Ownership structure and firm patenting activity in Italy

Abstract

This paper sheds light on firm-level heterogeneity in patent propensity by studying the relationship between ownership structure and patenting activity in Italian manufacturing firms from 2006 to 2013. Both patent and accounting data are extracted from the Bureau van Dijk’s Orbis database. Our empirical findings show that ownership concentration increases the probability of successful patent applications, but at decreasing returns to scale. Moreover, there is a close association between several firm-level dimensions and innovative performance. Some differences arise when large firms and SMEs are examined separately, but the analysis as a whole would confirm the importance of ownership concentration for patenting activity. The empirical results hold also when the analysis explicitly deals with the endogeneity problem.

Appendix

1.1 Special regression method for binary choice model

To handle the problem of endogeneity, the empirical econometric literature suggests the use of instrumental variables. However, the latter are often unavailable or too weak and in same cases it is a hard task to find good instruments that fit well with models. To circumvent this difficulty, we adopt an alternative approach proposed by Lewbel: the special regressor method (Lewbel 2014; Lewbel et al. 2012; Dong and Lewbel 2012). This methodology, which is based on earlier seminal work by the same author (Lewbel 2000), is relatively easy to implement and relies on assumptions that are quite different from those required for maximum likelihood estimators. The special regressor approach does not impose restrictions on the model errors and does not require the relationship between the endogenous and exogenous regressors to be specified, but its consistency relies on the presence of one exogenous regressor that is conditionally independent of the model error, is continuously distributed, and has a large support. The special regressor thus provides a simple way of testing the validity of the modeling assumptions underlying more standard maximum likelihood approaches.

The special regressor approach proposed by Lewbel (2000) was designed in a broad context to improve the identification and estimation of parameters and their associated distributions in general threshold-crossing models such as the following binary decision model:

$${\text{D}} = {\text{I}}({\text{X}}^{\prime}\upbeta + \upvarepsilon \ge 0)$$

(1)

where D represents the binary decision variable, the vector X includes all observable regressors, ε has a zero mean distribution, and I(·) is the indicator function taking the value one if the latent variable X′β + ε is positive and zero otherwise. Traditional probit and logit models correspond to the case of ε following a normal and exponential distribution, respectively.

The special regressor model has the same form as model (1) but is rewritten so that one regressor V (that is called the special regressor) is separated from the other regressors X and its coefficient is normalized to one:

$${\text{D}} = {\text{I}}({\text{X}}^{\prime} \beta + {\text{V}} + \upvarepsilon \ge 0)$$

(2)

The special regressor V must satisfy three fundamental conditions:

• V is continuously distributed and has a large support (i.e., V varies on a support that is as large as the support of X′β + ε);

• V is exogenous;

• E(D|X, V) increases with V.

If some elements of X are endogenous, then the special regressor method requires instruments satisfying the following usual properties: E(Z′ε) = 0 and E(Z′X) has full rank. The special regressor V should not be included in the set of instruments Z which implies that a suitable V should only affect the binary decision of interest, and not the endogenous (binary) variable. Further, note that only one special regressor is needed whatever the number of endogenous variables in the model.

The basic idea behind the special regressor approach is briefly described below (while we refer to Lewbel (2014) for additional details).

Define T as:

$$T = \frac{D - I(V \ge 0)}{{f_{V|Z} (V|Z)}}$$

where f_V|Z(V|Z) denotes the conditional probability density function of V given Z. Under the above assumption, it can be shown that E(T|Z) = E(X′β + ε|Z), assuming ε is independent of V|Z (Lewbel 2014). It follows from the latter equality that E(ZX′)β = E (Z T) and so:

$$\beta = [E(XZ^{\prime})E(ZZ^{\prime})^{ - 1} E(Z^{\prime} X)]^{ - 1} E(XZ^{\prime} )E(ZZ^{\prime} )^{ - 1} E(ZT)$$

which is the definition of a linear two-stage least squares regression of T on X using instruments Z. We describe below the steps to be followed to estimate and the parameters of interest β (see Dong and Lewbel 2012 for more insight about technical details):

• Step 0: V must be of mean zero; if not, one must first de-mean it.

• Step 1: Run an Ordinary Least Squares (OLS) regression of V on (X, Z) and, for each observation i, compute the residuals as the difference between the observed V_i and its prediction: ${\hat{U}}_{i} = V_{i} - (X^{\prime}_{{\hat{b}_{X}}} + Z^{\prime}_{{\hat{b}_{Z}}} )$, where $\hat{b}_{X} {\text{ and }}\hat{b}_{Z}$ are the OLS estimated coefficients for variables in X and Z, respectively.

• Step 2: Compute $\hat{f}_{h}$ as the non-parametric kernel estimator of the density f of $\hat{U}$ and for each I compute the estimates $\hat{f}_{i} = \hat{f}(\hat{U}_{i} )$. Note that such estimation requires a kernel K(·) and a bandwidth to be chosen. Alternatively, one may use the ordered data estimator proposed by Lewbel and Schennach (2007). See also Dong and Lewbel (2012) for details.

• Step 3: For each observation i construct:

  $$\hat{T}_{i} = \frac{{D_{i} - I(V_{i} \ge 0)}}{{\hat{f}_{i} }}.$$

  Note that in this ratio the denominator can take very small values especially for large absolute values of $\hat{U}_{i}$. As a consequence, some could have extremely large absolute values, which could induce large standard errors in the final two-stage least squares regression. Lewbel (2014) recommends either removing these extreme values for example using a trimming procedure.

• Step 4: Compute $\hat{\beta }$ as the coefficient of a two-stage least squares regression of $\hat{T}$ on X using instruments Z.

The estimation of the special regressor thus involves four steps that can be implemented relatively easily in most statistical software: a procedure is available in STATA (see Baum 2012). Further, classical tests of the validity of the instruments can be applied at the final two-stage least squares regression knowing that E(Zε) = E(Z $\tilde{\varvec{\varepsilon }}$) with $\tilde{\varvec{\varepsilon }}$ = T − X′β, the error term of the Step 4 regression (see Dong and Lewbel 2012).