Uncertain Productivity Growth and the Choice between FDI and Export

Uncertain Productivity Growth

which proves the consistency of the model as the result is equivalent to the previous certain case.
In figure 7 the areas F1 and F2 are equal to the areas C1 and C3 in figure 6 since they represent
the deterministic case. By taking the two relationships (64) and (65) into account the risk driven
adjustments of the option values and of equation (67) are straightforward. With an increase in
productivity uncertainty, βu decreases and becomes smaller than βc . Graphically, the continuous
line in figure 7 which represents relationship (67) becomes more convex as depicted by the dashed
line. As a consequence, the range of relative cost constellations which enforce FDI over time
increases by the area F3 . Differently expressed, a volatile growth in productivity broadens the
range of cost constellations favoring FDI as the first time market entry strategy compared with
a deterministic growth development. Uncertainty therefore acts as a compound force for the
derived deterministic growth effects.

Result 3:

For IE < IF and wEτ 1 > w_F the range of relative cost constellations which enforce FDI as
the optimal market entry mode is strictly bigger if productivity growth dθ_t is associated with
uncertainty. For σ → ∞, FDI becomes the only relevant market entry mode.

4 The Timing Effects of Uncertainty

The increasing dominance of the FDI mode as the optimal first time market entry strategy due
to an increase in σ implies according to the common real option theory an increase in the market
entry time (Dixit and Pindyck, 1994).¹¹ However, in contrast to the previous deterministic case
it is no longer possible to quantify the exact market entry time Ti* for both market entry modes
as the investor’s decision is based on a stochastic process. But, it is possible to calculate the
expected first time entry E(T_i*), if the initial productivity level $0 and the cut-off productivity $*
are known. The corresponding time T_i^* at which the stochastic process reaches its trigger value
$_i^* represents the first passage time.

¹¹ Dixit and Pindyck (1994) assume in their illustrative examples that the risk adjusted return rate is invariant in σ
which is the case for linear profit functions. In such cases, there is a positive relationship between the first time
market entry Ti* and σ.

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