FACTORES DE RIESGO RELATIVOS A LOS VALORES

The variable of interest (deal or no deal) is modelled as a binary variable outcome that can take only two values: either one or zero. The dependent variable y is a qualitative variable and indicates whether a cooperative deal has been signed or not. Specifically, y = 1 means that the outcome cooperation deal has been signed, whereas y = 0 means that no deal is signed. The dependent variable is then regressed on the explanatory variable.

The standard linear regression model for y would be yi = x0iβ +i, ∀i, with xi0β = β0+ ˜xiβ1,

where ˜xirepresents the proxy for the competence factor, β0is a constant and β1 measures the

impact of the competence factor on the probability of making a deal. The model can be written in term of expectation operator as:

E[yi|xi] = x0iβ

for some explanatory variable x0_iand parameter vector β.

In the simplest model the probability of success (the event cooperation deal is going ahead), is given by p under the following Bernoulli scheme:

yi=      1 probability p 0 probability 1 − p and E[yi] = p

Under this model if the probability of concluding a deal depends for example on the competence factor xiof parties involved, then p should depend on xi. As probability of success

is the same as the expected value of y

E[yi|xi] = p(xi) = x0iβ (3.5)

The conditional mean of yi is the conditional probability that the company signs a deal.

The set of parameters β represent the impact of the regressors x on the probability. The model defined by equation (3.5) above implies that the probability of success p(xi)is a linear function

of xi.

The linear regression model, with a binary dependent variable, is defined by the (LPM) Linear probability model (Wooldridge 2006). Estimating the LPM model via least squares has two main drawbacks: it can produce probabilities that are outside the interval [0, 1] and is not based on a maximum likelihood estimator as the errors are not normally distributed. Both

drawbacks are overcome by using suitable binary response models: the Logit and Probit mod- els.

3.4.1 The Logit model

To compensate for the LPM limitations, the Logit model considers a class of binary response models in the form of:

E[yi|xi] = p(xi) = f (x0iβ),

where f is a logistic function in the form of f (x0_iβ) = ex0iβ

1+ex0iβ taking on values strictly between

zero and one. This automatically ensures that the estimated probabilities of making a deal are inside the interval [0, 1].

Similarly the cumulative Normal distribution can be used, i.e. f (x0_iβ) = Rx0iβ

−∞ϕ(t)dt, giv-

ing rise to the Probit model, where ϕ(t) is the normal density function.

Unlike the linear probability model, the estimation of the Logit and Probit model is based on the method of maximum likelihood (Greene 2008).

Conditionally on the regressors, the model with success probability P (yi = 1) assumes

independent observation (and therefore probabilities) and leads to the likelihood function:

Likelihood(β) = P (y1 = 1)P (y2= 0) · · · P (yn= 0),

when the sequence of observed dependent variables is 1, 0, . . . , 0. For example in the Logit model the Likelihood function takes the form

Likelihood(β) = Y yi=1 ex0iβ 1 + ex0iβ Y yi=0 1 − e x0_iβ 1 + ex0iβ !

That is the likelihood that the product of the Logit function for those “deal event” oc- curring multiplied by the product of one minus the Logit function for those “no deal event” occurring.

By maximizing the likelihood function (ML) with respect to the vector β, the Logit coef- ficient ˆβ_MLE is estimated . This suggests that the probability of signing a deal for company i predicted by the model is given by:

ex0iβMLE

1 + ex0iβMLE =

eβ0+β1x˜i

Given the difficulty of justifying the choice of one distribution or another on the basis of a theoretical discussion, both models will be considered in the analysis. The fitting performance of the model will determine the decision to favour the Logit versus the Probit model.

3.4.2 Analysis of the data

The statistical evidence is based on the assumption that the ratios of sales (as defined in eq. (3.1) are a proxy for the competence factor. Various factors (such as strategic or future outlook, for example) enter into play when the decision to embark on a deal is taken. Among these factors, the competence parameter is considered the most prominent.

To proceed with the analysis, the monthly ratios of Novartis sales over total sales are first considered. The averages of ratios for each semester are next calculated and used as a reference. The analysis covers the period 2003-2011, or 18 semesters of data.

The next step is to consider the number of deals, per semester, performed between 2003 and 2011 in the Hypertension market. This is considered as the number of deals that could potentially be signed by a company in the CVM area. Based on the Pharma Deals database, this number of potential deals varies from a minimum of 16 in 2007 (or 8 deals per semester) to a maximum of 28 (or 14 per semester) in 2010. The last piece of information is represented by the deals signed by Novartis over the same period which amount to 10, whereas the number of deals signed by Pfizer over the same period is only 4. The challenge represented by the limited amount of deals by Pfizer forces the decision to take Novartis as reference. The total deals signed per semester divided by the number of potential deals represents the proportion or percentage frequency of deals.

