Uncertain Productivity Growth
2 THEORETICAL FRAMEWORK
where t is assumed to be a Gaussian random variable. Therefore, the expected value and the
variance of the standard Wiener process’ increment result as E(dzt) = 0 and V(dzt) = dt.
0 10 20 30 40 50 60
Time in months
Figure 2: Exemplary Productivity Paths
Figure 2 illustratively depicts the realizations of the above mentioned productivity paths. The
increasing dashed line exhibits a yearly growth rate of 6% and no volatility as E(dzt) = 0. In
such a case after 5 years, productivity can be expected to be 33% higher than initially. For a
volatile productivity growth with σ > 0, it is no longer possible to predict a unique path. The
dotted trajectories represent 2 potential developments for a scenario with σ = 4% out of infinite
possibilities. The simplest case is depicted by the horizontal curve which represents a scenario
without growth.3
Due to its coverage of all possible productivity developments, the Geometric Brownian motion in
equation (11) represents the second pillar in this model. By combining the established proximity-
concentration trade-off framework with the Geometric Brownian motion in productivity, the
succeeding analysis examines the optimal first time market entry strategy of an international
investor in all these scenarios separately.
3 The chosen values are illustrative examples. Faggio et al. (2007) e.g. present empirical data about productivity
developments for different sectors in the U.K.