Near universal values of social inequality indices in self-organized critical models

We have studied few social inequality measures associated with the sub-critical dynamical features (measured in terms of the avalanche size distributions) of four self-organized critical models while the corresponding systems approach their respective stationary critical states. It has been observed that these inequality measures (specifically the Gini and Kolkata indices) exhibit nearly universal values though the models studied here are widely different, namely the Bak-Tang-Wiesenfeld sandpile, the Manna sandpile and the quenched Edwards-Wilkinson interface, and the fiber bundle interface. These observations suggest that the self-organized critical systems have broad similarity in terms of these inequality measures. A comparison with similar earlier observations in the data of socio-economic systems with unrestricted competitions suggest the emergent inequality as a result of the possible proximity to the self-organized critical states.

Introduction
Unequal distributions of resources (for example income or wealth) among the population are ubiquitous. Social scientists, economists in particular, traditionally quantify such inequalities in distributions using some inequality indices, defined through the Lorenz function L(p) [1]. After ordering the population from the poorest to the richest, the Lorenz function L(p) is given by the cumulative wealth fraction possessed by the p fraction of the population staring from the poorest: L(0) = 0 and L(1) = 1 (see Fig. 1). If everyone had equal share of wealth, L(p) = p would be linear (called the equality line) and the old and still most popular inequality index, namely the Gini (g) index [2] is given by the ratio of the area between the equality line and the Lorenz curve and the entire area (1/2) below the equality line. As such, g = 0 corresponds to perfect equality and g = 1 corresponds to extreme inequality. Another recently introduced inequality index, namely the Kolkata (k) index [3], can be defined as the nontrivial fixed point of the complementary Lorenz functionL(p) ≡ 1 − L(p):L(k) = k. It says, (1 − k) fraction of people possess k fraction of wealth (k = 1/2 corresponds to perfect equality and k = 1 corresponds to extreme inequality). As such, k index quantifies and generalizes (see e.g., [4]) the (more than a) century old 80-20 law (k = 0.8) of Pareto [5]. Extensive analysis of social data (see e.g., [6,7]) indicated that in extremely competitive situations, the indices k and g equals each other in magnitude and becomes about 0.87. In physics, starting from kinetic theory models to that of the phase transitions, unequal distributions of quantities like energy, domain sizes, avalanche sizes, etc. are widely observed. In the renormalization group theory, we look for the self-similar limit (fixed point) of the generators of such distributions, where inequalities become extreme and one dominant (fractal) cluster emerges and eventually brings about the phase transition. Because of this, while the fractal dimensions (exponents) become universal, the fixed point itself (where only a single dominant cluster emerges) do not become so. Social statistics, on the other hand, look for the fixed point of the inequality distribution, where the larger inequalities set in, but they appear with commensurately large frequencies (or numbers). This some times (most likely due to self-organization induced by extreme competition) leads to some universal value of the inequality indices (fixed points) like those of g or k indices discussed above. Indeed, a recent study [8] of the k index near the breaking point of the bundle in the Fiber Bundle model, showed that k attains a stable value of about 0.62 (or inverse of the Golden Ratio). This, however, is not a self-organized critical system and the terminal values of g and k are not equal.
In this work, we consider four models where self-organized criticality (SOC) was well investigated before. Specifically, we study the Bak-Tang-Wiesenfeld (BTW) [9] and Manna [10] sandpile models and the driven Edwards-Wilkinson (EW) [11] and the centrally loaded fiber bundle [12] interface models. In each of these models, a slow external drive brings the activity rate (toppling rate of the sand grains, or the velocity of the interface) from zero to a higher value, where it saturates upon reaching the SOC state. On the path to reach the SOC state, the avalanches or the cluster of activities are of unequal sizes. We measure the inequality indices (g and k) of the avalanche sizes for these models along their paths towards the respective SOC states. We find that in all these four SOC models the two indices (g and k) become equal (about 0.87) where the SOC sets in, even though the models represent very different universality classes.
In view of the fact that the socio-economic systems mentioned before have long been conjectured to operate near the SOC state, and the inequality analysis of those systems reveal g c = k c ≈ 0.87, there are two main implications of our observations in the SOC models here. First, it stands as the quantitative evidence of social systems with unrestricted competitions operating near the SOC state. Second, the time evolution of g and k can help in estimating the 'distance' from the SOC state, where such systems reach a steady state.

Inequality measures in the BTW and Manna sandpile models
In this section, we first describe the dynamics of the BTW [9] and Manna [10] sandpile models. In the following sub-section we describe the method used for the estimation of inequality measures and report the results obtained for these models.

Dynamics of the BTW sandpile model
On a square lattice of size L × L sand grains are dropped one at a time at the randomly selected lattice sites with coordinates (i, j). Let us denote the number of sand grains at a site by h(i, j). Therefore, the addition of a grain implies the unit increase of the height of the sand column: A threshold value h c = 4 for the height of the sand column has been pre-assigned for its stability which is assumed to be the same for all sites. If the height of a sand column becomes equal to, or larger than the threshold height i.e., h(i, j) ≥ h c , that sand column becomes unstable and it topples immediately. In a toppling, the sand column looses 4 grains which are then distributed to the neighboring sites uniformly: On receiving sand grains, some of the neighboring sites may topple again which distribute grains leading to further toppling. In this way, a cascade of sand column toppling takes place as a domino effect. The sequence of topplings is referred as an 'avalanche' which terminates only when none of the lattice sites remain unstable. The boundary of the lattice is assumed to be open on all four sides. In the case of toppling at a boundary site, one or two sand grains leave the system and never come back. A typical measure of the strength of the avalanche is the total number of toppings in an avalanche and is referred as the 'size' s of the avalanche. Usually, one starts from an empty lattice and adds sand grains one by one at randomly selected sites. Therefore, the sizes of the avalanches in the early stage are quite small which gradually become larger. Eventually, a stationary state is reached when the outflow rate sand mass becomes equal to the inflow rate on the average. In the stationary state of an infinitely large systems L → ∞ the avalanche sizes are expected to be of 'all' length and time scales and their probability distributions are characterized by the power law decays, a signature of the self-organized critical state. However, for the finite size systems the avalanche sizes are limited to some L dependent cut-off values: s c (L) ∼ L β . The average height h per site of the sand column initially grows but eventually reaches a steady value h(L) in the stationary state. For the infinitely large system h = 17/8 is an analytically estimated value [13].

