# Regional Informatization and Economic Growth in Japan: An Empirical Study Based on Spatial Econometric Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Construction of the Analytical Model

#### 2.1. Basic Model

_{it}, NICT

_{it}, ICT

_{it}, and L

_{it}represent regional output, non-ICT capital input, ICT capital input, and labor input, respectively. The formula helps isolate the contribution of informatization investment to economic growth from other factors. For statistical analysis, a logarithm is conducted on both sides of the formula with the divided labor input.

_{it}/ L

_{it}) = ln A + α

_{1}ln(NICT

_{it}/ L

_{it}) + β

_{1}ln(ICT

_{it}/ L

_{it}) + μ

_{i}+ λ

_{t}+ ε

_{it}

_{i}, λ

_{t}, and ε

_{it}represent the spatial fixed effect, time fixed effect, and random disturbance term, respectively.

_{it}/ L

_{it}) = ln A + α

_{2}ln(K

_{it}/ L

_{it}) + β

_{2}ln(ICT

_{it}) + μ

_{i}+ λ

_{t}+ ε

_{it}

_{it}represents all the capital inputs of the firm, including both ICT and non-ICT. Unlike Equation (2), ICT

_{it}in Equation (4) represents ICT capital inputs with public attributes, such as an optical fiber building. The formula provides the spillover effect of informatization investment on ICT.

#### 2.2. Spatial Model Selection

_{n}+ Xβ + ε

_{n}‒ ρWy)

^{‒1}(α ι

_{n}+ Xβ) + (I

_{n}‒ ρWy)

^{‒1}ε

ε ~ N (0, σ

^{2}I

_{n})

_{n}+ Xβ + WXγ + ε

_{n}‒ ρWy)

^{‒1}(α ι

_{n}+ Xβ+ WXγ + ε)

ε ~ N (0, σ

^{2}I

_{n})

#### 2.3. Selection of Control Variables

_{it}in Equations (1) and (3).

_{it}= Ae

^{(δ1ln R&Dit + η1ln Tranit + μi + λt + εit)}

A

_{it}= A e

^{(β2 ICTit + δ2ln R&Dit + η2ln Tranit + μi + λt + εit)}

_{it}, NICTit, ICT

_{it}, L

_{it}, R&D, and Tran represent regional output, non-ICT capital input, ICT capital input, labor input, R&D capital stock, and infrastructure capital stock, respectively.

_{it}and ICT

_{it}represent all the material capital inputs of the firm and ICT capital input with public attributes, respectively. Other variables have the same meaning as in Equation (11). In the subsequent analysis, we analyze Equations (11) and (12) with the Matlab software, employing the maximum likelihood method to estimate the model parameters and for the related tests.

#### 2.4. Direct and Indirect Spillover Effect of the Independent Variable

_{n}‒ ρW)y = Xβ + WXθ + ι

_{n}α + ε

_{r}(W) = V(W)(I

_{n}β

_{r}+ Wθ

_{r})

_{n}‒ ρW)

^{‒1}= I

_{n}+ ρW + ρ

^{2}W

^{2}+ ρ

^{3}W

^{3}+ ∙∙∙

_{ir}on the dependent variable, which represents the direct effect. For region j, , i ≠ j, measures the influential effect of the independent variable x

_{jr}on the dependent variable, which represents the indirect effect. The diagonal elements in S

_{r}(W) represent the direct effects and the off-diagonal elements the indirect effects.

## 3. Data Source

#### 3.1. Sample Selection

#### 3.2. Sources of Data

## 4. Empirical Analysis

#### 4.1. The Construction of Spatial Weight Matrix

#### 4.2. Contribution of Informatization Investment to Economic Growth

^{2}values for 1980–2007, 1980–1996, and 1997–2007 are 0.9344, 0.9683, and 0.9725, respectively, and the corrected R

^{2}values are 0.6549, 0.5732, and 0.3728, respectively. Here, the difference between R

^{2}and the corrected R

^{2}is that the latter neglects the variance explained by the spatial fixed effect, implying that the fixed effect explains the whole variation. What is more, when taking the spatial lag of the explained variable as explanatory variable it takes R

^{2}to explain, and when taking the spatial lag of the explained variable as no explanatory variable it takes corrected R

^{2}to explain. It can be seen that spatial fixed effect should be incorporated into the model, which has a good fit overall.

