# The Impact of Thailand’s Openness on Bilateral Trade between Thailand and Japan: Copula-Based Markov Switching Seemingly Unrelated Regression Model

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. The Gravity Model

- $GD{P}_{TH,t}$ and $GD{P}_{JP,t}$ are the growth of the gross domestic products of Thailand and Japan at time $t$, which represents the economic sizes of Thailand and Japan;
- $DIS{T}_{THJP,t}$ is the gross domestic product weighted distance between Bangkok, Thailand and Tokyo, Japan. $DIS{T}_{TH,t}$ is calculated by:$$DIS{T}_{TH,t}={{\displaystyle \sum}}^{\text{}}\left(dis{t}_{TH,JP}\left(\frac{GD{P}_{TH,t}}{GD{P}_{TH,t}+GD{P}_{JP,t}}\right)\right)$$
- $OPE{N}_{TH,t}$ and $OPE{N}_{JP,t}$ are the level of trade openness of Thailand and Japan at time $t$.

- $EX{C}_{THJP,t}$ is the exchange rate between the currency of Thailand (Thai Baht) and Japan (Japanese Yen) at time t.

#### 2.2. Seemingly Unrelated Regression (SUR) Model

#### 2.3. Markov Switching Model with Seemingly Unrelated Regression (MS-SUR) Model

- Assume the initial value of transition probabilities ${P}_{ij}$. This probability refers to the switching probabilities from regime $i$ to regime $j$. The transition probabilities ${P}_{ij}$ can be written by:$${P}_{ij}=\mathrm{Pr}\left({S}_{t+1}=j|{S}_{t}=i\right)$$$$P=\left[\left[\begin{array}{ccc}{P}_{11}& \cdots & {P}_{h1}\\ \vdots & \ddots & \vdots \\ {P}_{1h}& \cdots & {P}_{hh}\end{array}\right]\right]$$
- Update the transition probability in order to compute the likelihood equation in each state $f\left({y}_{t}|\left({S}_{t}\right)=j,{\phi}_{t-1}\right)$ based on not only previous information, but also on all the parameters which are in the equation consisting of ${\mathsf{\Theta}}_{t-1}$ and ${P}_{ij}$. The form of the updated probability for each state is:$$\mathrm{Pr}\left({S}_{t}=j|\phi \right)=\frac{\text{}f\left({y}_{t}|{S}_{t-j},{\phi}_{t-1}\right)\mathrm{Pr}\left({S}_{t-j}|{\phi}_{t-1}\right)}{{{\displaystyle \sum}}_{j=1}^{k}\text{}f\left({y}_{t}|{S}_{t-j},{\phi}_{t-1}\right)\mathrm{Pr}\left({S}_{t-j}|{\phi}_{t-1}\right)}$$
- Iterate both step 1 and step 2 for $t=1,\dots ,T$

#### 2.4. Copula Model

#### 2.5. Copula-Based Markov Switching Seemingly Unrelated Regression (MS-SUR) Model

## 3. Data

## 4. Empirical results

#### Stationary Process

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Table 1.**Unit root test result. ADF test: augmented Dickey–Fuller test; PP test: Phillips–Perron test.

Variable | ADF Test | PP Test | ||||||
---|---|---|---|---|---|---|---|---|

Level | 1st Diff | Level | 1st Diff | |||||

Intercept | Trend and Intercept | Intercept | Trend and Intercept | Intercept | Trend and Intercept | Intercept | Trend and Intercept | |

EXP | −2.418 | −2.886 | −10.251 *** | −8.859 *** | −2.879 | −2.886 | −10.429 *** | −11.526 *** |

(0.065) | (0.284) | (0.000) | (0.000) | (0.051) | (0.171) | (0.000) | (0.000) | |

[0.483] | [0.972] | [0.000] | [0.000] | [0.414] | [0.822] | [0.000] | [0.000] | |

IMP | −1.367 | −2.019 | −8.378 *** | −8.337 *** | −1.482 | −2.342 | −8.290 *** | −8.246 *** |

(0.595) | (0.584) | (0.000) | (0.000) | (0.051) | (0.408) | (0.000) | (0.000) | |

