Uncertain Productivity Growth and the Choice between FDI and Export

Uncertain Productivity Growth

3.3 FDI or Export with Uncertain Productivity Growth

Although the introduction of productivity growth accounts for empirically important effects still
one crucial aspect is neglected. Productivity growth is not a deterministic phenomenon but
represents a continuously volatile process over time (Baily et al., 2001). As a consequence of
this stochastic characteristic, the investor is no longer confronted with a simple choice problem
between two types of market entry over time. Additionally, he has to adjust his expectations
to the prevailing continuous productivity uncertainty. A natural and convenient way to extend
the previous settings, in order to account for productivity uncertainty, is the introduction of a
Geometric Brownian motion represented by (11) whose solution is derived as

$t = $0 _eR0 (^{α-1 σ}2)^dt+R0 ^σdzt.                                   (44)

Within this final framework the investor assesses any uncertain investment with respect to the
capital market where an appropriate return (including a risk-premium) is derived. In order
to evaluate the appropriate investment return for both market entry modes it is assumed that
there exists an asset on a complete capital market which is perfectly correlated with the latter
Geometric Brownian motion.⁸ Furthermore, this replication asset is assumed to pay no dividends
and therefore, its complete return can be attributed to its capital gain. With reference to the
capital asset pricing model (CAPM) the risk adjusted expected return μ of such an investment
is derived from

μ = r + ——r) UcM σi                       (45)

σM

where υcM specifies the correlation between the spanned asset and the market portfolio. rM and
σM represent the expected return and the volatility of the latter one. Within this framework
the market price of risk is measured as ^rM^-r and is referred to as the Sharpe ratio (Sharpe,
1964). Based on the linear relationship in equation (45) it is possible to derive an appropriate
risk-adjusted expected rate of return for any degree of uncertainty described by σ .

Once the adjusted expected return μ is known, it is possible to derive the risk-adjusted opportunity
costs in order to evaluate the export and FDI strategy under uncertainty. In equilibrium, the

⁸ Within the option theory such a procedure is referred to as asset spanning or asset replication (Schwartz and
Trigeorgis, 2004)

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