Dynamics of the Manna sandpile model
This is a variant of the BTW sandpile model where the threshold height for stability is assumed to be h c = 2. When a sand column topples, it looses only 2 grains which are then distributed to the four neighboring sites, each grain is transferred to one of the neighboring sites, selected randomly.
where (i n , j n ) is a randomly selected neighboring site and the second equation is executed twice.
Using the similar open boundary condition, one finds the average height per site in the stationary state is approximately 0.717157 [14].

Inequality analysis of the sandpile models
We have studied both the BTW and Manna sandpile models in the subcritical state. Starting from a completely empty lattice, sand grains have been added on to the lattice sequentially one after another. In general, each sand grain addition results an avalanche whose size may be zero or larger. The data for only the non-zero avalanche sizes have been collected till the average height of the sand column per site reaches a pre-assigned value. The total number N of the non-zero avalanches depend on the value of the terminating average height h(L) where we stop the simulation. In Fig.  2(a) we have plotted this fluctuating sequence of the avalanche sizes s i as they occur during the sand dropping process, against their serial number i. The avalanche cluster sizes are then sorted out in an ordered increasing sequence {s i , i = 1, N }. Further, we have defined a quantity p which is the fraction of avalanches, starting from the smallest to the largest. Simultaneously, we have defined the Lorenz function which represents the fractional cumulative size and its value has been plotted against p (Fig. 2(b)). On this plot both the axes have been normalized to unity. We also draw the y = 1 − x line and the value of the Kolkata index k is obtained by the value of p coordinate of the point of intersection of the L(p) vs. p curve (shown in red) and the y = 1 − x line. In addition, the Gini coefficient g is obtained by doubling the area between the Lorenz curve and the diagonal y = x line. The values of the Kolkata index (k) and the Gini coefficient (g) have been plotted for the BTW and Manna sandpile models in Fig. 3(a) and Fig. 3 The values of the system size dependent indices are then extrapolated to obtain their asymptotic values in the limit of infinite system size. First, the values of k c (L) = g c (L) have been plotted against L in Fig. 4 (a) for the BTW model. In the lower panel Fig. 4(b) the same values have been plotted against L −1/ν and the value of ν has been tuned so that the data fits best to a linear least square fit. We obtain 1/ν = 1.776 and asymptotic values of the indices k c = g c = 0.863 in the limit of L → ∞. A similar plot in the Fig. 5(a) and Fig. 5(b) for the Manna sandpile yields the best fitted results 1/ν = 2.162 and k c = g c = 0.855 in the limit of L → ∞. A similar method of data analysis had been used to find the asymptotic value of the terminating average height h(L) . In Fig. 6(a) the average heights per site of the BTW model had been extrapolated against L −1.459 to obtain the best linear fit. In the limit of L → ∞, we get h c = 2.087. This value is somewhat smaller than the value of the average height 17/8 [13] per site for the BTW model in the limit of L → ∞. Similarly, in Fig. 6(b) we have extrapolated the same data of the Manna sandpile and on extrapolation against L −1.449 we obtained h c = 0.6859 to be compared with h c ≈ 0.717157 [14].
In Figs. 7(a) and 7(b), k vs g are plotted for the BTW and Manna models respectively. The initial part of the plots fit a straight line, with slopes 0.3876 and 0.3815 in the BTW and Manna models respectively. The plots intersect the k = g line at 0.8628 and 0.8556 for the two models (for system size L × L = 512 × 512).

Inequality measures in the boundary driven Edwards-Wilkinson and centrally loaded fiber bundle models
Quasistatically driven interfaces through a quenched disordered medium can show self-organized critical behavior. Here we analyze two such models, namely the Edwards-Wilkinson mode [11] and the centrally loaded fiber bundle model [12]. Below we first describe the dynamics of these models and then report the inequality measures in the avalanche sizes leading to the critical point.

Dynamics of the quenched Edwards-Wilkinson model
The Edwards-Wilkinson (EW) model [11] in 1+1 dimension is the simplest model for driven interfaces through random media. For an interface height h(x, t), it reads where η(x, h) is a quenched noise (pinning force) and F is the driving force. The dynamics of the model can be represented in the discrete form as follows The random pinning forces η i (h) are drawn from some probability distribution. While a depinning tradition can be observed for F > F c , we study here the self-organized critical dynamics of the model, which is driven only at the boundaries [15]. We take a chain of length L and in each stable configuration, move the 0th and L − 1st points by one unit. There is n other external force anywhere else on the chain. The drive may cause instabilities i.e., other points may move, resulting in an avalanche. The total number of steps moved by all elements until the next stable configuration is reached, is defined as the avalanche size s. Following some transient behavior, the model reaches a self-organized critical state, where the height difference between the end points and the middle point of the chain reaches a stationary value and fluctuates around it. The size distribution of avalanches follow a power law.

Dynamics of the centrally loaded fiber bundle model
The fiber bundle model [16] is a generic model for failures in disordered materials. For almost a century, the model have been studied by engineers and physicists in the context of catastrophic breakdown processes in driven disordered materials. The centrally loaded fiber bundle model [12], however, does not lead to catastrophic breakdown, but reaches a steady state. The model consists of linear elastic fibers, arranged in a square grid, that are clamped between two plates. The fibers are linear elastic, until the load on it reaches a threshold, beyond which it breaks irreversibly. While the elastic moduli of all fibers are the same, the failure thresholds are in general different and are drawn from a distribution function. The width of the distribution function is a measure of the disorder in the system.
The top plate, from which the fibers are hanging, is rigid, but the bottom plate is very soft. Then a load is applied on a central location, whih is carried by one centrally located fiber. When the load is gradually increased, it crosses the failure threshold of the fiber and the fiber breaks. The load is then carried by it's four nearest neighbors. If that leads to breaking of any one of those neighboring fibers, then the load carried by that fiber is redistributed equally between the surviving neighbors of that broken fiber. For any given load, the centrally located damaged area will continue to increase until a point when all fibers along the damage boundary carry loads that are less than their respective failure thresholds. The load on all fibers along the damage boundary is then increased uniformly until the point when one more fiber breaks and the dynamics is restarted. The numbers of fibers breaking between two successive stable states is the size of the avalanche. Given that the damage boundary, hence the numbers of fibers carrying the applied load will keep  on increasing, the model will never show catastrophic breakdown in the thermodynamic limit. It turns out that the average load per fiber reaches a value 1/3, if the threshold distribution is uniform in (0,1). This is a self-organized critical point and the avalanche sizes show a power law distribution with exponent value −3/2 [12].
Here we look at the avalanches, starting from the breaking of the first centrally located fiber, as the system reaches the self-organized critical point and measure inequalities in the avalanche sizes.

