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Credit depth, government intervention and innovation in China: evidence from the provincial data

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Abstract

This paper investigates the role of regional credit systems for Chinese regional innovation, using data for the period 2000–2008. Both the effects of credit depth and government intervention are investigated. Results show that regional credit depth has a significantly positive effect on regional innovation performance. Credit depth has more marked impacts on major innovations (i.e., invention patents) than on less complicated innovations (i.e., utility model and external design patents). Additionally, our results do not suggest a reduction in the efficiency of regional innovation from increased government intervention via state-owned commercial banks.

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Notes

  1. See Wang and Thornhill (2010) for a good review of this literature.

  2. However, we should qualify this by noting that Allen and Gale (2001) have hinted that more work needs to be done on which factors cause firms to take up a bank loan vis-à-vis which factors induce a firm to favour internal finance. An example of this kind of work for the Chinese context is Lian et al. (2011).

  3. Despite their IPO after 2004, the Big Four are still ultimately controlled by the Chinese government (Ye et al. 2012).

  4. Financing via stock market and venture capital funds could have similar effects on innovation as well. Both alternative financing channels in China have been far from being well-developed. This keeps their relevance for innovation financing low (OECD 2008; Wong 2006). Wong (2006) specifically indicated that the stock market is not yet an attractive investment venue “because its regulations to improve transparency are still inadequate (Wong 2006: 420)”.

  5. A fact that, for instance, also emerges from Ortega-Argilés et al. (2014).

  6. Notwithstanding the pervasiveness of Levine’s credit depth measure, there are some caveats in its application. The 2008 financial crisis revealed that some of the countries with the highest values of this measure were most vulnerable if excessive use of bank credit is synonymous with a lack of market discipline. We are grateful to an anonymous referee for highlighting this fact. It will appear clear also from our results below that credit quality and bank cost efficiency are likely to matter as well.

  7. The related data (SOCBCREDIT) are only available for the period from 2001 to 2004. After 2004, such data are only available for some but not all four SOCBs. In addition, PBC (2002b–2008b) provides data on loans in RMB approved by individual SOCB and on loans in foreign currency offered by the corresponding SOCB. The latter one is presented in US$ in PBC (2002b–2008b). The total amount of SOCBCREDIT by year is the sum of both types of loans over the four SOCBs. The exchange rate used to recalculate the loans offered in US$ in the year t into RMB is an average rate based on monthly data in the year t (PBC 2000a–2008a). Data from the Industrial and Commercial Bank in 2004 represents the only exception. For that year, the bank only provides data on loans offered in US$ and data for total loans in RMB.

  8. The average exchange rate for the period from 2000 to 2008 was 8.01 [RMB/$] (PBC 2000a–2008a).

  9. We should also note that we use the first lag of the legal environment variable for the analysis. This helps to maximize the number of observations. A further reason for using the first lag is that its first order autocorrelation is about 0.95.

  10. One might well consider also the province with the second highest correlation or even the one with the third highest correlation and so on. However, we experimented with first stage regressions and including these further instruments does not seem advisable as they are not significantly correlated with the instrumented variable. In principle, it would be possible to conjecture that similar provinces in terms of financial development are so because they are similar in terms of innovation activity. However, it is possible to verify this hypothesis by checking the most correlated provinces regarding our innovation output indicators. In fact, they do not coincide with the most correlated provinces in terms of CREDIT/GDP. Therefore, our instrument is not challenged by this conjecture. More details are available from the authors upon request.

  11. The same definition as Cheung and Lin (2004) is applied: Coastal provinces (Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Guangxi, Hainan), Central provinces (Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan), and Western provinces (Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang).

  12. More information on why we decide to deal with the potential outlier problem in this way can be obtained from the authors upon request.

  13. Given the small size of the Hausman test statistics, we double check our results by running a test in the spirit of Mundlak (1978) as described by Hsiao (2003: 49–50). This test consists in inserting as auxiliary regressors the cross-sectional averages of explanatory variables and running an F-test that their coefficients are equal to zero. This can be interpreted as a consequence of absence of correlation between independent variables and cross-sectional effects and, therefore, of the suitability of the random effects estimator. Given that we are using a two-way error component model, we additionally insert time averages as auxiliary regressors. However, we have to drop the time and cross-sectional averages of the first three regressors in order to avoid multi collinarity problems. Once again we obtain very small statistics: 0.021 for all patents and for utility model patents, 0.018 for invention patents and 0.02 for external design patents. p values are always equal to one. After all, the coefficients of the within and the random effect estimators are almost identical.

