A crucial number of papers suggest the channels through which fiscal decentralization has positive effects on fiscal efficiency and economic growth [9] . First, the main theory of fiscal decentralization, the “first generation” theory developed by [10] [11] , argues that fiscal decentralization boosts economic efficiency because local governments deeply perceive better local circumstances and preferences in the supply of public goods and services than central governments. These informal advantages may help local governments to deliver public goods and services at lower cost that are highly appropriate to local needs. Thus, first generation theory suggests that central governments should distribute corresponding grants to local governments. Secondly, through diversifying local output based on local needs, fiscal decentralization may increase local social welfare [12] . In cases where there are differences in local needs for public goods and services among regions, uniform distribution of public goods and services across regions may be inefficient [12] . This diversification also enables residents to move freely to the region that best meets their individual demand for public goods and services, and lower local tax rate. Hence, a Tiebout classification (A jurisdiction is a group of individuals who collectively provide public goods for themselves exclusively—the public goods are local. Tiebout also suggested that individuals would sort into taste-homogeneous jurisdictions) of individuals into demand-homogeneous communities further improves efficiency in resource allocation. Thirdly, local governments may closely be monitored by their constituencies. Fiscal decentralization leads to greater local accountability. This greater accountability helps to enhance the efficiency in the production and supply of public goods and services [3] . In addition, fiscal decentralization reduces the relative share of unproductive component and increases the productive component in public investment because fiscal competition boosts the quality of public spending [13] . So, by changing the public investment composition toward the economic productive, fiscal decentralization can consequently foster economic growth. Finally, fiscal decentralization is connected with improved level of policy innovation, greater transparency, and better ability of governments to adapt appropriate policies to local preferences [2] .

However, there also exist some mechanisms through which fiscal decentralization is detrimental to economic development. First, it is not easy to link advantageous factors of fiscal decentralization with increased economic performance specially in countries lacking the appropriate institutions, fully legal systems, and human capital, economic growth does not seem to rise as a direct result of fiscal decentralization [14] . On one hand, fiscal decentralization may negatively affect the allocation of public goods and services among regions because the mobility of households and firms can restrict attempts to redistribute effectively income. Redistribution policies may induce low income individuals to move into the jurisdiction while rich individuals (who bear a high tax rate) move out [15] . On the other hand, concentration of public goods and services in a few geographical locations may impede per capita growth because regional inequalities in healthcare, education, and infrastructure development can constrain full use of production factors [15] . In particular, fiscal decentralization may lead to a race to the top among local governments and an oversupply of tax incentives for foreign investors, restricting the investment and development of private sector [16] and make local administration reluctant to reinforce environmental policy stringency and the polluted environment casts a shadow on the economic success [17] .

The empirical evidence on fiscal decentralization-growth nexus can be drawn from the recent literature review. First, some papers use only one measure of fiscal decentralization to examine the fiscal decentralization-growth relationship [18] [19] . [18] find the positive impact of fiscal decentralization in Spain using S-GMM for a panel data of 17 regions over the period 1970-2000. Similarly, [19] indicate a positive fiscal decentralization-growth relationship in 28 provinces in China in both short run and long run through ARDL (Autoregressive-Distributed Lag) bounds tests and PMG (Pooled Mean Group) estimators with time series data from the period 1979-2009. They argue close relations between provincial governments and their constituents may promote to invest in human capital, and education and training at the local level, which results in a high growth rate.

