Business Networks and Performance: A Spatial Approach

exported product (PSE) are functions of some observable characteristics of the firm and
of the entrepreneur as:

y_i = f (x_i)                                                                                              (3)

Both these percentages are bounded from below by 0 and above by 100. The most
appropriate econometric formulation of the relationship in equation (3) is a tobit model

as:

where the y_i is either the variable PMIR or the variable PSE in turn, while the vector x_i

includes network characteristics, and enterprise and entrepreneurial characteristics of
the firm. The marginal effects of the tobit model presented in equation (4), given
censoring from below at 0 and from above by 100 is given by:

'^r[^{y X}i] = β[φ(_z,₀₀ )-φ(z■ 0 )]

∂x_i

^z0 =^- xi^βσ                                                                 (5)

^z100 = ⁽¹⁰⁰ - xi^β)/^σ

where Φ(.) denotes the cumulative normal distribution function and σ the variance,
while Φ(z₁₀₀)- Φ(z₀) represents the probability of observing a noncensored
observation.

Furthermore, we assume that the percentage of material inputs used by a firm and
produced by local firms affects various dimensions of performance. Due to the dummy
nature of the variables showing performance, an appropriate econometric formulation is
a logit model as:

β^'x_i
eⁱ

Pr ob (У = 1, Positive Change of Performance Indicator) =-----—

1 + e^βxi

where У can be in turn the variables indicating performance (PEREMP, PERPM,
PERTS, PERINV), x_i is a vector of factors influencing performance and including,
among others, the percentage of material inputs produced by local firms or the
percentage of exported product, β is a vector of parameters to be estimated by the
model and Λ(.) indicates the logistic cumulative distribution function. The log-
likelihood function for the logit model in equation (6) is estimated as:

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