Inequality analysis of the interface models
In Fig. 8(a), the averaged values of g, k and the height difference between the boundary points and the middle point scaled by a factor, are shown for uniform distributions of the pinning forces in (0,2) in the EW model. The crossing points of g and k are surprisingly close to 0.86. The same observation is found for triangular and Gaussian distributions of the pinning forces (not shown). In Fig. 8(b), we plot the same for the centrally loaded fiber bundle model. The crossing point in this case is slightly higher (0.89).
In Fig. 9(a) k versus g is plotted for the EW model. The initial part is linear, with a slope 0.40. In Fig. 9(b) the same is plotted for the centrally loaded fiber bundle model. In this case, the initial linear slope is 0.42.
Other than the surprisingly close values of the crossing points of g and k in the various different models, the linear variation with a near-universal slope in k versus g plots seems to be rather crucial. Indeed, in the rel data for diverse socioeconomic systems, such behavior have been already observed [7]. This is particularly important in view of the fact that many socioeconomic systems with unrestricted competition are assumed to be in an SOC state.

Discussions and conclusions
In socio-economic systems with unrestricted competitions, emergence of inequality in resource distributions is observed very often [7,17]. Such inequalities are quantified using some indices, related to the distributions of the individual resources through the Lorenz function L(p). Here we have studied the Gini index g (given by the ratio of the area between the equality line and the Lorenz curve and the area under the equality line), and the Kolkata index k (given by the fixed point of the complementary Lorenz functionL(p) ≡ 1 − L(p)), giving the magnitude of the fraction k of resource possessed by the fraction 1 − k of the population (see Fig. 1). It was seen before that g c = k c ≈ 0.87 in systems with unrestricted competitions (see e.g., [7,17]).
We have shown here, through numerical analysis, that the same behavior are shown by four self-organized critical models, namely the BTW sandile [9], Manna sandpile [10], quenched EW model [11] and the centrally loaded fiber bundle model [12], in their course towards the respective self-organized critical points. Particularly, from the time series of the avalanches in these models, we first construct the Lorenz curve (see Fig. 1). Then from its fixed point the inequality index k is estimated and from the area between the equality line and the Lorenz curve the value of g is estimated. The Lorenz curve is discrete here and the corresponding error bars in g and k depends upon the point spacings, which in turn depend upon the system size. Finite size scaling reveals that the crossing points of g and k as functions of the average sandpile height differ only slightly (less than 3%) from the respective critical heights. Specifically, for the BTW model, the crossing point for k and g is at k c = g c = 0.863 (Fig. 3) when extrapolated to L → ∞ while the average height of the BTW sandpile at that point is 2.087 (Fig. 5), which is slightly less than the critical height [13] of the BTW sandpile (17/8). For the Manna sandpile model, the crossing point of k and g is at k c = g c = 0.8554 (Fig. 4) The average sandpile height at that point is 0.6859 (Fig. 5), while the critical height is at 0.717157 [14] for the Manna model. Also, the slope of the k versus g line at the initial stage (prior to reaching SOC state) is 0.3876 and 0.3815 for the BTW and Manna model (Fig. 7) respectively. In the EW interface, the crossing point of k versus g is k c = g c ≃ 0.86 and that for the centrally loaded fiber bundle model is about 0.89 (Fig. 8). The initial linear part of the k versus g plots have slope 0.40 and 0.42 respectively for the EW and the centrally loaded FBM (Fig. 9). A comparison with similar observations in socio-economic data (see e.g., [17]) suggests similar emergent inequality as a result of unconstrained competitions in the social dynamics.
The underlying physical origin of this numerical observation, seen here in SOC models of distinct universality classes, and also seen elsewhere in socio-economic systems [7,17] presumably operating in SOC points, is an important open question. While some recent progresses have been made in analytically (see e.g., [18]), further extensive analysis both in models and data (e.g., see [19]) are needed.
In conclusions, the self-organized critical (SOC) models we studied here show near universal characteristics in terms of the inequality measures of their 'avalanche' statistics in their respective approach to the SOC points. This stands as a quantitative support the existence of SOC behavior in socio-economic systems. Such observations can also help in estimating the 'distance' from the imminent disaster or SOC points for those complex systems for which such model studies are not possible.


The Effect of Financial Literacy and Financial Inclusion on Economic Growth in Indonesia

Increasing financial literacy and inclusion become a global issue that are believed affecteconomic growth. However, in Indonesia, increasing financial literacy and inclusion inseveral provinces is not followed by the economic growth. The purpose of this research is toanalyze the effect of financial literacy and financial inclusion on economic growth inIndonesia.This study analyzed 34 provinces in Indonesia with 2 survey periods, 2016 and2019. The method of the data analysis used panel data regression with e-views 10 software.Moreover, Chow test and Hausman test are carried out to determine the best model. Theresults of the hypothesis test showed that financial literacy and financial inclusion have nosignificant effect on economic growth in Indonesia, neither partially or simultaneously. Itshowed that the financial literacy and inclusion improvement in Indonesia need to beenhanced in order to achieve inclusive growth as the main goal.