[0.839] | [0.854] | [0.000] | [0.000] | [0.906] | [0.994] | [0.000] | [0.000] | |

${\mathrm{GDP}}_{\mathrm{TH}}$ | −0.763 | −2.282 | −9.958 *** | −9.924 *** | −0.763 | −2.505 | −9.967 *** | −9.935 *** |

(0.825) | (0.440) | (0.000) | (0.000) | (0.825) | (0.325) | (0.000) | (0.000) | |

[0.432] | [0.982] | [0.000] | [0.000] | [0.431] | [0.993] | [0.000] | [0.000] | |

${\mathrm{GDP}}_{\mathrm{JP}}$ | −0.977 | −2.543 | −8.962 *** | −8.931 *** | −1.009 | −2.711 | −8.909 *** | −8.875 *** |

(0.759) | (0.307) | (0.000) | (0.000) | (0.748) | (0.235) | (0.000) | (0.000) | |

[0.568] | [0.986] | [0.000] | [0.000] | [0.591] | [0.925] | [0.000] | [0.000] | |

DIST | −1.533 | −2.259 | −7.845 *** | −7.815 *** | −1.260 | −1.968 | −7.884 *** | −7.758 *** |

(0.513) | (0.513) | (0.000) | (0.000) | (0.646) | (0.612) | (0.000) | (0.000) | |

[0.931] | [0.931] | [0.000] | [0.000] | [0.768] | [0.818] | [0.000] | [0.000] | |

${\mathrm{OPEN}}_{TH}$ | −1.847 | −2.480 | −8.492 *** | -8.506 *** | −0.763 | −2.505 | −9.967 *** | −9.935 *** |

(0.356) | (0.337) | (0.000) | (0.000) | (0.193) | (0.244) | (0.000) | (0.000) | |

(0.999] | [0.996] | [0.000] | [0.000] | [0.863] | [0.935] | [0.000] | [0.000] | |

${\mathrm{OPEN}}_{\mathrm{JP}}$ | −2.251 | −2.586 | −8.684 *** | −8.725 *** | −1.845 | −2.614 | −8.884 *** | −8.898 *** |

(0.190) | (0.288) | (0.000) | (0.000) | (0.357) | (0.275) | (0.000) | (0.000) | |

[0.858] | [0.974] | [0.000] | [0.000] | [1.000] | [0.965] | [0.000] | [0.000] | |

EXC | −2.778 | −2.592 | −7.825 *** | −7.935 *** | −2.830 | −2.314 | −7.877 *** | −7.830 *** |

(0.065) | (0.285) | (0.000) | (0.000) | (0.058) | (0.423) | (0.000) | (0.000) | |