**Table 1.**Regional informatization and economic growth in Japan: spatial and time-period fixed effects (1980–2007).

1980–2007 | 1980–1996 | 1997–2007 | |
---|---|---|---|

Spatial Random Effects | Spatial Random Effects | Spatial and Time-Period Fixed Effects | |

W × ln(GDP/L) | 0.1160 | 0.1360 | 0.0216 |

(3.3661) | (3.0992) | (0.3908) | |

ln(NICT/L) | 0.3689 | 0.3557 | 0.7658 |

(13.7340) | (10.7594) | (11.4621) | |

ln(ICT/L) | 0.0441 | 0.0438 | −0.1143 |

(3.6558) | (2.9222) | (−2.1016) | |

ln(R&D) | 0.0063 | 0.0021 | 0.0071 |

(5.0761) | (1.2910) | (3.0808) | |

ln(Tran) | 0.0232 | 0.0023 | 0.0907 |

(3.3592) | (0.2918) | (3.3162) | |

W × ln(NICT/L) | 0.1247 | −0.0055 | −0.4220 |

(2.6262) | (−0.0905) | (−4.1424) | |

W × ln(ICT/L) | −0.0384 | −0.0426 | 0.2800 |

(−2.2990) | (−2.1397) | (4.0379) | |

W × ln(R&D) | 0.0051 | 0.0070 | −0.0140 |

(1.9789) | (2.0104) | (−3.1874) | |

W × ln(Tran) | 0.0078 | 0.0119 | 0.4549 |

(0.5605) | (0.7603) | (7.5783) | |

phi | 0.0929 | 0.0684 | |

(6.8830) | (6.8698) | ||

σ^{2} | 0.0003 | 0.0002 | 0.0001 |

R^{2} | 0.9344 | 0.9683 | 0.9725 |

Corrected R^{2} | 0.6549 | 0.5732 | 0.3728 |

Log L | 2941.6 | 2101.9 | 1606.5 |

Wald test spatial lag | 20.1575 (p = 0.001) | 10.02 (p = 0.04) | 90.83 (p = 0.001) |

Wald test spatial error | 32.3197 (p = 0.001) | 11.45 (p = 0.01) | 87.55 (p = 0.001) |