INTRODUCTION
In the last few decades, increasing financial literacy and inclusion has become a global issue to play an important role in promoting economic growth. According to Otoritas Jasa Keuangan (OJK) (2007), empowering consumers through financial literacy will encourage the achievement of financial system stability, improve people's welfare, reduce poverty and income inequality, as well as achieve more inclusive development. The 7th President of the Republic of Indonesia, Joko Widodo, launched the National Strategy for Indonesian Financial Literacy (SNLKI) on November 19, 2013. The SNKLI is part of the Trilogy of Policy Instruments to increase market confidence and consumer equality as well as financial services industry (level playing field).
Otoritas Jasa Keuangan (2017a), defines financial literacy as knowledge, beliefs and skills possessed by the community that can influence attitudes and behavior of the community in improving the quality of decision making and financial management to achieve public welfare.
Thus, according to the definition, it can be seen that financial service business actors, financial products consumers, and society are expected not only to know and understand financial services, but also to improve their ability to make financial decisions. Moreover, it changes their attitudes in managing finance to enhance the public welfare.
For Indonesian people, financial literacy has become a necessity for living. Therefore, the knowledge of financial literacy becomes life skill which is owned by individual in living his life for a long term. People who have high financial literacy (well literate) will more easily understand things related to financial services industry, including its products, services, and procedural. Also, they will have comprehensive information, so that they can access the products and services of the financial services industry as needed in daily life activities.
People who have high financial literacy (well literate) tend to find it easier to choose and determine financial products or services according to their respective needs and abilities, so that in the end they can improve their welfare. In addition, people who have high financial literacy (well literate) tend to have better financial management skills in supporting their financial well-being. Thus, the creation of a society that is well literate and financially inclusive will ultimately support economic growth.
The Center for Financial Inclusion defines financial inclusion (financially inclusive) as access to financial products or services as needed, including products or services in the form of credits, savings, insurance and payments. Financial inclusion also contains quality access, which includes convenience, affordability and suitability of financial products or services with regard to consumer protection. In addition, the access to these financial products or services is available to everyone.
According to the Indonesian Financial Literacy National Strategy (SNLKI), a good public financial literacy (well literate) will be followed by public financial inclusion. People who have knowledge and understanding regarding financial service institutions, skills in utilizing financial products and services, also have confidence in financial service institutions must be supported by access availability to financial institutions, financial products and financial services. Indonesian government gives special attention to increase financial inclusion in Indonesia, because national financial inclusion plays an important role in encouraging sustainable national economic growth. In addition, financial inclusion can reduce poverty and income inequality, which in turn can improve people's welfare.
According to Levine (2005), there are four roles of the financial sector that beneficial to the economy i.e., reducing risk, mobilizing savings, reducing transaction and information costs, and encouraging specialization. Through this role, the financial sector able to create capital accumulation and technological innovation to increase economic growth. Financial inclusion can increase savings mobilization, reduce transaction and information costs, increase capital allocation and asset liquidity and encourage specialization, so that can create capital accumulation which further enhances the economic growth. In addition, financial inclusion through increasing the number of credits will encourage investment in activities that have high added value and ultimately accelerate economic growth (Fabya, 2011). By making finance available and reached to all economic agents, it will affect the growth of economic activity which will increase the country's output.
The 2019 National Financial Literacy and Inclusion Survey (SNLIK) conducted by Otoritas Jasa Keuangan illustrates that Indonesia's financial literacy condition still low despite an increase from the 2 previous surveys, namely in 2013 and 2016. Indonesia's financial literacy level has increased from 21, 84% in 2013, to 29.66% in 2016, and increased to 38.03% in 2019. The survey results also showed that the financial inclusion index of the Indonesian people has increased from 59.74% in 2013 to 67.82% in in 2016 and increased again to 76.19% in 2019. However, the increase in financial literacy and inclusion in Indonesia was not accompanied by economic growth. Based on BPS data, economic growth in 2013 reached 5.56%, decreased to 5.03% in 2016, and declined again to 5.02% in 2019.
[ Figure 1 about here.] Based on Figure 1, it can be seen that the increase in Indonesia's financial literacy and inclusion in 2016 and 2019 was not accompanied by an increase in Indonesia's economic growth. This phenomenon contrast to the objectives of the National Strategy for Financial Literacy in Indonesia (SNLKI) and the National Strategy for Financial Inclusion (SNKI) which target the increasing financial literacy and inclusion to achieve inclusive economic growth. Therefore, this study will examine the effect of financial literacy and financial inclusion on economic growth in Indonesia. The results of this study are expected to be able to add a comprehensive source of reference and insight on financial literacy and financial inclusion and their impact on economic growth. The results of this study are also expected to be one of the government's considerations in making and designing policies and strategies to increase economic growth through financial literacy and inclusion. This study is also an evaluation of whether the efforts that have been made by the government to increase financial literacy and inclusion in Indonesia are in line with the targets to be achieved or still need to add steps to increase financial literacy and inclusion in order to achieve inclusive growth.

Financial Literacy
Otoritas Jasa Keuangan (20117a) provides a definition of financial literacy as outlined in Otoritas Jasa Keuangan Regulation Number 76/POJK.07/2016. The regulation explains that financial literacy is the knowledge, belief, and skills possessed by the community that can influence the attitudes and behavior of the community in improving the quality of decision making and the quality of financial management so that can achieve public welfare. Otoritas Jasa Keuangan (2017b) also provides a more detailed definition in the SNLKI (Revisit 2017). The document explains that financial literacy is public knowledge and understanding of the concepts and risks of products or services in the financial services industry, including the skills, motivations and beliefs possessed by the community to apply their knowledge and understanding in effective decision making to improve financial welfare of individuals and communities and can increase community participation in national economic activities.
When Indonesian people do not have adequate financial literacy, every individual in Indonesia cannot choose savings or investment product that is suitable for him/her. Thus, there is high potential for fraud risk. Financial literacy will occur if someone has expertise or ability that makes that person achieve his goals by utilizing existing resources (Widayati, 2010). According to Manurung (2009), financial literacy is a person's ability or knowledge in managing all of his financial resources effectively.
The purpose of financial literacy is to improve the quality of individual financial decision-making and change individual attitudes and behavior in financial management, so that to be able to determine and utilize financial institutions, products and services that are in accordance with needs and abilities of consumers and community to achieve prosperity (Financial Services Authority, 2017).
Based on National Survey of Financial Literacy and Inclusion (SNLIK) in 2013 (Financial Services Authority, 2014), the level of financial literacy of the Indonesian population is divided into four parts, i.e: 1. Well literate: it means that the public has knowledge and confidence about financial service institutions and financial service products. Knowing the features, benefits and risks, as well as rights and obligations related to financial products and services, as well as having skills in using these financial products and services. 2. Sufficient literate: the public has knowledge and confidence about financial service institutions and financial products and services. Knowing features, benefits and risks, as well as rights and obligations related to financial products and services without having skills in using these financial products and services. 3. Less literate: is when people only have knowledge about financial service institutions, financial products and services. They do not know in detail about the features, benefits and risks, as well as rights and obligations related to financial products and services. 4. Not literate, people do not have knowledge and confidence in financial institutions and services as well as financial products and services, as well as do not have skills in using financial products and services.