  14. We also normalized all innovation variables by the province population and our results hardly changed. Further details are available from the authors upon request.

  15. Full details on first stage regression results are available from the authors upon request.

  16. Note that the interaction term is not statistically significant at the 5 % level in Table 6 for external design patents. However, once dropping insignificant regressors such as GOV/GDP, Commu_infra_pop and Legal environment, the interaction term is significant. Further results are available from the authors upon request. Given the smaller time span of the sample underlying estimates in Table 6, we prefer our baseline estimate when gauging the relative effect of financial depth on different kinds of patents.

  17. Further results are available from the authors upon request. Recall that, when, in a model, lags of the dependent variable are included alongside other explanatory variables, the short-run effect of a given explanatory variable is its regression coefficient, while the long-run effect is the regression coefficient over one minus the sum of the coefficients of the lags of the dependent variable.

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Acknowledgments

We would like to thank Michaela Rank for her excellent research and technical assistance. Liu would also like to thank the German Research Foundation (DFG) for its financial support of the cooperative project Regional Agility and Upgrading in Hong Kong and the PRD (Priority Program 1233: Megacities—Megachallenge: Informal Dynamics of Global Change). Finally, we would like to thank participants of the 14th Uddevalla Symposium 2011 at the University of Bergamo and participants of the 2011 ZEW workshop on ‘Economics of Information and Patenting’ in Mannheim for constructive comments. This paper was also presented as a guest lectures in the PhD Programme in Economics and Management at the University of Trento in February 2012 and in the MA in Business Management of the Department of Economic and Social Sciences at the Catholic University of Piacenza in May 2014. We thank for the lecture participants’ useful feedback as well.

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Technical appendix

Technical appendix

The present appendix illustrates our instrumental variable estimator. Consider a panel dataset, which has both a time and a cross-sectional dimension. In our case, cross-sectional units are provinces. Define Δ N and Δ T as two matrices containing province and time dummies, being N the number of provinces and T the one of time periods. We use bold characters to denote matrices. Call X, Z, Z ins the matrices of regressors without the constant, of regressors with the constant and the matrix of instruments respectively. In our case, Z ins is constituted of our instrument for CREDIT/GDP, the other regressors and a constant. u WI is a vector containing the residuals of the fixed effects estimator. Our computations are as follows

$$ {\mathbf{P}}_{{\mathbf{B}}} = {\varvec{\Delta}}_{{\mathbf{T}}} ({\varvec{\Delta}}_{{\mathbf{T}}}^{{\mathbf{\prime }}} {\varvec{\Delta}}_{{\mathbf{T}}} )^{{ - {\bf\it{1}}}} {\varvec{\Delta}}_{{\mathbf{T}}}^{{\mathbf{\prime }}} $$

where denotes transposition and −1 is the pseudo inverse operator.

$$ {\mathbf{Q}}_{{\mathbf{B}}} {\mathbf{ = I}}_{{{\mathbf{NT}}}} - {\mathbf{P}}_{{\mathbf{B}}} $$

where I NT is an identity matrix of size NT.

$$ {\mathbf{P}}_{{\mathbf{C}}} = {\mathbf{Q}}_{{\mathbf{B}}} {\varvec{\Delta}}_{{\mathbf{N}}} ({\varvec{\Delta}}_{{\mathbf{N}}}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{\mathbf{B}}} {\varvec{\Delta}}_{{\mathbf{N}}} )^{{ - {\bf\it{1}}}} {\varvec{\Delta}}_{{\mathbf{N}}}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{\mathbf{B}}} $$
$$ {\mathbf{Q}}_{{\mathbf{D}}} = {\mathbf{Q}}_{{\mathbf{B}}} - {\mathbf{P}}_{{\mathbf{C}}}$$
$$ {\mathbf{P}}_{{{\mathbf{QZ}}}} = {\mathbf{Q}}_{{\mathbf{D}}} {\mathbf{Z}}_{{{\mathbf{ins}}}} \left( {{\mathbf{Z}}_{{{\mathbf{ins}}}}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{\mathbf{D}}} {\mathbf{Z}}_{{{\mathbf{ins}}}} } \right)^{{ - {\bf\it{1}}}} {\mathbf{Z}}_{{{\mathbf{ins}}}}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{\mathbf{D}}} $$

where the “−1” exponential is, as customary, the inversion operator.

