{it}^* = (1 - \gamma)g_{it-1}^* + a_{it}^*$ is goodwill capital and $a_{it}$ the annual flow of advertising.

As we do not observe advertising capital, we take the following transformation of the sales equation:
$$
\begin{align*}
S_{it}^* - (1-\gamma)S_{it-1}^* &= b_1 \times [g_{it}^* - (1-\gamma)g_{it-1}^*] + b_2 \times [\sum_{j \neq i} g_{jt}^* - (1-\gamma)\sum_{j \neq i} g_{jt-1}^*] \\
&\quad + \gamma\mu_i + \delta_t - (1-\gamma)\delta_{t-1} + u_{it} - (1-\gamma)u_{it-1} \\
&= b_1 \times [g_{it}^* - (1-\gamma)g_{it-1}^*] + b_2 \times \sum_{j \neq i} [g_{jt}^* - (1-\gamma)g_{jt-1}^*] \\
&\quad + v_i + \eta_t + v_{it} \\
&= b_1 \times a_{it}^* + b_2 \times \sum_{j \neq i} a_{jt}^* + v_i + \eta_t + v_{it}
\end{align*}
$$

This model can be rewritten under the autoregressive form:

$$
S_{it}^{*} - b_{0} \times S_{it-1}^{*} - b_{1} \times g_{it}^{*} - b_{2} \sum_{j \neq i} g_{jt}^{*} = v_{i} + \eta_{t} + v_{it}
$$

$$
\begin{array}{l}
\text{where } b_0 = 1-\gamma, b'_1 = 1/\alpha, b'_2 = \theta/\alpha, v_i = \gamma\mu_i, \eta_t = \delta_t - (1-\gamma)\delta_{t-1} \\
\text{and } v_{it} = u_{it} - (1-\gamma)u_{it-1}.
\end{array}
$$

There are two common points and one difference with the static model: the depreciation rate and the spillover parameter can always be estimated by $1-b_0$ and $b_2/b_1$ respectively. But the elasticity of price to advertising is no more given by $1/b_1$. We can even say that this model leads to *overstate* the effect of own advertising on sales, since:

$$
\alpha_S - \alpha_D = \frac{1}{b_1} \left( \frac{1-\gamma}{\gamma+r} \right) \geq 0 \quad \forall 0 \leq \gamma \leq 1
$$

where the subscripts S and D denote respectively the static and dynamic models.

4. The data

4.1 The sample

The statistical office of the French Ministry of Industry (Sessi) collects annually the
total amount of advertising expensed by each firm along with other accounting variables,
for all firms with at least 20 people operating in manufacturing<fnref n="6" />. Advertising concerns
many media: television, newspapers, radio and mail. But also gifts, exhibitions and
sponsoring of events. Unfortunately, there is no advertising data desegregated by media.

Our sample includes 4882 manufacturing firms with 7 years of continuous data
over the period 1988-1994. All manufacturing industries are included. For these firms,
we also have sales and operating profit<fnref n="7" />.

We needed to compute a third variable in a different way: competitors total advertising. As our sample is balanced, one must calculate this variable by using the global survey that is *unbalanced*. To do this, we define that two firms are competitors if they belong to the same industry according to the finest industry classification available (so called « level 600 » of the NAP<fnref n="8" />). It is important to notice that the competitor's advertising includes the expenditures of the firms that are not in the sample due to entry and exit over the period.

## 4.2 Descriptive statistics

### 4.2.1 Coverage of the balanced panel

Since our sample is balanced, we first need to look at its representativeness. We give the shares of our sample in manufacturing totals in 1991 (table 1). Our sample represents between 31% and 89% of sales depending on the industry, and between 34% and 97% of advertising. The four industries that are the best represented are transportation equipment (T16), steel (T8), glass (T10) and pharmaceuticals (T12), with about 70% of sales and advertising. The four industries that are the less represented in the sample are foundry (T13), printing and publishing (T22), leather and footwear (T19)

<footnote n="6">⁶ The source is the « Enquête Annuelle d'Entreprises », the Annual Census of Manufacturing.</footnote>

<footnote n="7">⁷ Defined as value added minus labor cost.</footnote>

<footnote n="8">⁸ NAP : Nomenclature d'Activités et de Produits. The « level 600 » breaks manufacturing in 255 industries, which is equivalent to a 3 to 4 digits classification according to international standards.</footnote>
and wood and furniture's (T20), with about 32% of sales and 40% of advertising.

### 4.2.2 Advertising to Sales ratios

Table 2 provides the average advertising to sales ratios by industry. These ratios remain fairly stable over the period under study and reveal that all the industries are involved in advertising. However, there are strong differences across industries. Overall, the advertising to sales ratios are the biggest in consumer goods. Pharmaceutical and other chemicals (T12) is well ahead of the others with a ratio of advertising to sales greater than 4%. Then come houseware and consumer electronics (2 to 3%) and the other consumer goods (1 to 1.5%). The intermediate goods industries have the lowest figures (0.2 to 1%).

### 4.2.3 Variance decomposition and correlations

Most of the variance is between firms (table 3). For sales, the within-firm variance represents less than 1% of the total variance, as it is usually the case when the variables are taken in levels. The within-firm variance is more important for advertising (up to 6%). Before turning to the regressions, we compute the within and between-firm correlation between sales and advertising. The between-firm correlation is high and ranges from 0.49 to 0.96. They are lower after the within transformation, from 0.09 to 0.68, but remain reasonably high in most industries.

Other correlations are interesting to look at: the ones on the first differences, since they are the basis of the GMM estimations. We have computed the partial correlation coefficients (table 4). Overall the correlations between sales and advertising are lower under the within transformation, around 0.3. Interestingly, the correlations between sales and competitors' advertising exhibit few significant coefficients (8 industries out of 18). Finally, collinearity is unlikely between the two advertising variables (the highest correlation in absolute value is 0.14).
## 5. Estimation

At first, we deliberately ignore the simultaneity between sales and advertising. We present the « between » and « within » estimations (Table 5). These first estimations allow us to perform two specification tests: the Fisher test for the existence of an individual effect and the test suggested by Hausman which compares « between » and « within » estimations, in order to know whether the individual effect is correlated with the explanatory variables or not. We can already say that for the great majority of industries there are firm-specific effects and that they are correlated to the explanatory variables.

To eliminate the individual effect, we estimate the equation in first differences. We also add a full set of times dummies to eliminate time effects. To take into account the endogeneity of the right-hand variables, we use the generalized method of moments (GMM) following Arellano and Bond (1991), under the assumption of weak exogeneity. In all cases, we provide the overidentification statistic (Sargan, 1958).

### 5.1 Between and Within

Our model can be written under the general form:

$$y_{it} = x_{it}b + \alpha_i + \delta_t + u_{it} \quad i = 1, \dots, n \quad t = 1, \dots, T$$

where y denotes sales and x a vector including the two advertising variables. The disturbance u is serially correlated. There are n = 4882 firms and T = 7 years of available data. We allow for both a firm level fixed effect, that summarizes all the unobservable variables constant for each firm over time, and a time fixed effect, common to all firms. The disturbance, denoted u, includes the remaining specification errors. We allow for this disturbance to be heteroskedastic both over individuals and over time. In order to compare our results with the previous works, we first estimate the model by the standard between and within methods (see Hsiao, 1992).