Financial Inclusion
The literature on financial inclusion has various concept definitions. Amidžić, Massara, and Mialou (2014) states that financial inclusion is an economic state in which individuals and companies are not denied access to financial services. The Global Financial Development Report (2014) defines financial inclusion as a condition where the majority of individuals can take advantage of available financial services and minimize the presence of groups of individuals who are not aware of the benefits of access to finance through access that is available at affordable costs. According to Bank Indonesia (2014), financial inclusion is all efforts to increase public access to banking services by eliminating all forms of obstacles. Hannig and Jansen (2010) reveals that financial inclusion is an effort to incorporate the unbanked into the formal financial system so that they have the opportunity to enjoy banking services. In addition, according to Sarma (2012) financial inclusion is a process that ensures easy access, availability, and benefits from the formal financial system for all economic actors.
According to Julie (2016) financial inclusion is an intervention strategy that seeks to overcome market frictions to prevent financial markets from operating for the poor or underprivileged. This intervention aims to attract the unbanked population into the formal financial system, so that they have the opportunity to access formal financial services ranging from savings, payments, transfers, credit and insurance. Chakrobarty (2011) says that financial inclusion promotes savings and develops a culture of saving, increases access to credit, both entrepreneurship and consumption and also enables efficient payment mechanisms, thereby strengthening the resource base of financial institutions that are able to provide economic benefits as a resource and the availability of efficient and allocative payment mechanisms. Policymakers are required to create effective opportunities for financial inclusion. Key to such interventions are policies that accelerate the introduction of innovative technologies, regulatory reforms, and infrastructure acquisitions that reduce transaction costs and enable faster, efficient and convenient delivery of financial services to a broad section of the population (Neaime and Gaysse, 2018).
Otoritas Jasa Keuangan (20117a) provides a definition of financial inclusion as outlined in Otoritas Jasa Keuangan Regulation Number 76/POJK.07/2016. According to the regulation, financial inclusion defined as the availability of access to various financial institutions, products and services in accordance with the needs and abilities of the community in order to improve the welfare of the community.
The Center for Financial Inclusion also provides a definition of financial inclusion, namely public access to financial products or services that meet community needs. These products or services include credit, savings, insurance and payments. The availability of quality access includes convenience, affordability, suitability with due regard to consumer protection, and its availability is also given to everyone.
According to Bank Indonesia (2014) financial inclusion is the right of everyone to have full access and services from financial institutions on time, convenient, informative, and affordable manner, with full respect for their dignity and worth. Financial services are available to all segments of society, with special attention to the poor, the productive poor, and residents in remote areas (Bank Indonesia, 2014).

Relationship between Financial Literacy, Financial Inclusion and Economic Growth
Economic growth is an achievement through a process that is supported by various sectors in the economy. One sector that plays an important role in supporting economic growth is the financial sector. According to Levine (2005), there are four roles of the financial sector that are beneficial to the economy, namely reducing risk, mobilizing savings, reducing transaction and information costs, and encouraging specialization. Through this role, the financial sector is able to create capital accumulation and technological innovation so as to increase economic growth. Financial inclusion can increase savings mobilization, reduce transaction and information costs, increase capital allocation and asset liquidity and encourage specialization, so as to create capital accumulation which in turn increases economic growth. In addition, financial inclusion through increasing the number of credits will encourage investment in activities that have high added value and ultimately accelerate economic growth (Fabya, 2011). By making finance available and affordable to all economic agents, it will affect the growth of economic activity which will increase the output of a country.
Several studies examine the relationship between financial inclusion and economic growth. There is substantial evidence in the literature that countries with high financial inclusion indexes tend to achieve high rates of economic growth. Kendall et al. (2010) and Ghosh (2011) evaluate the role of access to finance on economic growth with data at the Indian sub-national level which proves the positive impact of access to financial services and utilization of financial services on economic growth in India. Mihasonirina and Kangni (2011) also found the significance of financial inclusion and communication technology on economic growth. Martinez et al. (2011) argue that access to finance is an important policy tool used by governments and policy makers to stimulate economic growth. By making finance available and affordable to economic agents, it will affect the growth of economic activity which will increase output. Sarma and Pais (2011) found empirical evidence of a relationship between financial inclusion and economic growth using data from 49 countries. Masoud and Hardaker (2012); Demirgüç-Kunt and Klapper, (2012); Falahaty and Hook (2013) show that financial development is a significant determinant of economic growth. These findings indicate that improving the functioning of the banking sector is very important to spur economic growth. Law, Azman-Saini, and Hui (2014) emphasize that a well-developed financial system is essential for economic growth. Then Sarma (2016) continued his research by analyzing the causal relationship between various dimensions of financial inclusion and economic growth, which proves the existence of a two-way causal relationship between access to banking services and economic growth. Recently, Pradhan et al. (2016), Kim et al (2018), Gul et al., (2018), and Raza et al (2019) also prove that there is a significant positive relationship between financial inclusion and economic growth.
The above findings contradict the findings of Naceur and Ghazounai (2007) who examined the relationship between financial development and economic growth for 11 countries in the MENA region (Middle East and North Africa). The empirical results of this study indicate that bank development has a negative effect on economic growth. Khan's (2011) findings also show that financial inclusion has a negative impact on economic growth. Financial inclusion can lower credit standards because financial institutions try to reach the bottom of the poor by lowering loan terms, besides that it can increase bank reputation risk because in order to improve banking service facilities, some countries lower the standard for establishing a financial institution for rural areas, and can cause instability due to inadequate and immature regulations from Microfinance institutions.

Variables and Operational Definitions
The independent variables in this study are financial literacy (X1) and financial inclusion (X2). The dependent variable used is economic growth (Y). Operational definitions and indicators or proxies for each variable are described in table 1. [

Research Model
The research model is presented in Figure 2

Data and Data Sources
The type of data used is panel data, which is a combination of cross section data (34 provinces) and time series (2 survey periods). The data used in this study is secondary data collected from several sources, namely SNLIK 2016, SNLIK 2019, and BPS.

Data analysis method
This research is in the form of hypothesis testing which aims to examine the contribution of cost control effectiveness and working capital turnover on economic profitability. The form of data used in the study is in the form of panel data. Panel data is a combination of time series and cross section data. Substantially, panel data is able to overcome the problems caused by neglecting the relevant independent variables (omitted variables). Therefore, to overcome the problem of inter-correlation which ultimately results in inaccurate interpretation of the regression, the panel data regression method is used (Bond, 2002). The data is taken from 14 sample companies which are cross section units and time series data from the period 2012 -2016. The analytical method used in this research is descriptive statistical analysis and panel data regression analysis with the help of the EViews Program (Winarno, 2011). To determine the significance level of each independent variable regression coefficient on the dependent variable, multiple linear regression analysis (multiple regression linear analysis) or also known as Ordinary Least Square is used. Multiple linear regression is a statistical technique used to test the effect of several independent variables on the dependent variable (Sekaran, 2006). The panel regression equation used in this study is: Here, PEit is the Provincial Economic Growth at time t; α is a constant (intercept); β1, β2 is the Regression Coefficient; LK¬it is Provincial Financial Literacy at time t, IK¬it is Provincial Financial Inclusion at time t; and e is a disturbing factor (disturbance error) Common Effect Model (CEM), Fixed Effect Model (FEM), and Random Effect Model (REM) approaches were used in panel data regression analysis (Bond, 2002;Drukker, 2003). Determining which model is the most appropriate to use among the three models consists of several stages, namely: 1) Chow test, conducted to determine whether the Common Effect model is better to use than the Fixed Effect. 2) Hausman test, conducted to determine whether the Fixed Effect model is better to use than the Random Effect. A good regression model must produce an unbiased linear estimation (Best Linear Unbiased Estimator). The panel data model has the potential for heteroscedasticity and autocorrelation problems. This problem generally occurs because of a combination of two forms of data, namely cross section and time series. Therefore, the classical assumption test consists of heteroscedasticity and autocorrelation tests first. However, if it is known that the random effects model is a suitable model for panel data regression, then the classical assumption test is not relevant to be carried out. Because, random effects are believed to be able to overcome the problem of time series autocorrelation and the correlation between observations (cross section). The method used to estimate the random effect model is known as the Generalized Least Square (GLS) method.