$$ {\text{q}}_{\text{N}} = {\mathbf{u}}_{{{\mathbf{WI}}}}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{\mathbf{D}}} {\mathbf{u}}_{{{\mathbf{WI}}}} $$
$$ {\mathbf{P}}_{{{\mathbf{d1}}}} = {\varvec{\Delta}}_{{\mathbf{N}}} \left( {{\varvec{\Delta}}_{{\mathbf{N}}}^{{\mathbf{\prime }}} {\varvec{\Delta}}_{{\mathbf{N}}} } \right)^{{ - {\mathbf{1}}}} {\varvec{\Delta}}_{{\mathbf{N}}}^{{\mathbf{\prime }}} $$
$$ {\text{q}}_{ 1} = {\mathbf{u}}_{{{\mathbf{WI}}}}^{{\mathbf{\prime }}} {\mathbf{P}}_{{{\mathbf{d1}}}} {\mathbf{u}}_{{{\mathbf{WI}}}} $$
$$ {\text{q}}_{ 2} = {\mathbf{u}}_{{{\mathbf{WI}}}}^{{\mathbf{\prime }}} {\mathbf{P}}_{{\mathbf{B}}} {\mathbf{u}}_{{{\mathbf{WI}}}} $$
$$ {\text{k}}_{\text{n}} = {\text{tr}}\left[ {\left( {{\mathbf{X}}^{{\mathbf{\prime }}} {\mathbf{P}}_{{{\mathbf{QZ}}}} {\mathbf{X}}} \right)^{{ - {\mathbf{1}}}} {\mathbf{X}}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{\mathbf{D}}} {\mathbf{X}}} \right] $$

where tr[·] is the trace operator.

$$ {\text{k}}_{ 1} = {\text{tr}}\left[ {\left( {{\mathbf{X}}^{{\mathbf{\prime }}} {\mathbf{P}}_{{{\mathbf{QZ}}}} {\mathbf{X}}} \right)^{{ - {\mathbf{1}}}} {\mathbf{X}}^{{\mathbf{\prime }}} {\mathbf{P}}_{{{\mathbf{d1}}}} {\mathbf{X}}} \right] $$
$$ {\text{k}}_{ 2} = {\text{tr}}\left[ {\left( {{\mathbf{X}}^{{\mathbf{\prime }}} {\mathbf{P}}_{{{\mathbf{QZ}}}} {\mathbf{X}}} \right)^{{ - {\mathbf{1}}}} {\mathbf{X}}^{{\mathbf{\prime }}} {\mathbf{P}}_{{\mathbf{B}}} {\mathbf{X}}} \right] $$
$$ {\text{k}}_{ 1 2} = {\text{tr}}\left[ {{\varvec{\Delta}}_{{\mathbf{T}}}^{{\mathbf{\prime }}} {\mathbf{P}}_{{{\mathbf{d1}}}} {\varvec{\Delta}}_{{\mathbf{T}}} } \right] $$
$$ {\text{k}}_{ 2 1} = {\text{tr}}\left[ {{\varvec{\Delta}}_{{\mathbf{N}}}^{{\mathbf{\prime }}} {\mathbf{P}}_{{\mathbf{B}}} {\varvec{\Delta}}_{{\mathbf{N}}} } \right] $$
$$ {\text{t}}_{ 2} = {\text{rank}}\left[ {{\varvec{\Delta}}_{{\mathbf{T}}} } \right] $$
$$ {\text{t}}_{ 1} = {\text{rank}}\left[ {{\mathbf{Q}}_{{\mathbf{B}}} {\varvec{\Delta}}_{{\mathbf{N}}} } \right] $$

where rank [·] is the rank operator.