This is a basic fixed effect model. If there was no simultaneity between sales and
advertising, the between estimator would be biased and the within estimator would be consistent. As is well known, a discrepancy between these two indicates the existence of correlated effects. The null hypothesis is $\hat{b}_B = \hat{b}_W$. Since both estimators are independent by construction, we use the following statistic, similar to the Hausman statistic, but with robust covariance matrices:

$$H = (\hat{b}_B - \hat{b}_W)'[\hat{V}(\hat{b}_B) + \hat{V}(\hat{b}_W)]^{-1}(\hat{b}_B - \hat{b}_W)$$

Under the null, it is asymptotically chi-square distributed with as many degrees of freedom as there are common coefficients in the two regressions (here, 2).

But these estimation methods are unsatisfying for two reasons. First, we will see that one never accept the null of the previous test, so that there may exist firm level effects correlated with the regressors, which implies that the between estimations are biased.

Second, even the within estimator is biased when the regressors are endogenous (Sevestre and Trogon, 1996a). And it is likely to be the case for two reasons: on the one hand, we estimate an equilibrium relationship where sales and advertising are simultaneously determined; on the other hand, even if it was not the case, the feedback from sales to advertising takes less than one year, so that there would be a simultaneity due to temporal aggregation. Therefore, we pass to the Generalized Method of Moments (henceforth, GMM) to estimate the model.

## 5.2 GMM estimation

To eliminate the individual effects, we take the first difference of the equation. Moreover, we include a full set of time dummies among the regressors. To save notation, consider the *first-difference model*:

$$y = x b + u$$
where y include the annual variation of sales, the x matrix includes the annual variations of own and competitors' advertising and the time dummies. Matrix x possibly includes the lagged first-difference of sales, in the dynamic model. By assumption, the regressors are correlated with the disturbance u, that is $Plim x'u/n \neq 0$. In this case, none of the usual estimators of the fixed effects model is consistent<fnref n="9" />. Therefore, we have to turn to instrumental variables methods.

This is equivalent to looking for a set of variables z that satisfies the two well-known conditions: $Plim z'u/n = 0$ and $Plim z'x/n$ of the same rank as there are regressors in the model. Therefore, following White (1982), we obtain a consistent first-step estimator by using the 2SLS method with a robust covariance matrix<fnref n="10" />. Namely:

$$ \hat{\beta} = [x'Px]^{-1}x'Py $$

$$ \text{avar}(\hat{\beta}) = [x'Px]^{-1}x'z(z'z)^{-1}\Phi(z'z)^{-1}z'x[x'Px]^{-1} $$

where P is the projection matrix on $Im(z)$, $P = z(z'z)^{-1}z'$ and $\Phi = \text{avar}(z'u)$. The GMM estimator $\beta^*$ makes a more efficient use of the information available through $\Phi$ by minimizing the norm of the empirical counterpart of the orthogonality conditions (Hansen, 1982), that is:

$$ \beta^* = \arg\min_{\beta} u'z\Phi^{-1}z'u $$

We obtain:

$$ \beta^* = (x'z\Phi^{-1}z'x)^{-1}x'z\Phi^{-1}z'y $$

$$ \text{avar}(\beta^*) = (x'z\Phi^{-1}z'x)^{-1}. $$

<footnote n="9">⁹ For a comprehensive introduction to GMM estimation on static and dynamic models, and a discussion of the behaviour of the traditional estimators, see respectively Sevestre and Trognon 1996a and 1996b.</footnote>

<footnote n="10">¹⁰ Or first-step GMM.</footnote>
In practice, we need an estimate of $\Phi$, which is obtained from the first step 2SLS estimator in the following way. Let $\hat{u}_i$ be the (T,1) residual vector from the 2SLS regression for the i-th firm and $z_i$ the corresponding (T,p) instrument matrix. Then, since there is no correlation among individuals, a consistent estimate of $\Phi$ is given by (White, 1980, 1982):

$$ \hat{\Phi} = \frac{1}{n} \sum_{i=1}^{n} z_i' \hat{u}_i \hat{u}_i' z_i $$

One then has to test for the validity of the orthogonality conditions, that is the model specification itself. We use the following test of overidentifying restrictions from the two-step GMM estimator (Sargan, 1958):

$$ S = u^* Z \hat{\Phi}^{-1} Z' u^* $$

It is asymptotically distributed as a $\chi^2$ random variable with p-k degrees of freedom, where $u^*$ is the GMM residual vector (so called « two-step GMM »).

## 5.3 Instruments for the static model under weak exogeneity

The model is:

$$ y_{it} - y_{it-1} = (x_{it} - x_{it-1})b + d_t + u_{it} - u_{it-1} \quad \text{with} \quad d_t = \delta_t - \delta_{t-1} \\ i = 1,...,n \quad t = 3,...,7 $$

Since y and x are simultaneously determined, the instruments must be lagged at least two years (instead of one). Moreover, GMM allows taking a large number of moment conditions to estimate the model. Since T equals 7, there remain five years of instruments to estimate the model. We always assume that our explanatory variables are weakly exogenous, that is the disturbance is assumed to be uncorrelated with strictly past values of the regressors, not with current and futures values.
We take operating profit<fnref n="11" /> as an instrument (i.e., value added minus labor cost). Other choices are feasible, (see Arellano and Bondt, 1991). The reason for this instrument choice is that past profit determines advertising that itself affects current profit. There is no direct link between past and current profit. Hence, past profit is a valid instrument in our model since it is correlated to current advertising but not correlated to the deviation of sales from its predicted value.

We will use the largest instrument set available. Notice that we use the instruments in *levels*, not in first difference, in order to keep an additional year of data. That is:

$$ z_i = \begin{bmatrix} z_{i1} & 0 & 0 & 0 \\ 0 & z_{i1} & z_{i2} & \cdots \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & z_{i1} \cdots z_{iT-2} \end{bmatrix} \quad T \ge 3 $$

The timing of the instrument is important: since our disturbance is serially correlated of order 1 (i.e., we estimate the model in first-differences), we have to use our instruments lagged two years and more. We use all the available lags, which makes $(T-2)(T-1)/2 = 15$ instruments. Since we have added the 5 time dummies to this instrument set<fnref n="12" />, we finally get 20 instruments. Each time, we compute the Sargan overidentification statistic. The null hypothesis should not be rejected at the 5% level.

## 5.4 Instruments for the dynamic model

The relationship becomes

$$ y_{it} - y_{it-1} = a(y_{it} - y_{it-1}) + (x_{it} - x_{it-1})b + d_t + u_{it} - u_{it-1} \quad \text{with } d_t = \delta_t - \delta_{t-1} \\ i = 1,...,n \quad t = 3,...,7 $$

<footnote n="11">¹¹ In French, it is « Excédent Brut d'Exploitation » defined equivalently as Production – Intermediate consumptions – Labor cost = Value added – Labor cost.</footnote>

<footnote n="12">¹² They are valid instruments by definition.</footnote>
It appears as a simple extension of the previous case because we have already considered that the regressors are endogenous. For those reason the same instrument set is valid. The authors made all the estimation programs with SAS-IML software.