LR test spatial lag | 90.88 (p = 0.001) | ||

LR test spatial error | 88.59 (p = 0.001) | ||

Direct effect ln(NICT/L) | 0.3755 | 0.3573 | 0.7629 |

(14.160) | (10.789) | (11.540) | |

Direct effect ln(NICT/L) | 0.3755 | 0.3573 | 0.7629 |

(14.160) | (10.789) | (11.540) | |

Indirect effect ln(NICT/L) | 0.1845 | 0.0497 | −0.4112 |

(3.524) | (0.757) | (−4.248) | |

Total effect ln(NICT/L) | 0.5600 | 0.4070 | 0.3517 |

(9.145) | (5.079) | (4.062) | |

Direct effect ln(ICT/L) | 0.0433 | 0.0423 | −0.1095 |

(3.750) | (2.943) | (−2.017) | |

Indirect effect ln(ICT/L) | −0.0365 | −0.0405 | 0.2788 |

(−2.070) | (−1.955) | (4.148) | |

Total effect ln(ICT/L) | 0.0068 | 0.0018 | 0.1693 |

(0.438) | (0.104) | (3.772) | |

Direct effect ln(R&D) | 0.0064 | 0.0024 | 0.0070 |

(5.021) | (1.456) | (3.040) | |

Indirect effect ln(R&D) | 0.0064 | 0.0079 | −0.0140 |

(2.246) | (1.974) | (−3.094) | |

Total effect ln(R&D) | 0.0128 | 0.0103 | −0.0070 |

(3.812) | (2.178) | (−1.424) | |

Direct effect ln(Tran) | 0.0235 | 0.0026 | 0.0933 |

(3.407) | (0.321) | (3.457) | |

Indirect effect ln(Tran) | 0.0113 | 0.0134 | 0.4643 |

(0.726) | (0.767) | (7.542) | |

Total effect ln(Tran) | 0.0348 | 0.0160 | 0.5576 |

(2.060) | (0.838) | (8.219) |

#### 4.3. Spillover Effect and Network Effect of Informatization

_{it}) is used to explore the network externality of ICT investment. In a macroeconomic situation, we expect the variable to be positive, but in the context of a regional economy, the expected variable could be either positive or negative. Combined with the paradoxical geographies of the digital economy, if the variable is positive, it means there is a spillover or spreading effect, and the world is flat theory is verified. If the variable is negative, it means there is no spillover effect, while there could be a convergence effect, and the digital divide is supported. Based on Equation (4), the study has taken advantage of the cross-term of ICT to explore the informatization external effect under the interaction of enterprise ICT investment and the social information network. Thus, Equation (4) can be extended to Equation (19):

_{it}/ L

_{it}) = ln A + α

_{2}ln(K

_{it}/ L

_{it}) + β

_{2}ln(ICT

_{it}× U

_{it}) + μ

_{i}+ λ

_{t}+ ε

_{it}

^{2}is 0.9744, and the corrected R

^{2}is 0.4156; therefore, the model fits well. The Wald lag and Wald error test statistics are 128.18 (p = 0.001) and 118.57 (p = 0.001), respectively. The LR lag and LR error test statistics are 124.71 (p = 0.001) and 121.72 (p = 0.001), respectively. These results mean that the spatial Durbin model with spatial lag is an appropriate choice. The estimated coefficients with first-order weights are significant for all variables except W × ln(K/L), which is negative but not significant(t = −1.94). Both ln(ICT) and W×ln(ICT) are significant. ICT is negative but not significant, which means local ICT investment will not lead to an external effect or a spatial spillover effect. However, it is too early to draw a conclusion. In the local area, ln(ICT) is negative, which means that there may be an excessive investment problem. However, W × ln(ICT) is positive, and the coefficient is larger than ln(ICT), which suggests a significant spillover effect. This can be verified from the total effect (direct effect = 0.1885, t = 4.466).

OLS Estimation | Spatial Fixed Effects | Time-Period Fixed Effects | Spatial and Time-Period Fixed Effects | |
---|---|---|---|---|

ln(KL) | 0.375 | 0.208 | 0.307 | 0.615 |

(19.839) | (6.623) | (15.14) | (11.48) | |

ln(ICT) | 0.071 | −0.009 | 0.071 | 0.033 |

(14.09) | (−0.299) | (15.43) | (1.018) | |

ln(R&D) | 0.004 | 0.008 | 0.007 | 0.008 |

(2.926) | (2.959) | (5.148) | (3.490) | |

ln(Tran) | −0.007 | 0.178 | -0.012 | 0.107 |

(−1.914) | (10.67) | (-3.449) | (3.891) | |

Intercept | −1.339 | |||

(−38.66) | ||||

R^{2} | 0.724 | 0.806 | 0.716 | 0.251 |

Durbin-Watson | 1.871 | 1.497 | 2.029 | 1.730 |

Log L | 1009.80 | 1473.10 | 1058.20 | 1561.10 |

LM spatial lag | 107.10 | 27.25 | 46.39 | 2.34 |

LM spatial error | 27.17 | 31.72 | 5.45 | 3.63 |

Robust LM spatial lag | 84.55 | 0.00 | 51.88 | 0.38 |

Robust LM spatial error | 4.62 | 4.48 | 10.95 | 1.68 |

Spatial and Time-Period Fixed Effects W1 | Spatial and Time-Period Fixed Effects W2 | Spatial and Time-Period Fixed Effects W3 | |
---|---|---|---|