On the other hand, most researchers use two measures of fiscal decentralization, revenue decentralization and expenditure decentralization, in their papers. [9] [20] both show the positive impact of revenue decentralization and the negative impact of expenditure decentralization. [20] use fixed effects for a panel data of 61 provinces in Vietnam over the period 1997-2007 while [9] apply the PMG estimator for a panel data of 23 OECD countries during the period 1972-2005. Meanwhile, [14] [21] [22] all show the negative impacts of both revenue decentralization and expenditure decentralization. [14] use fixed effects for a panel data of 16 Central and Eastern European countries from 1990 to 2004 and [21] use OLS for 21 OECD countries during the period between 1990 and 2005 while [22] apply OLS and 2SLS estimators for a panel data of 56 countries over the period 1990-2007. Conversely, [23] note the negative impact of revenue decentralization and the positive impact of expenditure decentralization for a sample cross-section data (26 provinces) in Indonesia from 1992 to 2002 via GLS estimation (fixed and random effects), but [24] reports the positive impacts of both revenue decentralization and expenditure decentralization for a panel data set of 30 provinces in China during the period of 1994-2002 with fixed effects and random effects. In the same vein, [25] show the positive impact of revenue decentralization and the insignificant impact of expenditure decentralization using fixed effects and two-step system GMM Arellano-Bond for an unbalanced panel data of 17 regions in Spain over the period of 1985-2004. More interestingly, [26] present an inverted-U-shaped relationship between fiscal decentralization and economic growth with a panel dataset of 29 provinces in China over the 1995-2014 period through a simultaneous equations system. These findings show a threshold level of fiscal decentralization below which fiscal decentralization promotes economic growth and above which fiscal decentralization impedes growth rate.

Finally, through three measures of fiscal decentralization, [27] indicates decentralization is positively related to economic growth in 20 high-income OECD countries from 1972 to 2005 using pooled OLS estimator. He also emphasizes that economic freedom boosts the positive growth effects of fiscal decentralization.

In relevance to the FDI-growth relationship, a thorough review of the literature carried out by [28] indicates 108 empirical investigations with 880 regression estimations using data from around the world. Around half of the studies find a significantly positive effect (43%), about one-fifth note a significantly negative effect (17%), and remaining report an insignificant effect (40%). First, technology transfer helps human capital accumulation which can lead to facilitate economic development [29] . Using a simultaneous equations model based on GMM estimation for a panel data of 61 provinces in Vietnam over the period 1996-2005, [29] reveal a positive two-way linkage between FDI and economic growth. Similarly, [30] find FDI inflows and human capital development strongly affect economic growth in Malaysia over the period 1975-2010 using Johansen co-integration test and Hierarchical Multiple Regression analysis. Recently, [31] report a positive two-way relationship between FDI inflow and economic growth for Tunisia, Morocco, and Egypt from 1985 to 2011 through a simultaneous equations model and GMM estimator. Second, host countries have good opportunities to access foreign markets when FDI firms use these countries as an export platform to sell goods and services in the region. So, FDI inflows seem to offer good features such as financial resource augmentation, high level of stability, effects of positive productivity and access to foreign markets [28] [32] . [32] confirms that the relationship between FDI inflow and economic growth is a two-way by employing simultaneous system of equations for cross-country data of 124 countries during the period 1971-2010. [28] note FDI inflow positively affects economic growth by using the meta-regression analysis for a growing number of papers and a pooled OLS estimation of five-year averaged panel data for 140 countries over the period 1970-2009. Third, the positive contribution of FDI inflows to economic development in the host countries comes from an increase in national productivity by supplying new investment capitals, innovations in technology and skills in management [33] . FDI inflows can boost economic growth by crowding-in domestic investment, and via the interaction between advanced technology from FDI inflows and the host countries’ human capital. [33] shows a positive co-integrating relationship between FDI inflow and growth in long run for a panel data of 18 countries in the Eurozone during the period from 2002 to 2012 via the estimation methods of Fully Modified OLS (FMOLS) and Dynamic OLS (DOLS).

Conversely, the negative impact of FDI on economic growth is that foreign companies reduce the productivity of domestic enterprises via competition effects [34] . [34] confirms that FDI inflow has a significantly negative impact on growth a sample of 44 developing countries over the period 1970-2005 with group-mean panel dynamic OLS estimator.

In sum, no existing papers examine the role of FDI in the fiscal decentralization-growth relationship in the related literature so far. So, it is a research gap that this study will address to contribute to the literature.