In this context, it is important to notice that 10 deals represents a small set of data when considered against the total potential deals on the whole hypertensive market. This implies that the proportion of deals represented by the Novartis sample does not reach one (or 100%) . Both models (Logit and Probit) are considered but, the best fit is obtained by the Logit model. As previously discussed, there is no absolute criteria for choosing one model versus the other, but in this case the asymmetry of the deals’ distribution could explain why a logistic function fits the data better than a symmetric normal.

The scatter plot in figure 3.2 is a graphic representation of the Logit model predictions. The x axis represents the sales ratios (taken as proxy of the competence factor) while the y axis represents the proportion, or frequency, of deals. The dots represent sample observations and

correspond to the values of the dependent dummy variable equal to zero, when no deals were signed, and values different to zero, when a certain number of deals was signed. In this respect, notice how the proportion of deals signed by Novartis is always below 20%. An exception is represented by the observation on the top of the graph showing a higher proportion of about 33%6. The fitted values are represented by the regression line whose beta parameters are:

Intercept= 2.9 Slope= -40

The corresponding t statistics are: Intercept= 1.3

Slope= -2.5

The slope coefficient of the comptetence factor is statistically significant.

The negative slope of the fitted model expresses a negative relationship between the prob- ability of signing a deal and the competence factor (whose proxy is represented by the ratio of sales). This can be interpreted in business terms as evidence that when the competence factor increases, the probability of making deals decreases. This means that companies that are particularly strong in term of skill and competence, within the Hypertension disease area, tend not to enter into cooperation agreements. It can be inferred from the fitted model that the probability of Novartis to close a deal reaches a high percentage only when the competence factor tends to very low value.

Unreported estimation results of the probit model detected and analogous negative rela- tion between the probability of signing a deal and the competence factor. This funding further supports the empirical evidence above.

3.4.3 The economic impact

A closer look at the statistics concerning the number of deals reveals that the average number of deals signed is y = 6%. This means that “unconditionally” for every 100 potential deals, the company signs 6. A low figure such as this reflects the strength of a company’s position within the Hypertensive market. That only a few deals were signed indicates the high level of signif- icance of those few deals to the company. Considering the average “conditional” deals signed is of particular relevance in this situation, since such deals are conditional to the presence of a certain level of competence.

6_{In the specific case three deals (of which two were local small deals) were signed by Novartis over a total of}

Figure 3.2: Scatter Plot-Logit model

The Logit model identifies the negative relationship between a company’s competence factor and its propensity to implement a cooperative strategy. The function is not linear in x and therefore it becomes difficult to interpret the parameter β and draw conclusions about its value. It is therefore particularly important to analyse the impact of a percentage change in the competence factor over the probability of making deals. This will reveal the percentage decrease in the probability of making a deal that is driven by a % increase in the competence factor.

In the standard linear regression model, yi = β0 + ˜xiβ1 + i, the parameter β can be

interpreted in terms of derivative:

E[yi|xi] = β0+ β1x˜i

∂E[yi| ˜xi]

∂xi

= β1

That is, the change in probability is given by the partial derivative with respect to ˜xi.

In the Logit model, the partial derivative becomes:

β1ex

0

iβ(1 + ex 0

iβ)−2 (3.6)

The change in x, the competence factor, leads to a corresponding change in y, the prob- ability of making a deal. In this case, instead of considering the change in the explanatory

variable x in terms of units, it is more appropriate to consider the change in terms of standard deviations (SD) . This is because a change of one unit can be difficult to interpret economi- cally. It is therefore more appropriate to consider a change in relative terms using standard deviation.

Given expression (3.6), it is evident that the economic effect varies for each value of the explanatory variable. A common way to estimate the impact is to use the average values of the explanatory variable (Kennedy 2008).

In this case, the average value ¯xis 0.16 while the SD of x is 0.03. The standard deviation represents the average deviation, therefore each time the x value is increased by one unit of SD, the Logit model gives the average change in y. In this study, the average change in y, the probability of making deals, is equal to -0.0271, or -2.7%. This means that each time the competence factor is increased by a unit of average deviation, the probability of signing a deal decreases by 2.7%, which is an economically sizeable decrease.

3.4.4 The Logit model and the linear regression

The previous section recalled the theoretical drawbacks of the linear regression as compared to the Logit model in fitting the response values. To compare the two empirically, it is useful to show how linear regression is displayed in the same scatter plot as the Logit model, as shown in fig 3.3. The scatter plot shows an important limitation of the linear regression model: for high values of x, the regression line becomes negative, thus implying assuming negative probability values. In other words the prediction of the linear model is not suitable to represent probability values whose range span lies in the interval [0, 1].