W × ln(GDP/L) | 0.0219 | 0.2427 | −0.0585 |

(0.4002) | (3.4463) | (−0.5255) | |

ln(K/L) | 0.6770 | 0.6468 | 0.6720 |

(13.4205) | (12.2567) | (12.8019) | |

ln(ICT) | −0.3270 | −0.2757 | −0.2097 |

(−5.3955) | (−5.2624) | (−4.8450) | |

ln(R&D) | 0.0073 | 0.0073 | 0.0047 |

(3.2597) | (3.1083) | (2.0160) | |

ln(Tran) | 0.0912 | 0.0982 | 0.1049 |

(3.4579) | (3.5318) | (3.8223) | |

W × ln(K/L) | −0.1782 | −0.1819 | −0.2231 |

(−1.9370) | (−1.2550) | (−1.1099) | |

W × ln(ICT) | 0.5115 | 0.5248 | 0.6550 |

(6.9291) | (6.3031) | (6.7266) | |

W × ln(R&D) | −0.0129 | −0.0147 | −0.0290 |

(−3.0264) | (−1.9917) | (−2.5442) | |

W × ln(Tran) | 0.4593 | 0.2474 | 0.6359 |

(7.8760) | (2.4894) | (3.9463) | |

σ^{2} | 0.0001 | 0.0001 | 0.0001 |

R^{2} | 0.9744 | 0.9719 | 0.9725 |

Corrected R^{2} | 0.4156 | 0.3521 | 0.3707 |

Log L | 1624.8 | 1598.6 | 1607.0 |

Wald test spatial lag | 128.18(p=0.000) | 66.413(p=0.001) | 87.41(p=0.000) |

Wald test spatial error | 118.57(p=0.000) | 49.21(p=0.001) | 73.32(p=0.000) |

LR test spatial lag | 124.71(p=0.000) | 69.25(p=0.001) | 91.03(p=0.000) |

LR test spatial error | 121.72(p=0.000) | 59.87(p=0.001) | 90.21(p=0.000) |

Direct effect ln(K/L) | 0.6761 | 0.6456 | 0.6717 |

(14.099) | (11.971) | (12.760) | |

Indirect effect ln(K/L) | −0.1676 | −0.0363 | −0.2569 |

(−1.847) | (−0.207) | (−1.367) | |

Total effect ln(K/L) | 0.5085 | 0.6093 | 0.4147 |

(4.915) | (3.135) | (2.162) | |

Direct effect ln(ICT) | −0.3230 | −0.2606 | −0.2148 |

(−5.399) | (−5.177) | (−4.837) | |

Indirect effect ln(ICT) | 0.5115 | 0.5921 | 0.6375 |

(6.988) | (6.271) | (6.512) | |

Total effect ln(ICT) | 0.1885 | 0.3315 | 0.4228 |

(4.466) | (4.523) | (5.450) | |

Direct effect ln(R&D) | 0.0072 | 0.0069 | 0.0048 |

(3.295) | (2.919) | (2.003) | |

Indirect effect ln(R&D) | −0.0128 | −0.0167 | −0.0282 |

(−3.058) | (−1.721) | (−2.520) | |

Total effect ln(R&D) | −0.0055 | −0.0098 | −0.0234 |

(−1.200) | (−0.964) | (−1.987) | |

Direct effect ln(Tran) | 0.0943 | 0.1076 | 0.1033 |

(3.672) | (3.963) | (3.856) | |

Indirect effect ln(Tran) | 0.4674 | 0.3512 | 0.6036 |

(7.622) | (2.741) | (3.708) | |

Total effect ln(Tran) | 0.5618 | 0.4588 | 0.7069 |

(8.439) | (3.303) | (4.224) |

^{2}and the corrected R

^{2}are 0.9725 and 0.372, respectively, no different from Table 3. These passed the Wald test and the LR test, which means the spatial Durbin model is an appropriate choice.