Descriptive Statistical Analysis
Descriptive statistical test aims to provide an overview of the object of research. The calculation of descriptive statistics in this study includes the minimum, maximum, average, and standard deviation values of each variable. The dependent variable in this study is economic growth (Y) while the independent variables in this study are financial literacy (X1) and financial inclusion (X2). The statistical distribution for each variable in this study is presented in Table 2.
[ Table 2 about here.] The final data used in the study were 68 observation results derived from a combination of cross-sectional data of 34 provinces and time series of 2 survey periods, namely 2016 and 2019. Table 3 shows that the highest economic growth rate reached 9.9%, while the minimum reached -15.7%. The high and low levels of economic growth reflect that the ability of a province to produce Gross Domestic Product (GDP) per capita in different observation periods.

Description of Research Variables
Data on the financial literacy index, financial inclusion index and Indonesia's economic growth in 2016 and 2019 are presented in the Table 3. [ Table 3 about here.]

Panel Data Regression Selection
The analysis steps used to determine the best estimation model in the panel data are by estimating the Common Effect (CEM), Fixed Effect (FEM) and Random Effect (REM) models. The regression equation used to estimate the model is as follows: The equation is obtained after carrying out a number of testing stages which identified deviations from the classical assumptions. The statistical results obtained in estimating the CEM, FEM, and REM models are presented in the Table 4.
[ Table 4 about here.] The table above shows that the t-statistical and probability values for each model are the basis for selecting the best model in panel data regression. The estimation results explain that each model has a different significance value. Therefore, to find which model is the best, further analysis is carried out using the Chow Test and Hausman Test.
[ The chow test aims to determine which model is better to use between the Common Effect and Fixed Effect models. Based on the table above, the prob value in the Chi-square cross-section is smaller than alpha (α) (0.0000 < 0.05), so H0 is rejected. This means that the Fixed Effect model is better used than the Common Effect model.
[ Hausman test aims to determine which model is better between the Fixed Effect model and the Random Effect model. Table 6 shows that the probability value in the random cross-section is greater than alpha (α) (0.5481 > 0.05), so H0 is accepted. Thus, it is concluded that the suitable model used in panel data regression is the Random Effect Model (REM). With the selection of the Random Effect Model (REM), the classical assumption test is irrelevant.

Panel Data Regression Analysis and Hypothesis Testing
This research was conducted to see the effect of the independent variable on the dependent variable. Panel data regression analysis is used to see whether the hypothesis that has been made will be accepted or rejected. The significance level used is 5%. The estimated statistical model is the best model and is free from deviations from classical assumptions. To find out the results of hypothesis testing from panel data regression analysis, it can be seen in Table  7.
[ Table 7 about here.] Based on the table above, the panel data regression equation is obtained as follows: The t-statistic test shows how far the influence of one independent variable individually in explaining the dependent variable. The test criteria use a significance rate of 0.05. If the significance value is < 5% then H0 is rejected or Ha is accepted and if the significance value is 5% then H0 is accepted or Ha is rejected. Table 7 shows the results of the significance test between financial literacy and financial inclusion on economic growth. The table shows that neither financial literacy nor financial inclusion has a significant effect on economic growth. This is indicated by the significance value of financial literacy and financial inclusion greater than alpha (0.9647 > 0.05; 0.7509 > 0.05). Based on these results, it can be concluded that the first hypothesis and the second hypothesis in this study were rejected. Table 7 also shows the results of the F-Statistics test. The F-statistical test shows how far the influence of the independent variables simultaneously in explaining the dependent variable. The test criteria use a significance rate of 0.05. If the significance value is < 5% then H0 is rejected or Ha is accepted and if the significance value is 5% then H0 is accepted or Ha is rejected. Based on table 7, it is known that the significance value of F-statistics is greater than alpha (0.901369 > 0.05). Therefore, it can be concluded that the third hypothesis in this study is rejected.

Discussion
The results of data analysis for the first hypothesis which states that there is an effect of financial literacy on economic growth, it is found that partially financial literacy has no significant effect on economic growth in Indonesia. The results of data analysis for the second hypothesis which states that there is an effect of financial inclusion on economic growth also found that partially financial inclusion has no significant effect on economic growth in Indonesia. Likewise, the results of data analysis for the third hypothesis which states that there is an effect of financial literacy and financial inclusion on economic growth, it is found that simultaneously financial literacy and inclusion have no significant effect on economic growth in Indonesia.
However, this rejected hypothesis can be explained by the phenomenon of the global economy which is keep slowing down from 2018 to 2019 which is one of the research periods. The global economic slowdown was caused, among others, by the escalation of the trade war between the United States and China, the decline in global demand, stagnation in world commodity prices, as well as the economic crisis and political tensions in a number of regions.
In the midst of the weakening condition and uncertainty of the global economy throughout 2019, Indonesia was able to demonstrate its economic resilience, as can be seen from Indonesia's ability to maintain economic growth in the range of 5%, namely by growing at 5.02%, as well as several important achievements in macroeconomic terms. and the financial sector. This shows that financial literacy and inclusion actually play an important role in maintaining economic growth in Indonesia in the midst of a slowing global economy.
This lack of evidence of the effect of financial literacy and inclusion on economic growth in Indonesia shows that efforts to increase financial literacy and inclusion in Indonesia still need to be further improved in order to achieve its main goal, namely inclusive growth. In the era of globalization and dynamic economic conditions, the Government needs to optimize all resources to encourage the public to be involved in economic development, including in the financial sector. Community involvement in the financial sector can be realized in a condition when every member of the community has access to take advantage of various formal financial services that are in accordance with their needs and abilities in order to achieve prosperity.
The findings of this study can be used by Otoritas Jasa Keuangan (OJK) as a material consideration in the preparation and improvement of policy strategies in order to increase financial literacy and inclusion as stated in the National Strategy for Financial Literacy and Inclusion. Not only for OJK, this strategy is expected to be a guide for Financial Services Businesses in preparing programs in order to increase financial literacy and inclusion.
Furthermore, the findings of this study can be used as a measuring tool to evaluate the effectiveness and efficiency of financial literacy and inclusion programs that have been jointly pursued by both the Otoritas Jasa Keuangan (OJK) and the financial services industry.
The results of this research become valuable input for OJK and Financial Services Businesses in determining educational activities and innovation of financial products or services in the midst of the financial services industry which is undergoing dynamic changes and continues to move forward.