## 5.5 Getting back to the structural parameters

Considering the actualization rate r as a constant, we use Slutsky theorem to find back the structural parameters and their standard errors. We have:

$$ \sqrt{N}(g(b^*) - g(b)) \xrightarrow{A} N\left[0, \frac{\partial g}{\partial b}(b) \text{avar}(b^*) \frac{\partial g}{\partial b}(b')\right] $$

where $b^*$ is the two step GMM estimator and:

$$ g(b) = \begin{pmatrix} \gamma \\ \alpha \\ \theta \end{pmatrix} = \begin{bmatrix} 1 - b_0 \\ \frac{1}{b_1} \left( 1 - \frac{b_0}{1+r} \right) \\ \frac{b_2}{b_1} \end{bmatrix} $$

We replace all the theoretical parameters by their GMM estimations. Since we have found few variations according to the actualization parameter, we provide the estimation results for $r = 0$ and $r = 0.2$.

# 6. Results

## 6.1 Between and Within

Our first finding is that the elasticity of price (i.e., inverse demand) to advertising, $\alpha$, is positive in all the industries at the 5% level in the between regressions (table 5). The highest elasticity is 0.16 in pharmaceutical and other chemicals (T12) and close to 0.07 in houseware and consumer electronics (T15B) and printing and publishing (T22). For all the other sectors, we find elasticities below 0.05, significant but small. So,
an increase of 10% of the advertising's budget would result into a maximal inverse demand increase of 1.6%. The spillover parameter which sums up the impact of rival's advertising, θ is negative in 5 sectors, positive in 4, and not significant in the others. So, the issue of overinvestment in advertising could be mitigated.

But it is well known that the between estimator is biased when there is a firm level fixed effects. We provide two specification tests. The Fisher test always concludes to the existence of an individual effect. Moreover, the Hausman test leads to the rejection of the model in 15 industries out of 18 at the 5% level. Then, we conclude that the between estimates are biased in most of the industries. A first approach to correct for this bias is to use the within estimator.

In the within regressions, the elasticity of the inverse demand to advertising, α, is non-negative in all of the sectors and significant in 13 sectors out of 18. We find greater values than in the between regressions<fnref n="13" />, but there are only 5 industries in which the effect of advertising is important. The biggest price to advertising elasticities are found in pharmaceutical (0.31), followed by printing and publishing (0.29), textile and wearing apparel (0.19), metal working (0.18) and wood and furniture (0.13). But the strongest deviations from the between estimates deals with the spillover parameter. Two industries only exhibit significant spillovers (at the 5% level): pharmaceuticals and rubber and plastics (both 0.02). But the within estimator does not account for simultaneity, so that it is also biased. Therefore, we turn to the GMM estimations.

## 6.2 GMM estimations

We had first to exclude the industries where there are too few firms, since we use asymptotic theory. These are: ferrous and non-ferrous metals, glass, houseware and shipbuilding and aircraft. These industries represent about 5% of our sample advertising, so that the loss is reasonably low.

<footnote n="13">¹³ It is well known that the within estimates are lower than the between estimates, but the coefficient α is defined as the *inverse* of the advertising regression coefficient. Therefore we find higher values.</footnote>
For the remaining industries, the estimation strategy is the following: when the estimated depreciation rate is higher than one, we comment the static model results (i.e., under perfect depreciation). The reason is that the static model can be interpreted as a constrained estimation with $\gamma = 1$. In the other cases we comment upon the dynamic model estimates. The detailed regression results are given in tables 6, 7 and 8. The summary of these estimates and additional descriptive statistics are given in table 9.

First, we find that the majority of industries accumulate a goodwill capital, the lowest depreciation rates are found in printing and publishing, electrical machinery, clay products, wood and furniture, leather and footwear and pharmaceuticals. These are mostly consumer goods industries.

Second, if we except basic chemicals, the elasticity of the inverse demand to advertising always takes reasonable values, ranging from 0.03 to 0.34. Since theoretical models assume values between 0 and 1, this is good news. The industries where advertising has a strong effect on demand are few: printing and publishing (0.34), pharmaceuticals (0.20), textile and wearing apparel (0.20) and rubber products (0.10). In the other industries, advertising is still significant but weak.

Third, the spillover parameter is always non-negative. This suggests that in most industries firms can free ride on their competitors advertising. If we except the case of basic chemicals, which exhibit an unrealistic value (3.16), the spillovers, when significant, ranges from 0.05 to 1. They are the strongest in rubber products (1.00) where competitors advertising would be as efficient as own advertising to increase sales, followed by transportation equipment (0.22) and pharmaceuticals (0.20) where own advertising is five times more efficient<fnref n="14" /> than competitors’ advertising. This difference in spillover may well reflect the goods characteristics: setting a brand in rubber products may be more difficult than in the car industry or in cosmetics, hence firms advertise more often for their competitors in the former case. These results suggest that homogenous

<footnote n="14">¹⁴ One dollar invested in advertising by competitors increases the advertising pool by θ dollars. Thus it measures the « efficiency » of competitors advertising to increase own sales.</footnote>
goods producers could free ride more easily than the other producers on the advertising
of their competitors.

Overall, if we consider that pharmaceuticals, transportation equipment, printing
and textile represent 77% of our sample advertising; the representative model looks as
follows.

On the one hand there are industries where the accumulation of goodwill is
significant (printing and pharmaceuticals) and advertising allows for differentiating the
products while firms free ride on their competitors advertising. On the other hand, there
are industries (transportation equipment and textile) where the two last features hold, but
where advertising has to be renewed frequently to be efficient.

Some puzzling results remain, however. The first one is the negative elasticity of
advertising in leather and footwear, which suggests that advertising would decrease
product differentiation. The second one is the spillover value around 3 in basic chemicals,
which would imply that advertising by competitors would be more efficient than own
advertising. Although the overidentification tests are not rejected at the 5% level in these
industries, it is likely that there are some specification errors. One is suggested by
table 1: sample selection. Our sample represents 46% of sales in basic chemicals and only
32% in leather and footwear. Panel data methods with entry and exit could perhaps solve
these puzzles.

6.3 Comparison with previous studies

The results of two comparable previous studies are given in table 10. We see that
our estimates of depreciation are, in general, larger and that the values of α are
comparable. The only strong difference is the sign of the spillover effect. The two other
studies find negative values. But this difference can be explained as follows: we also find
negative values for the *between* regressions, and we show these estimates are biased.
This suggests that the previous estimates of the spillover parameters could suffer from
the same specification error.
# 7. Conclusion

This work shows that most sales and advertising models estimated in the past can be derived from a simple oligopoly model with spillovers. We find that it is important to account for the accumulation of a goodwill capital because its ignorance leads to overstate the impact of advertising on sales. Moreover, the industries in which advertising accumulates in a goodwill capital perform about the two thirds of industry advertising. The depreciation rates that we find are higher than the previous ones, from 60% to a complete depreciation. Then, this immaterial investment has to be renewed frequently.

