Heterogeneous Goods, Strategic Investment, and First Mover Advantages: Real Options Theory and Empirical Study

Abstract

This study uses Real Options Analysis to receive information regarding market uncertainty. Traditional studies assume that the market is perfectly competitive and homogeneous. However, the automobile market is imperfectly competitive and its goods are heterogeneous. Automobile firms may obtain first mover advantages through irreversible investment when the market is imperfectly competitive. First mover advantages can be regarded as barriers to entry because followers cannot earn profits by entering the market and raising market share. Moreover, traditional surveys exploited the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to estimate the uncertainty (volatility). In this study, the Kalman Filter is adopted for replacing the GARCH model to improve the weaknesses in the traditional estimation method. In this study, the significant level is 0.05, and the adjusted R2 of Toyota and Honda are 0.87 and 0.58.

Appendices

Appendix 1: Process of Theoretical Model Calculation

Proposition 1: $\frac{{\partial \theta_{j}^{*} }}{\partial a} > 0$

$$ \theta_{ic}^{ *} = \frac{{\beta_{1} }}{{\beta_{1} - 2}} \cdot \frac{{ ( 2 {\text{a + b)}}^{ 2} }}{{{\text{a}} \cdot \theta^{ 2} }} \cdot \delta \cdot^{ '} I $$

Let

$$ \begin{aligned} \frac{{\partial \theta_{j}^{*} }}{\partial a} & = B \cdot \delta^{'} \cdot I \cdot 2(2a + b)(2)(a^{ - 1} \theta^{ - 2} ) + \, B \cdot \delta^{'} \cdot I \cdot (2a + b)^{2} ( - 1)(a^{ - 2} \theta^{ - 2} ) \\ \, & = B \cdot \delta^{'} \cdot I \cdot (a^{ - 1} \theta^{ - 2} )\left[ {4(2a + b) + ( - 1)(2a + b)^{2} \cdot a^{ - 1} } \right] \\ & = \left( {\frac{{B \cdot \delta^{'} \cdot I}}{{a\theta^{2} }}} \right) \cdot \left[ {4 - \frac{{(2a + b)^{2} }}{a}} \right] > 0 \\ \end{aligned} $$

Appendix 2: Process of Kalman Filter Estimation

The dynamic model is used in the Kalman Filter to estimate uncertainty. The recursive processes comprise the following steps. The State equation is the dynamic process and the Observation equation is used to calculate the solution.

State equation:

$$ \xi_{t + 1} = F\xi_{t} + v_{t + 1} $$

(A.1)

Observation equation:

$$ y_{t} = A^{'} x_{t} + H^{'} \xi_{t} + w_{t} $$

(A.2)

where A’, H’, and F are known; $x_{t}$ is an exogenous variable, $\xi_{t}$ is the variable of the impact of behavior. In the dynamic process, $\xi_{t}$ is given as a starting value. The value of y_t can be calculated by implementing these variables and starting value.

Thereafter, the systematic matrix is exploited to consider the uncertainty factor Q:

$$ \begin{aligned} E\left( {v_{t} ,v_{t}^{'} } \right) = \left\{ {\begin{array}{*{20}c} {Q, \, t = \tau } \\ 0 \\ \end{array} } \right. \hfill \\ E\left( {\omega_{t} ,\omega_{t}^{'} } \right) = \left\{ {\begin{array}{*{20}c} {R, \, t = \tau } \\ 0 \\ \end{array} } \right. \hfill \\ \end{aligned} $$

where Q and R are the ($r \times r$) and ($n \times n$) matrix. Covariance is present when $t = \tau$ Moreover, if $t \ne \tau$, the co-variances are 0.

The calculation steps of the Kalman Filter are the following: 1) implementing the recursive process; 2) calculating the y_t; and 3) renewing the value. The recursive process involves providing the starting value of $\xi_{1}$ and using $\xi_{1}$ in the Observation equation to obtain y_t, and using the $\xi_{1}$ in the State equation to obtain $\xi_{2}$.

The Kalman Filter is used to calculate estimates. The Kalman Filter obtains the value of estimates and the uncertainty of estimates with the original value, and can be used to calculate the weight average expected value.