CONCLUSIONS
Increasing financial literacy and financial inclusion has become a global issue believed to play an important role in increasing economic growth. However, the phenomenon that occurred in Indonesia, the increases in financial literacy and financial inclusion in several provinces were not followed by the economic growth of the province. Therefore, this study aims to analyze the effect of financial literacy and financial inclusion on economic growth in Indonesia. The object in this study is 34 provinces in Indonesia with 2 survey periods, 2016 and 2019. The data analysis method used is panel data regression using EViews 10 software. Chow test and Hausman test are carried out to determine the best model. The results of the hypothesis test show that financial literacy and financial inclusion have no significant effect on economic growth in Indonesia, either partially or simultaneously. This shows that efforts to increase financial literacy and inclusion in Indonesia need to be increased more in order to achieve its main goal of inclusive growth. The results of this research become valuable input for OJK and Financial Services Businesses in determining educational activities and innovation of financial products or services in the midst of the financial services industry which is undergoing dynamic changes and continues to move forward.

Variable Operational Definitions Indicator
Financial Literacy (X1) The knowledge, beliefs and skills possessed by the community that can influence the attitudes and behavior of the community in improving the quality of decision making and the quality of financial management so as to achieve community welfare Financial Literacy Index (in %) Financial Inclusion (X2) he availability of access to various financial institutions, products, and services in accordance with the needs and capabilities of the community in order to improve the welfare of the community.

Financial Inclusion Index (in %)
Economic Growth (Y) An increase in the production capacity of an economy embodied in national income.
GDP per capita growth (in %) Source: Data processed by researchers, 2021


Fiscal policy and economic growth: some evidence from China

China has experienced profound economic and social changes in recent decades. During this period, China’s fiscal policy framework has been substantially reformed. The objective of this paper is to better understand the key features of the Chinese fiscal system and their impact on China’s economic growth. The study performs empirical analysis to identify the relationship between fiscal policy variables and economic growth. Its evidence suggests that local expenditures growth has a larger impact on output growth than central expenditures growth. The results also reveal that the response of output growth to anticipated changes in taxation was impeded by liquidity constraints. During the initial stages of market-oriented reform, growth of public investment in manufacturing sector contributed the most to output growth. During more recent periods, public investment in R&D made a substantial contribution. In addition, evidence indicates that long-term debt has a significant influence on China’s fiscal system, especially on government revenues.

Introduction
The strategic challenge facing Chinese policymakers is to ensure a gradual and smooth transition toward a more sustainable growth paradigm while maintaining healthy growth rates. The COVID-19 pandemic further strengthens the case for sustainable growth which protects the environment and benefits the poor. While Chinese policymakers have a number of policy tools at their disposal, fiscal policy-i.e. 1 3 taxation and government expenditure is likely to be at the front and center of any policy package which can help China build back better after the pandemic. For example, fiscal spending on social safety nets may reduce risk and uncertainty facing households and thus encourage them to save less and spend more, thus strengthening domestic demand and economic recovery. Likewise, fiscal spending on COVID-19 vaccines can restore the health of the workforce and reduce social distancing restrictions which limit mobility, thus paving the way for the normalization of economic activity. Furthermore, an effective taxation system is needed to secure the fiscal resources for fiscal spending that promotes sustainable growth.
More generally, fiscal policy can influence economic growth through both macroeconomic and microeconomic channels (IMF, 2015a). At the macroeconomic level, fiscal sustainability is the cornerstone of macroeconomic stability, which, in turn, is indispensable for economic growth. When the government spends more than its income-i.e. tax and non-tax revenues it collects on a sustained basis, the inevitable outcome is macroeconomic instability, which creates uncertainty among companies and deters private investment. At the microeconomic level, both taxes and spending can influence the behavior of firms in ways that can promote growth. For example, well-targeted tax incentives can promote greater investment by companies and foster higher productivity through research and development (R&D). Another example is public spending on education and health care, which contribute to human capital formation, a core ingredient of economic growth.
The central objective of our paper is to empirically examine the relationship between fiscal policy and economic growth in China. The effectiveness of China's countercyclical fiscal response to the global financial crisis highlighted the sizable impact of fiscal policy on short-term growth. However, in this paper, we are interested in the effect of fiscal policy on China's growth beyond the short term.
Our paper contributes to the existing empirical literature on the nexus between fiscal policy and economic growth in China in a number of ways. Above all, we look at the growth impact of not only central government's fiscal policy but also the impact of local governments' fiscal policy. In light of the substantial role of local governments in China's fiscal policy, examining the impact both central and local governments on China's economic growth gives us a more accurate understanding of the effect of fiscal policy on China's growth. In addition, our empirical analysis is enriched and extended in several significant directions. In particular, we incorporate both investment and external debt into our empirical analysis of the link between fiscal policy and economic growth in China. Furthermore, we divide the sample period into three different sub-sample periods of China's economic development. In addition, our analysis distinguishes between automatic fiscal policy and discretionary fiscal policy.
Our econometric analysis yields a number of interesting findings. Our evidence suggests that local government expenditures have a larger impact on output growth than central government expenditures or net taxes. In addition, both government expenditure and net tax multipliers seem to change during the course of a business cycle. However, net tax growth becomes relatively but progressively more influential in the long run. The rest of this paper is organized as follows. Section 2 briefly 1 3 Fiscal policy and economic growth: some evidence from China reviews the relevant literature, Sect. 3 describes the data and methodology, Sect. 4 reports and discusses the empirical results, and Sect. 5 concludes the paper.