We also find that advertising increase product differentiation in a number of industries. Our results also allow us to extend the analysis beyond the few products studied in the past, and are robust to simultaneity and fixed effects. However the effect of advertising is strong in few industries. Most of the effect is concentrated in four industries: printing and publishing, pharmaceuticals, textile and rubber products.

Another important issue is whether there are « goodwill spillovers » and what is their sign. We find that the spillovers are always non-negative so that industrial firms free ride on their competitors advertising. This result suggests that excessive advertising is unlikely. The strongest spillovers are found in rubber products, transportation equipment and pharmaceuticals that account for the bulk of advertising (about the two thirds).

Still, there are several ways this work could be improved. The most important to us seems to bridge the gap between the first empirical works on industry level data and firm level studies. The former studies on advertising were mostly interested in barriers to entry. In our model, advertising could become a determinant of the entry and exit decisions of firms, generating an unbalanced panel. The only way to account properly for this feature would be to use both an unbalanced panel and an explicit modeling of the entry and exit decisions of the firms. And it is precisely what the robust sample selection panel data literature has begun (e.g., Kyriazidou, 1997). One can then hope to join the oldest and the most recent studies on the topic in the near future.
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<table><caption>Table 1 - Coverage of the balanced sample in 1991</caption><thead><tr><th></th><th>Sales</th><th>Advertising</th></tr></thead><tbody><tr><td>T07-Ferrous metal ore mining, steel basic industries</td><td>43.3</td><td>37.8</td></tr><tr><td>T08- Non ferrous metal ore mining, steel basic industries</td><td>76.3</td><td>69.2</td></tr><tr><td>T09-Clay products</td><td>35.7</td><td>43.1</td></tr><tr><td>T10-Glass industry</td><td>73.3</td><td>85.8</td></tr><tr><td>T11-Basic chemicals</td><td>45.8</td><td>59.7</td></tr><tr><td>T12-Pharmaceutical and other chemicals</td><td>64.4</td><td>75.5</td></tr><tr><td>T13-Metal-founding, metalworking</td><td>31.2</td><td>39.2</td></tr><tr><td>T14-Non electrical machinery</td><td>45.5</td><td>45.3</td></tr><tr><td>T15A-Electrical machinery</td><td>36.0</td><td>33.8</td></tr><tr><td>T15B- Houseware and consumer electronics</td><td>53.3</td><td>58.9</td></tr><tr><td>T16-Rail and road transportation equipment</td><td>88.7</td><td>97.0</td></tr><tr><td>T17-Shipbuilding and aircraft</td><td>39.2</td><td>79.1</td></tr><tr><td>T18-Textile and wearing apparel</td><td>34.6</td><td>48.5</td></tr><tr><td>T19-Leather and footwear</td><td>32.5</td><td>34.1</td></tr><tr><td>T20-Wood and furniture</td><td>34.4</td><td>48.4</td></tr><tr><td>T21-Paper and board industry</td><td>42.2</td><td>44.5</td></tr><tr><td>T22-Printing and publishing</td><td>32.3</td><td>37.7</td></tr><tr><td>T23-Rubber products</td><td>48.2</td><td>58.4</td></tr></tbody></table>

Balanced sample total / Industry total %

Source: SESSI, Ministry of Industry and INSEE.
<table><caption>Table 2 - Advertising to sales ratio by industry 1988-1994</caption><thead><tr><th></th><th>1988</th><th>1989</th><th>1990</th><th>1991</th><th>1992</th><th>1993</th><th>1994</th><th>Number of firms</th></tr></thead><tbody><tr><td>T07-Ferrous metal ore mining, steel basic industries</td><td>0.25</td><td>0.21</td><td>0.23</td><td>0.25</td><td>0.24</td><td>0.20</td><td>0.20</td><td>61</td></tr><tr><td>T08- Non ferrous metal ore mining, steel basic industries</td><td>0.19</td><td>0.17</td><td>0.14</td><td>0.18</td><td>0.22</td><td>0.20</td><td>0.19</td><td>43</td></tr><tr><td>T09-Clay products</td><td>0.62</td><td>0.74</td><td>0.80</td><td>0.81</td><td>0.81</td><td>0.86</td><td>0.85</td><td>270</td></tr><tr><td>T10-Glass industry</td><td>1.00</td><td>1.05</td><td>1.09</td><td>1.01</td><td>0.98</td><td>0.89</td><td>0.97</td><td>48</td></tr><tr><td>T11-Basic chemicals</td><td>0.29</td><td>0.33</td><td>0.38</td><td>0.38</td><td>0.30</td><td>0.28</td><td>0.22</td><td>99</td></tr><tr><td>T12-Pharmaceutical and other chemicals</td><td>4.19</td><td>4.27</td><td>4.37</td><td>4.24</td><td>4.29</td><td>4.25</td><td>4.38</td><td>314</td></tr><tr><td>T13-Metal-founding, metalworking</td><td>0.60</td><td>0.57</td><td>0.62</td><td>0.63</td><td>0.63</td><td>0.60</td><td>0.56</td><td>747</td></tr><tr><td>T14-Non electrical machinery</td><td>0.80</td><td>0.82</td><td>0.81</td><td>0.90</td><td>0.89</td><td>0.83</td><td>0.83</td><td>764</td></tr><tr><td>T15A-Electrical machinery</td><td>0.69</td><td>0.68</td><td>0.72</td><td>0.73</td><td>0.70</td><td>0.64</td><td>0.70</td><td>342</td></tr><tr><td>T15B-Houseware and consumer electronics</td><td>2.20</td><td>2.50</td><td>2.01</td><td>2.14</td><td>2.16</td><td>2.73</td><td>2.19</td><td>35</td></tr><tr><td>T16-Rail and road transportation equipment</td><td>0.65</td><td>0.61</td><td>0.67</td><td>0.66</td><td>0.66</td><td>0.62</td><td>0.60</td><td>232</td></tr><tr><td>T17-Shipbuilding and aircraft</td><td>0.36</td><td>0.44</td><td>0.39</td><td>0.45</td><td>0.38</td><td>0.47</td><td>0.32</td><td>71</td></tr><tr><td>T18-Textile and wearing apparel</td><td>1.22</td><td>1.50</td><td>1.38</td><td>1.37</td><td>1.40</td><td>1.32</td><td>1.35</td><td>504</td></tr><tr><td>T19-Leather and footwear</td><td>0.89</td><td>0.89</td><td>1.11</td><td>1.13</td><td>1.01</td><td>0.95</td><td>0.99</td><td>99</td></tr><tr><td>T20-Wood and furniture</td><td>1.42</td><td>1.52</td><td>1.58</td><td>1.66</td><td>1.66</td><td>1.67</td><td>1.64</td><td>425</td></tr><tr><td>T21-Paper and board industry</td><td>0.57</td><td>0.55</td><td>0.55</td><td>0.59</td><td>0.58</td><td>0.59</td><td>0.60</td><td>185</td></tr><tr><td>T22-Printing and publishing</td><td>1.42</td><td>1.49</td><td>1.48</td><td>1.42</td><td>1.38</td><td>1.35</td><td>1.44</td><td>344</td></tr><tr><td>T23- Rubber products</td><td>0.57</td><td>0.63</td><td>0.64</td><td>0.69</td><td>0.70</td><td>0.68</td><td>0.65</td><td>299</td></tr></tbody></table>