$$ {\text{N}}_{ 1} = {\text{tr}}\left[ {{\mathbf{P}}_{{{\mathbf{d1}}}} } \right] $$
$$ {\text{N}}_{ 2} = {\text{tr}}\left[ {{\mathbf{P}}_{{\mathbf{B}}} } \right] $$
$$ S = \left[ \begin{gathered} {\text{NT}} - t_{1} - t_{2} + k_{n} \quad 0\quad \quad0 \hfill \\ N_{1} + k_{1} \quad \quad \quad \quad \quad{\text{NT}}\quad k_{12} \hfill \\ N_{2} + K_{2} \quad \quad \quad \quad \quad k_{21} \quad {\text{NT}} \hfill \\ \end{gathered} \right] $$
$$ {\mathbf{q}}_{u} = \left[ \begin{gathered} q_{n} \hfill \\ q_{1} \hfill \\ q_{2} \hfill \\ \end{gathered} \right] $$
$$ {\mathbf{s}}_{{{\mathbf{22}}}} = \left( {\mathbf{S}} \right)^{ - 1} {\mathbf{q}}_{{\mathbf{u}}} $$

Let us call s0, s1, and s2 the first, second and third elements of s 22 respectively.

$$ {\mathbf{Y}}_{ 2} \,{ = }\,\left( {\sqrt{\tfrac {{\text{s}}_{ 2} }{{\text{s}}_{ 0} }}} \right){\varvec{\Delta}}_{{\mathbf{T}}} $$
$$ {\mathbf{Y}}_{ 1} \,{ = }\,\left( {\sqrt {\tfrac{{\text{s}}_{1} } {{\text{s}}_{ 0} }}} \right){\varvec{\Delta}}_{{\mathbf{N}}} $$
$$ {\mathbf{S}}_{{{\mathbf{d2}}}} \,{ = }\,{\mathbf{I}}_{{\mathbf{T}}} + {\mathbf{Y}}_{2}^{{\mathbf{\prime }}} {\mathbf{I}}_{{{\mathbf{NT}}}} {\mathbf{Y}}_{2} $$
$$ {\mathbf{Q}}_{{{\mathbf{d2d3}}}} \,{ = }\,{\mathbf{I}}_{{{\mathbf{NT}}}} - {\mathbf{I}}_{{{\mathbf{NT}}}} {\mathbf{Y}}_{2} \left( {{\mathbf{S}}_{{{\mathbf{d2}}}} } \right)^{{ - {\mathbf{1}}}} {\mathbf{Y}}_{2}^{{\mathbf{\prime }}} {\mathbf{I}}_{{{\mathbf{NT}}}} $$
$$ {\mathbf{S}}_{{{\mathbf{d1}}}} \,{ = }\,{\mathbf{I}}_{{\mathbf{N}}} + {\mathbf{Y}}_{1}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{{\mathbf{d2d3}}}} {\mathbf{Y}}_{{\mathbf{1}}} $$
$$ {\varvec{\Omega}}^{{ - \text{1}}} \,{ = }\,\left( {{\text{s}}_{{\text{0}}} } \right)^{{ - \text{1}}} \left( {{\mathbf{Q}}_{{{\mathbf{d2d3}}}} - {\mathbf{Q}}_{{{\mathbf{d2d3}}}} {\mathbf{Y}}_{\text{1}} \left( {{\mathbf{S}}_{{{\mathbf{d1}}}} } \right)^{{ - \text{1}}} {\mathbf{Y}}_{1}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{{\mathbf{d2d3}}}} } \right) $$
$$ {\mathbf{R}}\,{ = }\,{\varvec{\Omega}}^{ - 1} \times \left( {{\mathbf{I}}_{{{\mathbf{NT}}}} - {\mathbf{X}}\left( {{\mathbf{X}}^{{\mathbf{\prime }}} {\varvec{\Omega}}^{ - 1} {\mathbf{X}}} \right)^{ - 1} {\mathbf{X}}^{{\mathbf{\prime }}} {\varvec{\Omega}}^{ - 1} } \right) $$
$$ {\mathbf{V}}_{{\mathbf{0}}} \,{ = }\,{\mathbf{ I}}_{{{\mathbf{NT}}}} {\mathbf{I}}^{{\mathbf{\prime }}}_{{{\mathbf{NT}}}} $$
$$ {\mathbf{V}}_{{\mathbf{1}}} \,{ = }\,{\varvec{\Delta}}_{{\mathbf{N}}} {\varvec{\Delta}}_{{\mathbf{N}}}^{{\mathbf{\prime }}} $$
$$ {\mathbf{V}}_{{\mathbf{2}}} \,{ = }\,{\varvec{\Delta}}_{{\mathbf{T}}} {\varvec{\Delta}}_{{\mathbf{T}}}^{{\mathbf{\prime }}} $$
$$ {\mathbf{W}}\,{ = }\,\left[ \begin{gathered} {\text{tr(}}{\mathbf{V}}_{{\mathbf{0}}} {\mathbf{RV}}_{{\mathbf{0}}} {\mathbf{R}} )\quad {\text{tr(}}{\mathbf{V}}_{{\mathbf{0}}} {\mathbf{RV}}_{{\mathbf{1}}} {\mathbf{R}} )\quad {\text{tr(}}{\mathbf{V}}_{{\mathbf{0}}} {\mathbf{RV}}_{{\mathbf{2}}} {\mathbf{R}} )\hfill \\ {\text{tr(}}{\mathbf{V}}_{{\mathbf{1}}} {\mathbf{RV}}_{{\mathbf{0}}} {\mathbf{R}} )\quad {\text{tr(}}{\mathbf{V}}_{{\mathbf{1}}} {\mathbf{RV}}_{{\mathbf{1}}} {\mathbf{R}} )\quad {\text{tr(}}{\mathbf{V}}_{{\mathbf{1}}} {\mathbf{RV}}_{{\mathbf{2}}} {\mathbf{R}} )\hfill \\ {\text{tr(}}{\mathbf{V}}_{{\mathbf{2}}} {\mathbf{RV}}_{{\mathbf{0}}} {\mathbf{R}} )\quad {\text{tr(}}{\mathbf{V}}_{{\mathbf{2}}} {\mathbf{RV}}_{{\mathbf{1}}} {\mathbf{R}} )\quad {\text{tr(}}{\mathbf{V}}_{{\mathbf{2}}} {\mathbf{RV}}_{{\mathbf{2}}} {\mathbf{R}} )\hfill \\ \end{gathered} \right] $$
$$ {\mathbf{u}}\,{ = }\,\,\left[ \begin{gathered} {\mathbf{y}}^{{\mathbf{\prime }}} {\mathbf{RV}}_{{\mathbf{0}}} {\mathbf{Ry}} \hfill \\ {\mathbf{y}}^{{\mathbf{\prime }}} {\mathbf{RV}}_{{\mathbf{1}}} {\mathbf{Ry}} \hfill \\ {\mathbf{y}}^{{\mathbf{\prime }}} {\mathbf{RV}}_{{\mathbf{2}}} {\mathbf{Ry}} \hfill \\ \end{gathered} \right] $$
$$ \uptheta\,{ = }\,\left( {\mathbf{W}} \right)^{ - 1} {\mathbf{u}} $$