[0.483] | [0.972] | [0.000] | [0.000] | [0.447] | [0.990] | [0.000] | [0.000] |

Model | 1 | 2 | Copula | AIC | BIC |
---|---|---|---|---|---|

1 | Normal | Normal | Gaussian | −1431.922 | −1347.611 |

2 | Normal | Student-t | Gaussian | −1353.038 | −1263.457 |

3 | Student-t | Normal | Gaussian | −1331.857 | −1242.276 |

4 | Student-t | Student-t | Gaussian | −1441.685 | −1346.835 |

5 | Normal | Normal | Student-t | −1282.491 | −1198.180 |

6 | Normal | Student-t | Student-t | −1484.628 * | −1389.778 |

7 | Student-t | Normal | Student-t | −1357.210 | −1267.630 |

8 | Student-t | Student-t | Student-t | −1352.715 | −1263.134 |

9 | Normal | Normal | Clayton | −1089.794 | −1005.483 |

10 | Normal | Student-t | Clayton | −934.110 | −844.529 |

11 | Student-t | Normal | Clayton | −935.906 | −846.325 |

12 | Student-t | Student-t | Clayton | −1119.558 | −1024.708 |

13 | Normal | Normal | Gumbel | −920.353 | −836.042 |

14 | Normal | Student-t | Gumbel | −917.966 | −828.385 |

15 | Student-t | Normal | Gumbel | −916.802 | −827.222 |

16 | Student-t | Student-t | Gumbel | −915.163 | −820.313 |

17 | Normal | Normal | Joe | −939.800 | −855.489 |

18 | Normal | Student-t | Joe | −936.221 | −846.641 |

19 | Student-t | Normal | Joe | −937.162 | −847.581 |

20 | Student-t | Student-t | Joe | −934.500 | −839.650 |

Variables | Regime 1 | Regime 2 | ||||
---|---|---|---|---|---|---|

Coefficient | Std. Err | B Factor | Coefficient | Std. Err | B Factor | |

Intercept | 0.002 | 0.012 | 0.317 | 0.002 | 0.014 | 0.310 |

GDPTH | 0.512 | 0.838 | 0.903 | 0.527 | 2.615 | 0.397 |

GDPJP | 0.470 | 1.699 | 0.522 | 0.029 | 0.385 | 0.156 |

DIST | 0.003 | 0.282 | 0.025 | −0.007 | 0.271 | 0.057 |

OPNSTH | 2.233 | 2.645 | 0.997 | 3.649 | 2.696 | 0.831 |

EXC | 0.342 | 0.607 | 0.868 | −0.324 | 0.646 | 0.812 |

Sigma | 0.023 | 0.004 | 0.000 | 0.067 | 0.073 | 1.000 |

_{0}includes weak (1–0.333), moderate (0.333–0.1), substantial (0.1–0.033), strong (0.033–0.01), very strong (0.01–0.003), and decisive (<0.003) (Held and Ott 2016).

Variables | Regime 1 | Regime 2 | ||||
---|---|---|---|---|---|---|

Coefficient | Std. Err | B Factor | Coefficient | Std. Err | B Factor | |

Intercept | 0.055 | 1.161 | 0.001 | 0.282 | 2.132 | 0.029 |

GDPJP | 0.409 | 2.739 | 0.000 | 0.259 | 2.463 | 0.000 |

GDPTH | 0.231 | 2.535 | 0.000 | 0.140 | 1.274 | 0.000 |

DIST | −0.029 | 3.117 | 0.000 | 0.100 | 8.673 | 0.002 |

OPNSJP | 1.048 | 4.329 | 0.000 | 1.808 | 1.274 | 0.003 |

EXC | 0.191 | 1.647 | 0.000 | −0.183 | 3.246 | 0.001 |

SIGMA | 0.557 | 3.111 | 0.039 | 0.557 | 1.717 | 0.069 |

_{0}includes weak (1–0.333), moderate (0.333–0.1), substantial (0.1–0.033), strong (0.033–0.01), very strong (0.01–0.003), and decisive (<0.003) (Held and Ott 2016).

Switching Probability | Coefficient | Std. Err | B Factor |
---|---|---|---|

P_{11} | 0.999 | 2.201 | 0.09 |

P_{22} | 0.559 | 9.895 | 0.12 |

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**MDPI and ACS Style**

Pastpipatkul, P.; Boonyakunakorn, P.; Phetsakda, K.
The Impact of Thailand’s Openness on Bilateral Trade between Thailand and Japan: Copula-Based Markov Switching Seemingly Unrelated Regression Model. *Economies* **2020**, *8*, 9.
https://doi.org/10.3390/economies8010009

**AMA Style**

Pastpipatkul P, Boonyakunakorn P, Phetsakda K.
The Impact of Thailand’s Openness on Bilateral Trade between Thailand and Japan: Copula-Based Markov Switching Seemingly Unrelated Regression Model. *Economies*. 2020; 8(1):9.
https://doi.org/10.3390/economies8010009

**Chicago/Turabian Style**

Pastpipatkul, Pathairat, Petchaluck Boonyakunakorn, and Kanyaphon Phetsakda.
2020. "The Impact of Thailand’s Openness on Bilateral Trade between Thailand and Japan: Copula-Based Markov Switching Seemingly Unrelated Regression Model" *Economies* 8, no. 1: 9.
https://doi.org/10.3390/economies8010009