Sample: 4882 firms with 20 employees or more with continuous data over the period 1988 to 1994

Source: SESSI, Ministry of Industry and INSEE.
<table><caption>Table 3 - Variance decomposition and correlations</caption><thead><tr><th rowspan="2"></th><th colspan="3">% of within firm variance (levels)</th><th colspan="2">Correlation of sales and advertising</th></tr><tr><th>Sales</th><th>Own ad.</th><th>Rivals' ad.</th><th>Within</th><th>Between</th></tr></thead><tbody><tr><td>T07-Ferrous metal ore mining, steel basic industries</td><td>0.93</td><td>3.99</td><td>2.41</td><td>0.36</td><td>0.52</td></tr><tr><td>T08- Non ferrous metal ore mining, steel basic industries</td><td>0.55</td><td>5.73</td><td>5.35</td><td>-0.26</td><td>0.83</td></tr><tr><td>T09-Clay products</td><td>0.18</td><td>1.44</td><td>0.68</td><td>0.38</td><td>0.59</td></tr><tr><td>T10-Glass industry</td><td>0.10</td><td>0.37</td><td>0.30</td><td>0.56</td><td>0.69</td></tr><tr><td>T11-Basic chemicals</td><td>0.19</td><td>3.37</td><td>1.83</td><td>0.59</td><td>0.72</td></tr><tr><td>T12-Pharmaceutical and other chemicals</td><td>0.53</td><td>0.71</td><td>0.40</td><td>0.46</td><td>0.68</td></tr><tr><td>T13-Metal-founding, metalworking</td><td>0.37</td><td>3.17</td><td>1.51</td><td>0.25</td><td>0.61</td></tr><tr><td>T14-Non electrical machinery</td><td>0.90</td><td>1.00</td><td>0.87</td><td>0.35</td><td>0.71</td></tr><tr><td>T15A-Electrical machinery</td><td>0.37</td><td>4.41</td><td>1.72</td><td>0.31</td><td>0.83</td></tr><tr><td>T15B-Houseware and consumer electronics</td><td>0.32</td><td>2.12</td><td>0.40</td><td>0.09</td><td>0.55</td></tr><tr><td>T16-Rail and road transportation equipment</td><td>0.08</td><td>0.48</td><td>0.52</td><td>0.68</td><td>0.96</td></tr><tr><td>T17-Shipbuilding and aircraft</td><td>0.18</td><td>0.40</td><td>0.66</td><td>0.25</td><td>0.96</td></tr><tr><td>T18-Textile and wearing apparel</td><td>0.72</td><td>1.63</td><td>1.49</td><td>0.28</td><td>0.66</td></tr><tr><td>T19-Leather and footwear</td><td>0.28</td><td>1.34</td><td>3.30</td><td>0.29</td><td>0.89</td></tr><tr><td>T20-Wood and furniture's</td><td>0.45</td><td>1.24</td><td>1.23</td><td>0.38</td><td>0.80</td></tr><tr><td>T21-Paper and board industry</td><td>0.43</td><td>1.17</td><td>0.20</td><td>0.07</td><td>0.60</td></tr><tr><td>T22-Printing and publishing</td><td>0.24</td><td>1.89</td><td>0.13</td><td>0.49</td><td>0.81</td></tr><tr><td>T23- Rubber products</td><td>0.03</td><td>0.52</td><td>3.62</td><td>0.49</td><td>0.49</td></tr></tbody></table>

Sample: 4882 firms with 20 employees or more with continuous data over the period 1988 to 1994.

Source: SESSI, Ministry of Industry and INSEE.
<caption>Table 4 - Partial correlation coefficients on the first differences</caption>

Correlations between couples of variables, holding the third one constant
p value between parentheses.
*: significant at the 5% level

<table><thead><tr><th>Variables</th><th>Sales and firm ad</th><th>Sales and rivals' ad</th><th>Firm and rival's ad</th><th>Number of first differences</th></tr></thead><tbody><tr><td>Control</td><td>Competitors ad</td><td>Firm ad</td><td>Sales</td><td>N(T-1)</td></tr><tr><td>T7-Ferrous metal ore mining, steel</td><td>.224*<br>(.001)</td><td>.166*<br>(.001)</td><td>.038<br>(.469)</td><td>366</td></tr><tr><td>T8-Non ferrous metal ore mining</td><td>-.001<br>(.991)</td><td>.016<br>(.793)</td><td>.015<br>(.807)</td><td>258</td></tr><tr><td>T9-Clay products</td><td>.412*<br>(.001)</td><td>.098*<br>(.001)</td><td>-.038<br>(.121)</td><td>1620</td></tr><tr><td>T10-Glass</td><td>.256*<br>(.001)</td><td>.209*<br>(.001)</td><td>-.089<br>(.130)</td><td>288</td></tr><tr><td>T11-Basic chemicals</td><td>.340*<br>(.001)</td><td>.001<br>(.991)</td><td>-.022<br>(.584)</td><td>594</td></tr><tr><td>T12- Pharmaceutical and other chemicals</td><td>.308*<br>(.001)</td><td>.047*<br>(.041)</td><td>.013<br>(.576)</td><td>1884</td></tr><tr><td>T13-Foundry</td><td>.045*<br>(.003)</td><td>.037*<br>(.012)</td><td>-.012<br>(.433)</td><td>4482</td></tr><tr><td>T14-Non electrical machinery</td><td>.200*<br>(.001)</td><td>-.014<br>(.329)</td><td>.049*<br>(.001)</td><td>4584</td></tr><tr><td>T15A-Electrical machinery</td><td>.209*<br>(.001)</td><td>.040<br>(.066)</td><td>.027<br>(.245)</td><td>2052</td></tr><tr><td>T15B-Houseware, consumer electronics</td><td>.010<br>(.890)</td><td>.027<br>(.694)</td><td>-.032<br>(.642)</td><td>210</td></tr><tr><td>T16-Rail and road transportation equipment</td><td>.660*<br>(.001)</td><td>.154*<br>(.001)</td><td>-.139*<br>(.001)</td><td>1392</td></tr><tr><td>T17-Ships, aircraft</td><td>.316*<br>(.001)</td><td>.010<br>(.823)</td><td>.038<br>(.436)</td><td>426</td></tr><tr><td>T18-Textile and wearing apparel</td><td>.264*<br>(ε)</td><td>.015<br>(.400)</td><td>.043*<br>(.018)</td><td>3024</td></tr><tr><td>T19-Leather and footwear</td><td>.232*<br>(.001)</td><td>.082*<br>(.047)</td><td>.047<br>(.252)</td><td>594</td></tr><tr><td>T20-Wood and furniture</td><td>.271*<br>(.001)</td><td>.003<br>(.881)</td><td>.063*<br>(.001)</td><td>2550</td></tr><tr><td>T21-Paper and board</td><td>.070*<br>(.019)</td><td>.051<br>(.088)</td><td>-.021<br>(.487)</td><td>1110</td></tr><tr><td>T22-Printing and publishing</td><td>.322*<br>(.001)</td><td>.087*<br>(ε)</td><td>.014<br>(.534)</td><td>2064</td></tr><tr><td>T23-Rubber products</td><td>.273*<br>(.001)</td><td>.059*<br>(.012)</td><td>.011<br>(.649)</td><td>1794</td></tr></tbody></table>

