Uncertain Productivity Growth and the Choice between FDI and Export

Uncertain Productivity Growth

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(dz_t) = 0 and V(dz_t) = 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.

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