The following empirical model is basically relied on the analytical framework developed by [39] . However, it has been modified considerably by incorporating FDI and some other variables. The final empirical equation is as follows

Y i t = α 0 + γ 0 Y i t − 1 + X i t γ ′ 1 + Z i t γ ′ 2 + η i + ζ i t (1)

where subscript i and t are the province and time index, respectively. Variable Y i t is the natural logarithm of real GDP per capita, Y i t − 1 is proxy for initial level of income, X_it is the main variables of interest (revenue/expenditure decentralization FDI, and their interaction term), Z_it is a set of control variables (private investment, government investment, labor force, trade openness, infrastructure, and consumer price index); η i is an unobserved time-invariant, province-specific effect and ζ i t is an observation-specific error term. The coefficient γ₀ in Equation (1) will be positive if it is conditional convergent and negative if divergent [40] [41] .

For Equation (1), the presence of the lagged dependent variable gives rise to autocorrelation. It can make OLS inconsistency and estimates bias for short time dimension (small T) [42] . Therefore, we decide to use the Arellano-Bond S-GMM [43] first proposed by [44] . The Arellano-Bond estimator was designed for dynamic “small-T large-N” panels [42] [45] . In the standard GMM procedure, it is essential to distinguish instrumented variables and instruments. Endogenous variables are put in the group of instrumented variables by lags of these variables [42] . Strictly exogenous regressors, as well as extra instruments, are put in the group of instrument variables and included in standard IV procedure. For exogenous variables, level and lags of them are the suitable instruments [42] .

The validity of instruments in S-GMM is assessed through Sargan statistic and Arellano-Bond statistic. The Sargan test with null hypothesis H₀: the instrument is strictly exogenous, which means that it does not correlate with errors. Thus, the p-value of Sargan statistic is as big as possible. The Arellano-Bond test is used to detect the autocorrelation of errors in first difference. Thus, the test result of first autocorrelation of errors, AR (1) is ignored while the second autocorrelation of errors, AR (2), is tested on the first difference series of errors to detect the phenomenon of first autocorrelation of errors, AR (1).

To further check the robustness of estimates, we perform two ways. The first one is to use an alternative measure of fiscal decentralization in the empirical model, and the second is to apply two alternative estimators, D-GMM and FE-2SLS. FE-2SLS is proposed by [46] since it performs better if the empirical equation of interest contains endogenous explanatory variables and unobserved heterogeneity.

¹Ha Noi, Vinh Phuc, Bac Ninh, Quang Ninh, Hai Duong, Hai Phong, Hung Yen, Thai Binh, Ha Nam, Nam Dinh, Ninh Binh, Cao Bang, Lao Cai, Yen Bai, Thai Nguyen, Lang Son, Bac Giang, Phu Tho, Son La, Hoa Binh, Thanh Hoa, Nghe An, Ha Tinh, Quang Tri, Thua Thien-Hue, Da Nang, Quang Nam, Quang Ngai, Binh Dinh, Phu Yen, Khanh Hoa, Ninh Thuan, Binh Thuan, Dak Nong, Lam Dong, Binh Phuoc, Tay Ninh, Binh Duong, Dong Nai, Ba Ria-Vung Tau, Ho Chi Minh City, Long An, Tien Giang, Ben Tre, Tra Vinh, Vinh Long, An Giang, Kien Giang, Can Tho, Hau Giang, Bac Lieu, and Ca Mau.

²Ha Giang, Bac Kan, Tuyen Quang, Dien Bien, Lai Chau, Quang Tri, Kom Tum, Gia Lai, Dak Lak, Dong Thap, Soc Trang.

The dataset is extracted from annual data of General Statistics Office of Vietnam (GSO) to accommodate the panel data of 52 provinces¹ in the period of 2007-2016. Due to data not available, 11² out of 63 provinces are eliminated. The definition and calculation of variables are given in Appendix A. The statistical description of all data from GSO is presented in Table 1.