Partial correlation coefficient between x and y, keeping z constant:

$$ \rho_{xy|z} = \frac{\rho_{xy} - \rho_{xz}\rho_{yz}}{\sqrt{1 - \rho_{xz}^2} \sqrt{1 - \rho_{yz}^2}} \quad \text{where } \rho_{xy}, \rho_{xz} \text{ and } \rho_{yz} \text{ are the Pearson correlation coefficients.} $$
<caption>Table 5-Between, Within and FGLS estimations</caption>

α: elasticity of inverse demand to advertising; θ: spillover parameter. Asymptotic t-statistics are given in parentheses and are robust to any kind of heteroskedasticity
F: Fisher's test of existence of an individual random effect, H: equality test of « between » and « within » coefficients.

<table><thead><tr><th rowspan="2"></th><th colspan="3">Between</th><th colspan="3">Within</th><th colspan="3">FGLS</th><th colspan="3">Tests</th></tr><tr><th>α</th><th>θ</th><th>R<sup>2</sup></th><th>α</th><th>θ</th><th>R<sup>2</sup></th><th>α</th><th>θ</th><th>R<sup>2</sup></th><th>Fisher</th><th>Hausman</th></tr></thead><tbody><tr><td>T07-Ferrous metal ore mining, steel basic industries</td><td>.003<br>(3.61)</td><td>.042<br>(2.27)</td><td>.410</td><td>.008<br>(2.31)</td><td>.019<br>(1.13)</td><td>.218</td><td>.007<br>(2.50)</td><td>.040<br>(1.76)</td><td>.226</td><td>9.66</td><td>9.38</td></tr><tr><td>T08- Non ferrous metal ore mining, steel basic industries</td><td>.002<br>(12.46)</td><td>.020<br>(0.37)</td><td>.696</td><td>-.022<br>(1.91)</td><td>.242<br>(0.87)</td><td>.182</td><td>-.051<br>(0.82)</td><td>.482<br>(0.65)</td><td>.105</td><td>8.06</td><td>139.02</td></tr><tr><td>T09-Clay products</td><td>.016<br>(2.53)</td><td>-.014<br>(2.42)</td><td>.353</td><td>.071<br>(6.69)</td><td>.012<br>(0.58)</td><td>.164</td><td>.064<br>(6.01)</td><td>.012<br>(0.62)</td><td>.161</td><td>53.17</td><td>3.90</td></tr><tr><td>T10-Glass industry</td><td>.020<br>(3.78)</td><td>.099<br>(1.81)</td><td>.549</td><td>.043<br>(2.62)</td><td>.116<br>(1.82)</td><td>.384</td><td>.039<br>(3.67)</td><td>.129<br>(2.31)</td><td>.392</td><td>86.8</td><td>3.73</td></tr><tr><td>T11-Basic chemicals</td><td>.006<br>(2.33)</td><td>-.010<br>(0.68)</td><td>.524</td><td>.031<br>(2.72)</td><td>-.008<br>(0.24)</td><td>.376</td><td>.029<br>(2.79)</td><td>-.007<br>(0.22)</td><td>.340</td><td>49.38</td><td>3.99</td></tr><tr><td>T12-Pharmaceutical and other chemicals</td><td>.163<br>(8.61)</td><td>-.002<br>(0.65)</td><td>.461</td><td>.312<br>(5.18)</td><td>.020<br>(2.74)</td><td>.262</td><td>.273<br>(6.55)</td><td>.006<br>(1.43)</td><td>.291</td><td>16.86</td><td>12.60</td></tr><tr><td>T13-Metal-founding, metalworking</td><td>.025<br>(3.28)</td><td>-.011<br>(3.84)</td><td>.379</td><td>.181<br>(8.34)</td><td>-.016<br>(0.72)</td><td>.074</td><td>.153<br>(5.91)</td><td>-.023<br>(1.15)</td><td>.091</td><td>22.03</td><td>8.39</td></tr><tr><td>T14-Non electrical machinery</td><td>.010<br>(3.44)</td><td>-.004<br>(1.79)</td><td>.504</td><td>.021<br>(2.99)</td><td>.003<br>(0.90)</td><td>.126</td><td>.017<br>(3.41)</td><td>-.001<br>(0.89)</td><td>.193</td><td>7.67</td><td>8.66</td></tr><tr><td>T15A-Electrical machinery</td><td>.008<br>(4.29)</td><td>-.001<br>(0.37)</td><td>.692</td><td>.072<br>(1.56)</td><td>.034<br>(1.33)</td><td>.103</td><td>.053<br>(1.66)</td><td>.035<br>(1.47)</td><td>.127</td><td>11.44</td><td>13.54</td></tr><tr><td>T15B-Houseware and consumer electronics</td><td>.076<br>(2.92)</td><td>-.118<br>(1.93)</td><td>.384</td><td>.141<br>(1.22)</td><td>-.293<br>(0.88)</td><td>.046</td><td>.971<br>(2.27)</td><td>-.824<br>(1.36)</td><td>.065</td><td>23.77</td><td>7.53</td></tr><tr><td>T16-Rail and road transportation equipment</td><td>.020<br>(10.71)</td><td>.027<br>(3.10)</td><td>.944</td><td>.068<br>(6.41)</td><td>.016<br>(0.84)</td><td>.477</td><td>.044<br>(19.93)</td><td>.023<br>(1.94)</td><td>.534</td><td>17.02</td><td>49.55</td></tr><tr><td>T17-Shipbuilding and aircraft</td><td>.005<br>(12.10)</td><td>.001<br>(0.14)</td><td>.926</td><td>.029<br>(3.14)</td><td>-.042<br>(0.75)</td><td>.092</td><td>.008<br>(9.96)</td><td>-.002<br>(0.55)</td><td>.462</td><td>5.33</td><td>75.61</td></tr><tr><td>T18-Textile and wearing apparel</td><td>.053<br>(5.15)</td><td>-.011<br>(3.03)</td><td>.448</td><td>.192<br>(4.28)</td><td>.007<br>(1.27)</td><td>.086</td><td>.145<br>(5.27)</td><td>.002<br>(0.40)</td><td>.124</td><td>10.19</td><td>12.51</td></tr><tr><td>T19-Leather and footwear</td><td>.035<br>(5.83)</td><td>.004<br>(2.23)</td><td>.804</td><td>.239<br>(0.87)</td><td>.014<br>(1.12)</td><td>.100</td><td>.126<br>(1.58)</td><td>.005<br>(1.49)</td><td>.203</td><td>9.37</td><td>14.52</td></tr><tr><td>T20-Wood and furniture</td><td>.038<br>(5.92)</td><td>-.001<br>(0.41)</td><td>.634</td><td>.133<br>(5.28)</td><td>.002<br>(0.41)</td><td>.158</td><td>.100<br>(7.66)</td><td>-.003<br>(0.86)</td><td>.225</td><td>11.66</td><td>19.31</td></tr><tr><td>T21-Paper and board industry</td><td>.033<br>(2.88)</td><td>-.004<br>(1.46)</td><td>.359</td><td>.452<br>(0.77)</td><td>.020<br>(0.35)</td><td>.017</td><td>.207<br>(1.27)</td><td>.006<br>(0.40)</td><td>.032</td><td>18.57</td><td>7.58</td></tr><tr><td>T22-Printing and publishing</td><td>.065<br>(6.54)</td><td>.004<br>(2.74)</td><td>.667</td><td>.286<br>(3.84)</td><td>.012<br>(0.94)</td><td>.253</td><td>.246<br>(4.03)</td><td>.023<br>(2.69)</td><td>.282</td><td>22.69</td><td>26.02</td></tr><tr><td>T23- Rubber products</td><td>.007<br>(5.20)</td><td>-.024<br>(2.04)</td><td>.838</td><td>.051<br>(5.24)</td><td>.016<br>(2.11)</td><td>.258</td><td>.038<br>(4.60)</td><td>.011<br>(1.71)</td><td>.252</td><td>81.26</td><td>20.10</td></tr></tbody></table>
<table><caption>Table 6 - Static model with advertising expenditures</caption><caption>Two-step GMM estimation<br>20 instruments: gross operating profit lagged twice and more (weak exogeneity) plus 5 time dummies<br>α: elasticity of inverse demand to advertising<br>θ: spillover parameter<br>Robust standard errors between parentheses<br>(p-values for the Sargan statistic)</caption><thead><tr><th></th><th>α</th><th>θ</th><th>Sargan</th><th>N</th><th>N×T</th></tr></thead><tbody><tr><td>T09-Clay products</td><td>.045<br>(.004)</td><td>.130<br>(.018)</td><td>22.0<br>(.055)</td><td>270</td><td>1890</td></tr><tr><td>T11-Basic chemicals</td><td>.072<br>(.017)</td><td>2.508<br>(.328)</td><td>12.0<br>(.527)</td><td>98</td><td>686</td></tr><tr><td>T12-Pharmaceutical and other chemicals</td><td>.240<br>(.058)</td><td>.204<br>(.051)</td><td>26.5<br>(.014)</td><td>313</td><td>2191</td></tr><tr><td>T13-Metal-founding, metalworking</td><td>-4.990<br>(4.903)</td><td>-5.128<br>(4.678)</td><td>23.9<br>(.032)</td><td>677</td><td>4739</td></tr><tr><td>T14-Non electrical machinery</td><td>.010<br>(.001)</td><td>-.028<br>(.032)</td><td>14.9<br>(.316)</td><td>764</td><td>5248</td></tr><tr><td>T15A-Electrical machinery</td><td>.040<br>(.001)</td><td>.081<br>(.011)</td><td>17.9<br>(.161)</td><td>342</td><td>2394</td></tr><tr><td>T16-Rail and road transportation equipment</td><td>.048<br>(.001)</td><td>.222<br>(.002)</td><td>34.9<br>(.001)</td><td>231</td><td>1617</td></tr><tr><td>T18-Textile and wearing apparel</td><td>.199<br>(.049)</td><td>-.071<br>(.116)</td><td>9.0<br>(.770)</td><td>502</td><td>3514</td></tr><tr><td>T19-Leather and footwear</td><td>2.621<br>(1.473)</td><td>.576<br>(.412)</td><td>15.8<br>(.262)</td><td>99</td><td>693</td></tr><tr><td>T20-Wood and furniture</td><td>.082<br>(.007)</td><td>.195<br>(.091)</td><td>11.0<br>(.612)</td><td>425</td><td>2975</td></tr><tr><td>T21-Paper and board industry</td><td>.042<br>(.006)</td><td>-.010<br>(.009)</td><td>16.2<br>(.239)</td><td>185</td><td>1295</td></tr><tr><td>T22-Printing and publishing</td><td>.467<br>(.034)</td><td>.059<br>(.016)</td><td>10.9<br>(.618)</td><td>344</td><td>2408</td></tr><tr><td>T23-Rubber products</td><td>.104<br>(.012)</td><td>.996<br>(.238)</td><td>21.4<br>(.064)</td><td>299</td><td>2093</td></tr></tbody></table>