Spatial and Time-Period Fixed Effects W1 | Spatial and Time-Period Fixed Effects W2 | Spatial and Time-Period Fixed Effects W3 | |
---|---|---|---|

W × ln(GDP/L) | 0.0303 | 0.1954 | −0.0638 |

(0.5456) | (2.6482) | (−0.5579) | |

ln(K/L) | 0.7152 | 0.7323 | 0.7311 |

(13.4275) | (13.0346) | (13.0560) | |

ln(ICT × U) | 0.0372 | 0.0244 | 0.0388 |

(1.9332) | (1.2315) | (2.1657) | |

ln(R&D) | 0.0078 | 0.0094 | 0.0070 |

(3.3782) | (3.9636) | (2.8941) | |

ln(Tran) | 0.1056 | 0.1169 | 0.1300 |

(3.8423) | (4.0572) | (4.5437) | |

W × ln(K/L) | −0.0706 | 0.0627 | 0.0063 |

(−0.6756) | (0.3695) | (0.0261) | |

W × ln(ICT × U) | 0.0379 | 0.0938 | 0.0972 |

(1.3909) | (2.3452) | (1.8055) | |

W × ln(R&D) | −0.0138 | −0.0206 | −0.0421 |

(−3.1066) | (−2.7568) | (−3.6214) | |

W × ln(Tran) | 0.4445 | 0.2310 | 0.2976 |

(7.4031) | (2.2478) | (1.8457) | |

σ^{2} | 0.0001 | 0.0001 | 0.0001 |

R^{2} | 0.9725 | 0.9702 | 0.9705 |

Corrected R^{2} | 0.3720 | 0.3153 | 0.3237 |

Log L | 1606.5 | 1584.7 | 1588.5 |

Wald test spatial lag | 61.47 (p = 0.001) | 16.99 (p = 0.001) | 26.44 (p = 0.001) |

Wald test spatial error | 62.24 (p = 0.001) | 16.14 (p = 0.002) | 25.85 (p = 0.001) |

LR test spatial lag | 64.84 (p = 0.001) | 18.89 (p = 0.001) | 29.64 (p = 0.001) |

LR test spatial error | 65.93 (p = 0.001) | 18.58 (p = 0.001) | 30.77 (p = 0.001) |