Let us call s, s, and s the first, second and third elements of θ respectively

$$ {\mathbf{Y}}_{{{\mathbf{2\theta }}}} \,{ = }\,\left({\sqrt {\tfrac{{\text{s}}_{ 2\uptheta}}{{\text{s}}_{ 0\uptheta}}} }\right){\varvec{\Delta}}_{{\mathbf{T}}} $$
$$ {\mathbf{Y}}_{{ 1\uptheta}} { = }\left( {\sqrt {\tfrac{{\text{s}}_{ 1\uptheta} } {{\text{s}}_{ 0\theta } }} }\right){\varvec{\Delta}}_{{\mathbf{N}}} $$
$$ {\mathbf{S}}_{{{\mathbf{d2}}\uptheta}} = {\mathbf{I}}_{{\mathbf{T}}} + {\mathbf{Y}}_{{{2\theta }}}^{{\mathbf{\prime }}} {\mathbf{I}}_{{{\mathbf{NT}}}} {\mathbf{Y}}_{{{2\theta }}} $$
$$ {\mathbf{Q}}_{{{\mathbf{d2d3}}{\varvec{\uptheta}}}} = {\mathbf{I}}_{{{\mathbf{NT}}}} - {\mathbf{I}}_{{{\mathbf{NT}}}} {\mathbf{Y}}_{{{\mathbf{2}}{\varvec{\uptheta}}}} {\mathbf{S}}_{{{\mathbf{d2}}{\varvec{\uptheta}}}} {\mathbf{Y}}_{{{\mathbf{2}}{\varvec{\uptheta}}}}^{{\mathbf{\prime }}} {\mathbf{I}}_{{{\mathbf{NT}}}} $$
$$ {\mathbf{S}}_{{{\mathbf{d1}}{\varvec{\uptheta}}}} = {\mathbf{I}}_{{\mathbf{N}}} + {\mathbf{Y}}_{{{\mathbf{1}}{\varvec{\uptheta}}}}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{{\mathbf{d2d3}}{\varvec{\uptheta}}}} {\mathbf{Y}}_{{{\mathbf{1}}{\varvec{\uptheta}}}} $$
$$ {\mathbf{\Omega}}_{\varvec{\uptheta}}^{ - {\mathbf{1}}}= ({\text{s}}_{{0{\uptheta}}} )^{ - 1} ({\mathbf{Q}}_{{{\mathbf{d2d3}}{\varvec{\uptheta}}}} - {\mathbf{Q}}_{{{\mathbf{d2d3}}{\varvec{\uptheta}}}} {\mathbf{Y}}_{{{\mathbf{1}}{\varvec{\uptheta}}}} ({\mathbf{S}}_{{{\mathbf{d1}}{\varvec{\uptheta}}}} )^{{ - {\mathbf{1}}}} {\mathbf{Y}}_{{{\mathbf{1}}{\varvec{\uptheta}}}}^{{\mathbf{\prime }}} {\mathbf{Q}}_{{{\mathbf{d2d3}}{\varvec{\uptheta}}}} ) $$