Industries with few firms have been excluded from the regression analysis. See table 2 for the firm numbers.
<caption>Table 7 - Dynamic model with advertising capital</caption>

(case 1, r = 0)

Two-Step GMM estimators, under r=0

r=0 : actualization rate

γ : annual depreciation rate

α : elasticity of inverse demand to advertising

θ : spillover parameter

Robust standard errors between parentheses

(p-values for the Sargan statistic)

<table><thead><tr><th></th><th>γ</th><th>α</th><th>θ</th><th>Sargan</th></tr></thead><tbody><tr><td>T09-Clay products</td><td>.760<br>(.018)</td><td>.035<br>(.002)</td><td>.104<br>(.019)</td><td>21.8<br>(.040)</td></tr><tr><td>T11-Basic chemicals</td><td>.835<br>(.034)</td><td>.072<br>(.026)</td><td>3.157<br>(.645)</td><td>11.9<br>(.452)</td></tr><tr><td>T12-Pharmaceutical and other chemicals</td><td>.833<br>(.049)</td><td>.207<br>(.052)</td><td>.203<br>(.051)</td><td>20.8<br>(.053)</td></tr><tr><td>T13-Metal-founding, metalworking</td><td>.899<br>(.056)</td><td>-5.52<br>(7.21)</td><td>-4.79<br>(5.50)</td><td>18.0<br>(.116)</td></tr><tr><td>T14-Non electrical machinery</td><td>1.441<br>(.010)</td><td>.013<br>(.001)</td><td>-.037<br>(.031)</td><td>9.8<br>(.629)</td></tr><tr><td>T15A-Electrical machinery</td><td>.751<br>(.005)</td><td>.035<br>(.001)</td><td>.081<br>(.020)</td><td>13.1<br>(.359)</td></tr><tr><td>T16-Rail and road transportation equipment</td><td>1.526<br>(.002)</td><td>.093<br>(.001)</td><td>.318<br>(.003)</td><td>10.5<br>(.572)</td></tr><tr><td>T18-Textile and wearing apparel</td><td>.979<br>(.087)</td><td>.190<br>(.058)</td><td>-.084<br>(.108)</td><td>7.9<br>(.789)</td></tr><tr><td>T19-Leather and footwear</td><td>.799<br>(.008)</td><td>-.768<br>(.276)</td><td>-.181<br>(.100)</td><td>15.5<br>(.215)</td></tr><tr><td>T20-Wood and furniture</td><td>.773<br>(.061)</td><td>.060<br>(.006)</td><td>.154<br>(.099)</td><td>12.0<br>(.448)</td></tr><tr><td>T21-Paper and board industry</td><td>1.334<br>(.024)</td><td>.057<br>(.012)</td><td>.019<br>(.018)</td><td>16.6<br>(.163)</td></tr><tr><td>T22-Printing and publishing</td><td>.602<br>(.048)</td><td>.345<br>(.028)</td><td>.054<br>(.024)</td><td>8.6<br>(.739)</td></tr><tr><td>T23- Rubber products</td><td>1.692<br>(.079)</td><td>.134<br>(.012)</td><td>.370<br>(.252)</td><td>15.2<br>(.229)</td></tr></tbody></table>
<caption>Table 8 - Dynamic model with advertising capital
(case 2, r=0.2)</caption>