Direct effect ln(K/L) | 0.7173 | 0.7371 | 0.7284 |

(13.046) | (12.938) | (13.570) | |

Indirect effect ln(K/L) | −0.0500 | 0.2452 | −0.0457 |

(−0.504) | (1.265) | (−0.209) | |

Total effect ln(K/L) | 0.6673 | 0.9824 | 0.6827 |

(5.792) | (4.535) | (2.974) | |

Direct effect ln(ICT × U) | 0.0365 | 0.0284 | 0.0388 |

(1.892) | (1.447) | (2.106) | |

Indirect effect ln(ICT × U) | 0.0407 | 0.1175 | 0.0873 |

(1.494) | (2.626) | (1.713) | |

Total effect ln(ICT × U) | 0.0772 | 0.1458 | 0.1261 |

(3.338) | (3.568) | (2.746) | |

Direct effect ln(R&D) | 0.0078 | 0.0088 | 0.0071 |

(3.469) | (3.724) | (3.001) | |

Indirect effect ln(R&D) | −0.0138 | −0.0227 | −0.0403 |

(−3.006) | (−2.412) | (−3.424) | |

Total effect ln(R&D) | −0.0060 | −0.0139 | −0.0331 |

(−1.214) | (−1.386) | (−2.678) | |

Direct effect ln(Tran) | 0.1085 | 0.1239 | 0.1276 |

(4.065) | (4.207) | (4.406) | |

Indirect effect ln(Tran) | 0.4611 | 0.3062 | 0.2732 |

(7.283) | (2.365) | (1.803) | |

Total effect ln(Tran) | 0.5696 | 0.4301 | 0.4008 |

(8.326) | (3.052) | (2.508) |

## 5. Conclusions and Research Implications

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Graham, M. Warped geographies of development: The Internet and theories of economic development. Geogr. Compass
**2008**, 2, 771–789. [Google Scholar] - Moriset, B.; Malecki, E.J. Organization versus space: The paradoxical geographies of the digital economy. Geogr. Compass
**2009**, 3, 256–274. [Google Scholar] - Oliner, S.D.; Sichel, D.E.; Triplett, J.E.; Gordon, R.J. Computers and output growth revisited: How big is the puzzle. Brook. Pap. Econ. Act.
**1994**, 2, 273–334. [Google Scholar] - Stiroh, K.J. Computers, productivity, and input substitution. Econ. Inq.
**1998**, 6, 175–191. [Google Scholar] - Jorgenson, D.W.; Stiroh, K.J.; Gordon, R.J.; Sichel, D.E. Raising the speed limit: US economic growth in the information age. Brook. Pap. Econ. Act.
**2000**, 1, 125–235. [Google Scholar] - Jorgenson, D.W. Information technology and the US economy. Am. Econ. Rev.
**2001**, 91, 1–32. [Google Scholar] - Jorgenson, D.W. Information technology and the G7 economies. World Econ.
**2004**, 4, 139–169. [Google Scholar] - Organisation for Economic Co-operation and Development (OECD>. The Economic Impact of ICT: Measurement, Evidence and Implications; OECD: Paris, France, 2004. [Google Scholar]
- Jorgenson, D.W.; Vu, K. Information Technology and the World Economy*. Scand. J. Econ.
**2005**, 107, 631–650. [Google Scholar] - Jorgenson, D.W.; Vu, K. Information technology and the world growth resurgence. Ger. Econ. Rev.
**2007**, 8, 125–145. [Google Scholar] - Khuong, V. Determinants of Economic Growth over the Period 1995–2005. In Proceedings of the 6th International Conference of Socio network Strategies, Osaka, Japan, 28 December 2009.
- Quah, D. ICT clusters in development: Theory and evidence. Eur. Invest. Bank Pap.
**2004**, 6, 86–100. [Google Scholar] - Koski, H.; Rouvinen, P.; Ylä-Anttila, P. ICT clusters in Europe the great central banana and the small Nordic potato. Inf. Econ. Policy
**2002**, 14, 145–165. [Google Scholar] - Wong, P.K. ICT production and diffusion in Asia Digital dividends or digital divide. Inf. Econ. Policy
**2002**, 14, 167–187. [Google Scholar] - InfoCom Research, Inc. Investigation Report on Regional Economic Growth resulting from Ubiquitous Process; Ministry of Internal Affairs and Communications: Tokyo, Japan, 2008. [Google Scholar]
- Alessandra, C.; Schreyer, P. ICT investment and economic growth in the 1990s: Is the United States a unique case? A comparative study of nine OECD countries. Rev. Econ. Times
**2002**, 5, 408–442. [Google Scholar] - LeSage, J.P.; Pace, R.K. Introduction to Spatial Econometrics; CRC Press Taylor and Francis Group: Boca Raton, FL, USA, 2009. [Google Scholar]
- Lin, G.P.; Long, Z.H.; Wu, M. A Spatial Econometric Analysis of Regional Economic Convergence in China, 1978–2002. China Econ. Q.
**2005**, 5, 67–82. [Google Scholar] - Elhorst, J.P. Spatial Panel Data Models. In Handbook of Applied Spatial Analysis; Springer: Berlin/Heidelberg, Germany, 2010; pp. 377–407. [Google Scholar]
- Elhorst, J.P. Matlab Software for Spatial Panels. Available online: http://www.regroningen.nl (accessed on 12 March 2010).
- Pilat, D. ICT and Economic Growth: Evidence from OECD Countries, Industries and Firms; Organisation for Economic Co-operation and Development (OECD): Paris, France, 2003. [Google Scholar]

© 2014 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sun, C.; Jiao, H.; Ren, Y.
Regional Informatization and Economic Growth in Japan: An Empirical Study Based on Spatial Econometric Analysis. *Sustainability* **2014**, *6*, 7121-7141.
https://doi.org/10.3390/su6107121

**AMA Style**

Sun C, Jiao H, Ren Y.
Regional Informatization and Economic Growth in Japan: An Empirical Study Based on Spatial Econometric Analysis. *Sustainability*. 2014; 6(10):7121-7141.
https://doi.org/10.3390/su6107121

**Chicago/Turabian Style**

Sun, Chuan, Hao Jiao, and Yun Ren.
2014. "Regional Informatization and Economic Growth in Japan: An Empirical Study Based on Spatial Econometric Analysis" *Sustainability* 6, no. 10: 7121-7141.
https://doi.org/10.3390/su6107121