Our IV estimator finally is \( {\varvec{\upbeta}}_{{{\varvec{\uptheta}},{\mathbf{IV}}}} = ({\mathbf{Z}}^{{\mathbf{\prime }}} {\mathbf{\Omega}}_{{\varvec{\uptheta}}}^{{ - {\mathbf{1}}}} {\mathbf{Z}}_{{{\mathbf{ins}}}} ({\mathbf{Z}}_{{{\mathbf{ins}}}}^{{\mathbf{\prime }}} {\mathbf{\Omega}}_{{\varvec{\uptheta}}}^{{ - {\mathbf{1}}}} {\mathbf{Z}}_{{{\mathbf{ins}}}} )^{ - {\mathbf{1}}} {\mathbf{Z}}_{{{\mathbf{ins}}}}^{{\mathbf{\prime }}} {\mathbf{\Omega}}_{{\varvec{\uptheta}}}^{{ - {\mathbf{1}}}} {\mathbf{Z}})^{ - {\mathbf{1}}} {\mathbf{Z}}^{{\mathbf{\prime }}} {\mathbf{\Omega}}_{{\varvec{\uptheta}}}^{{ - {\mathbf{1}}}} {\mathbf{Z}}_{{{\mathbf{ins}}}} ({\mathbf{Z}}_{{{\mathbf{ins}}}}^{{\mathbf{\prime }}} {\mathbf{\Omega}}_{{\varvec{\uptheta}}}^{{ - {\mathbf{1}}}} {\mathbf{Z}}_{{{\mathbf{ins}}}} )^{ - {\mathbf{1}}} {\mathbf{Z}}_{{{\mathbf{ins}}}}^{{\mathbf{\prime }}} {\mathbf{\Omega}}_{{\varvec{\uptheta}}}^{{ - {\mathbf{1}}}} {\mathbf{y}} \) and its variance-covariance matrix is \( ({\mathbf{Z}}^{{\mathbf{\prime }}} {\mathbf{\Omega}}_{{\varvec{\uptheta}}}^{{ - {\mathbf{1}}}} {\mathbf{Z}}_{{{\mathbf{ins}}}} ({\mathbf{Z}}_{{{\mathbf{ins}}}}^{{\mathbf{\prime }}} {\mathbf{\Omega}}_{{\varvec{\uptheta}}}^{{ - {\mathbf{1}}}} {\mathbf{Z}}_{{{\mathbf{ins}}}} )^{ \mathbf{-1}} {\mathbf{Z}}_{{{\mathbf{ins}}}}^{{\mathbf{\prime }}} {\mathbf{\Omega}}_{{\varvec{\uptheta}}}^{{ {\mathbf{-1}}}} {\mathbf{Z}})^{ \mathbf{-1}} \).

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Hanley, A., Liu, WH. & Vaona, A. Credit depth, government intervention and innovation in China: evidence from the provincial data. Eurasian Bus Rev 5, 73–98 (2015). https://doi.org/10.1007/s40821-015-0016-2

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