Two-Step GMM estimators
r = 0.2 : actualization rate.
α : elasticity of inverse demand to advertising
The other parameters are given in table 7 (only α depends on r)

<table><thead><tr><th>Robust standard errors between parentheses</th><th>α</th></tr></thead><tbody><tr><td>T09-Clay products</td><td>.037<br>(.002)</td></tr><tr><td>T11-Basic chemicals</td><td>.074<br>(.026)</td></tr><tr><td>T12-Pharmaceutical and other chemicals</td><td>.214<br>(.053)</td></tr><tr><td>T13-Metal-founding, metalworking</td><td>-5.63<br>(7.32)</td></tr><tr><td>T14-Non electrical machinery</td><td>.013<br>(.001)</td></tr><tr><td>T15A-Electrical machinery</td><td>.037<br>(.001)</td></tr><tr><td>T16-Rail and road transportation equipment</td><td>.088<br>(.001)</td></tr><tr><td>T18-Textile and wearing apparel</td><td>.190<br>(.056)</td></tr><tr><td>T19-Leather and footwear</td><td>-.800<br>(.232)</td></tr><tr><td>T20-Wood and furniture</td><td>.063<br>(.006)</td></tr><tr><td>T21-Paper and board industry</td><td>.055<br>(.011)</td></tr><tr><td>T22-Printing and publishing</td><td>.383<br>(.035)</td></tr><tr><td>T23-Rubber products</td><td>.125<br>(.011)</td></tr></tbody></table>
<caption>Table 9 - Summary of the results</caption>

Two-step GMM estimations from tables 6 and 7. Significant coefficients only (at the 5% level).

<table><thead><tr><th></th><th>γ</th><th>α</th><th>θ</th><th>Sample share of advertising 1991</th><th>Implied share of advertising capital 1991</th></tr></thead><tbody><tr><td><strong>Industries with goodwill accumulation (dynamic model estimates)</strong></td><td></td><td></td><td></td><td>59.6%</td><td>65.7%</td></tr><tr><td>T22-Printing and publishing</td><td>0.60</td><td>0.34</td><td>0.05</td><td>5.4</td><td>7.8</td></tr><tr><td>T15A-Electrical machinery</td><td>0.75</td><td>0.03</td><td>0.08</td><td>3.6</td><td>4.2</td></tr><tr><td>T09-Clay products</td><td>0.76</td><td>0.03</td><td>0.10</td><td>1.3</td><td>1.5</td></tr><tr><td>T20-Wood and furniture</td><td>0.77</td><td>0.06</td><td>-</td><td>3.5</td><td>4.0</td></tr><tr><td>T19-Leather and footwear</td><td>0.80</td><td>-0.77</td><td>-</td><td>0.9</td><td>1.0</td></tr><tr><td>T12-Pharmaceutical and other chemicals</td><td>0.83</td><td>0.21</td><td>0.20</td><td>43.8</td><td>46.0</td></tr><tr><td>T11-Basic chemicals</td><td>0.83</td><td>0.07</td><td>3.16</td><td>1.1</td><td>1.2</td></tr><tr><td><strong>Industries with perfect depreciation (static model estimates)</strong></td><td></td><td></td><td></td><td>33.1%</td><td>28.9%</td></tr><tr><td>T14-Non electrical machinery</td><td>1</td><td>0.01</td><td>-</td><td>3.9</td><td>3.4</td></tr><tr><td>T16-Rail and road transportation equipment</td><td>1</td><td>0.05</td><td>0.22</td><td>21.0</td><td>18.3</td></tr><tr><td>T18-Textile and wearing apparel</td><td>1</td><td>0.20</td><td>-</td><td>4.6</td><td>4.0</td></tr><tr><td>T21-Paper and board industry</td><td>1</td><td>0.04</td><td>-</td><td>1.7</td><td>1.5</td></tr><tr><td>T23-Rubber products</td><td>1</td><td>0.10</td><td>1.00</td><td>1.9</td><td>1.7</td></tr><tr><td><strong>Industries without enough observations (number of firms between parentheses)</strong></td><td></td><td></td><td></td><td>4.7%</td><td>4.1%</td></tr><tr><td>T07-Ferrous metal ore mining, steel basic industries (44)</td><td>-</td><td>-</td><td>-</td><td>0.2</td><td>0.2</td></tr><tr><td>T08-Non ferrous metal ore mining (39)</td><td>-</td><td>-</td><td>-</td><td>0.2</td><td>0.2</td></tr><tr><td>T15B-Houseware and consumer electronics (35)</td><td>-</td><td>-</td><td>-</td><td>2.8</td><td>2.4</td></tr><tr><td>T17-Shipbuilding and aircraft (71)</td><td>-</td><td>-</td><td>-</td><td>1.5</td><td>1.3</td></tr><tr><td><strong>Industries with no effect of advertising</strong></td><td></td><td></td><td></td><td>1.6%</td><td>1.4%</td></tr><tr><td>T13-Metal-founding, metalworking</td><td>-</td><td>-</td><td>-</td><td>1.6</td><td>1.4</td></tr></tbody></table>

<table><caption>Table 10 - Results from previous studies</caption><thead><tr><th></th><th>Sample</th><th>Estimation method</th><th>γ</th><th>α</th><th>θ</th></tr></thead><tbody><tr><td>Netter (1982)</td><td>Largest firms in 12 industries (116 firms in 1973)</td><td>OLS (without fixed effects)</td><td>-</td><td>0.062 (0.009)</td><td>-0.039 (___)</td></tr><tr><td>Brown (1978)</td><td>14 brands of cigarettes</td><td>2SLS (without fixed effects)</td><td>0.590 (0.140)</td><td>0.376 (0.037)</td><td>-0.021 (___)</td></tr></tbody></table>

<footnote>(*) The advertising capital in 1991 is computed as advertising in 1991 divided by γ. For industries without enough observations or with no effect of advertising, we have assumed γ=1.</footnote>