The matrix of correlation coefficients is given in Table 2. All coefficients between independent variables and the dependent variable are statistically significant at least at 5%. Expenditure and revenue decentralization, FDI, trade openness, and infrastructure are positively correlated while government investment, private investment, labor force, and consumer price index are negatively associated with growth rate. In addition, the value of all correlation coefficients between independent variables is lower than 0.8, eliminating the possibility of co-linearity between these variables. However, the correlation coefficient between expenditure decentralization and revenue decentralization is 0.85, thus these two variables are separately used in the empirical equation.

Source: processing by Stata software.

Note: ***, ** and *denote significance at 1%, 5% and 10% respectively. Source: processing by Stata software.

The estimated results derived from S-GMM are shown in Table 3. Column 3 is the full model while Column 1 and Column 2 are the reduced models without one/two variable(s), respectively. Removing some variables out of model is applied to check the reliability of the sign and significance of estimated coefficients. The results show that sign, size and significance of estimated coefficients, especially the coefficients of revenue decentralization, expenditure decentralization, FDI, and interaction terms in Table 3 are nearly unchanged.

In the estimation procedure, we detect that trade openness is endogenous, so we use the lags of trade openness as instrumented while the remaining variables (GDP per capita, expenditure decentralization, revenue decentralization, FDI, government investment, private investment, labor force, and consumer price

Note: ***, ** and *denote significance at 1%, 5% and 10% respectively; Source: processing by Stata software.

index, and infrastructure) as instruments. In order to assess the validity of these instruments and the serial auto-correlation of residuals, we performs the Sargan and Hansen tests (test of over-identifying restrictions with the null hypothesis “the instruments as a group are exogenous”) as well as the Arellano-Bond test for serial correlation AR (2), which is applied to the difference residuals to purge the unobserved and perfectly auto-correlated. The results of these tests show that all null hypothesizes are accepted. Thus, instruments are appropriate and there is no phenomenon of serial correlation for residuals in second differences.

In short, the estimated results in Table 3 show that:

1) The coefficient of first lag of real GDP per capita is significantly positive, confirming the conditional convergence of per capita income among provinces in the long term [40] [41] .

2) The coefficients of revenue decentralization, expenditure decentralization and FDI are significantly positive, but the coefficients of their interaction terms are significantly negative.

3) The coefficient of public investment is significantly negative.

The positive effect of revenue decentralization is in agreement with some previous papers [9] [20] [25] while that of expenditure decentralization is similar to [23] . These results re-confirm the prior findings in [22] and [24] that revenue decentralization and expenditure decentralization both significantly foster economic growth. In line with previous literature [47] [48] [49] [50] , the findings in this study show that FDI significantly boosts economic growth in Vietnam.

Unlike the effects of revenue decentralization, expenditure decentralization and FDI, their interaction terms have significantly negative impacts on economic growth. Fiscal decentralization promotes more FDI inflows into local regions [6] [7] [51] . In the same time, fiscal decentralization may trigger a race to the top among local governments to attract FDI inflows, which leads to an oversupply of tax incentives for foreign investors [16] . Therefore, in Vietnam more fiscal decentralization may lead to more power to local governments in attracting FDI inflows. In order to attract more FDI inflows for local economic development, it does not exclude the possibility that local governments in Vietnam lower the environmental standards and give tax incentives for foreign investors. The extra increase in FDI inflows from fiscal decentralization may set up “the problems of FDI enterprises in Vietnam” such as activities of transfer pricing to evade tax, activities causing environmental pollution [50] , which can have a detrimental influence on local economic growth.

Contrary to some previous studies [52] [53] [54] [55] , in this study public investment has a negative impact on economic growth. Poor quality of policies and institutions may be a main cause. The design, formulation, and implementation of policies cannot take account of crowding-out effect of public sector on private sector as well as can not strictly monitor and supervise the efficiency and rationality of public investment projects, so public capital spending in Vietnam impedes economic growth.