Literature review
There is a growing literature on the relationship between fiscal policy and economic growth. Through government expenditure and taxation, fiscal policy can have lasting effects on medium-and long-term economic growth through several major channels. However, the mix of appropriate policies will depend on the idiosyncratic conditions, capacities, and preferences of each country (IMF, 2015b). The country-specific nature of policy mix ensures that the policy track is sustainable in the short-and long run and also enhances the credibility of authorities (Kumhof et al., 2010).
Fiscal policy can promote economic growth through both macroeconomic and microeconomic channels. At the macroeconomic level, sound and responsible fiscal policy can affect aggregate demand and stabilize the economic cycle, thus boosting business confidence, investment, and long-term growth. At the microeconomic level, fiscal policy can impact private sector behavior via encouraging employment, investment, and productivity. (IMF, 2015b;Gerson, 1999). For example, efficient public investment in infrastructure can boost the productivity of all firms and industries, and reforming capital income taxes can encourage private investment. It is also important to understand the feedback between microeconomic effects and aggregate effects (Ramey, 2009).
The distinctive features of new Keynesian conditions include imperfect competition, forward looking expectations by individuals and firms, and some form of rigidity in prices or wages. New Keynesian model arguably remains the dominant framework in most policy modeling (Gali, 2018). Since policy interest rates fell to their near-zero levels in the aftermath of the 2009 global financial crisis (GFC), there is a renewed enthusiasm in new Keynesian models to examine fiscal policy effectiveness at the zero lower bound of nominal interest (e.g. Christiano et al., 2011;Eggertson, 2009).
Policymakers around the world turned to fiscal stimulus packages to support economic growth during GFC (Ramey, 2009). US and European countries adopted countercyclical fiscal policies, including tax cuts and government purchases, mainly to boost short-run and medium-run growth (Ramey, 2009). Many economies in developing Asia too implemented countercyclical fiscal policy to support domestic demand during the global crisis (Jha et al., 2014). In comparing the magnitude of government spending multipliers in US, Cogan et al., (2010) found out that the GDP and employment impacts estimated by using new Keynesian model are much smaller than the estimates from old Keynesian models.
A growing number of studies on advanced economies based on various modelling refinements provide a mixed picture of size of the fiscal multiplier. For fiscal policy to be effective, the government multiplier should be large to make a difference in the direction of the economy. However, multipliers are largely dependent on varying country-specific circumstances (Ramey & Zubairy, 2014).

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Distinguishing between recessions and expansions, Riera-Crichton et al. (2014) found out that the response of the economy to changes in government spending is asymmetric. The long-run multiplier for bad times is 2.3 compared to 1.3 for good times, and up to 3.1 for extreme recessions. On the other hand, using US quarterly data covering wars and recessions, Ramey and Zubairy (2014) found that the estimated multipliers are below 1 irrespective of the amount of slack in the economy. But the results are more mixed for the lower zero bound state, with some specifications producing multipliers as high as 1.5. An extensive literature review by Hemming et al. (2002) concluded that fiscal multipliers are overwhelmingly positive but small. In a study of 10 developing Asian economies in 1985-1999, Jha et al. (2014 computed the tax-cut multipliers to be 2.0 at its maximum over a two-year horizon while government expenditure multipliers are around 1.0. A number of empirical studies support a positive relationship between fiscal policy and medium-and long-term economic growth. In advanced economies, the growth effect can be as high as 0.75 percentage points and even higher in developing countries. For example, IMF (2015c) finds that automatic fiscal stabilizers help prevent public debt accumulation and foster growth. Tax reform can lift long-term growth by as much as 0.5 percentage points while shifting the composition of government spending toward infrastructure can add 0.25 percentage points. Baldacci et al. (2010) concluded that fiscal deficit reductions based on broadening the tax base while maintaining public investment can support medium-term growth in both advanced and developing countries. Finally, macroeconomic instability associated with large fiscal deficits distorts price signals and thus causes volatility of returns on investment and misallocation of resources, see Fatás and Mihov (2013) and Fisher (1993).
The existing literature encompasses various empirical methodologies for assess the effect of fiscal policy shocks. The Cholesky identification approach assumes that fiscal policy variables and output variables do not have any structural effects on each other (e.g. Fatás & Mihov, 2001;Favero, 2002). The sign restriction approach, popularized by Uhlig (1997), identifies fiscal policy shocks using sign restrictions on impulse responses. The approach is traditionally used to assess the impact of monetary policy shocks (Mountford & Uhlig, 2002). Another is the strand of empirical studies which includes Romer (1994); Ramey and Shapiro (1999); Edelberg et al. (1998) and Perroti (1999, 2002). These studies distinguish between automatic policy and discretionary policy, and estimate the elasticity of tax on output using external information. Sims and Zha (1999) presented several issues related to the calculation of error bands using Monte Carlo integration, bootstrapping, and impulse response functions (IRFs) for structural vector autoregression (VAR). The methodology was further developed and refined by Perotti (2002). In contrast to monetary policy, decision and implementation lags in fiscal policy imply that there is limited scope for discretionary fiscal policy in response to unexpected movements in economic activity within a quarter.
Fiscal policy is making a substantial contribution to China's economic growth. For instance, a massive countercyclical fiscal stimulus during the GFC prevented a recession in China and contributed to the recovery of other emerging and developing 1 3 Fiscal policy and economic growth: some evidence from China economies (Fardoust et al., 2012). China's forceful fiscal response was made possible by the fact that China had ample fiscal space when the GFC hit. Kong and Feng (2019) find that China's fiscal policy is generally countercyclical and achieves its desired economic effects. Interestingly, a tax cut is found to have a positive impact on output in China (Jha et al. 2014;Kong & Feng, 2019). This can be attributed to taxation's function in promoting a more efficient resource allocation. For instance, Lam and Wingender (2015) find that improving the progressivity of personal income taxes, introducing property taxes, and setting up a comprehensive value-added tax can promote China's growth and boost fiscal revenues as well as reduce fiscal deficit.
Some studies have estimated China's fiscal multipliers. Using the IMF's GIMF model, Kumhof et al. (2010) find fiscal multipliers for China are broadly in line with United States. Chen et al. (2017) estimated that China's fiscal multiplier increased from 0.75 in 2001-2008 to 1.4 in 2010-2015, with the biggest impact on the manufacturing sector. Using annual data for 1,800 Chinese counties, Guo et al. (2016) obtained local government fiscal multipliers of approximately 0.6, which is much lower than the estimates of most previous studies. The effects of local public spending were most pronounced in non-tradable industries. Cove et al. (2010) calibrated New Keynesian model to China and finds that public expenditures which are managed by the local authority and can be financed by raising taxes on local households and issuing local government debt can have New Keynesian effects on output growth. Some province-level studies imply that that fiscal decentralization contributed to higher economic growth Liu, 2000 andJin et al. 2005).

Empirical framework
In this section, we describe the data and empirical framework used in our analysis. For developing countries such as China, monthly data are difficult to find even in statistical yearbook, so we use statistical way to transfer the yearly data into monthly data. For the Dickey-Fuller test and Phillips-Perron test, we converted all variables to first differences of natural logarithms to address the unit root problem in level data. Table 1 below lists the sources of our data and Table 2 below summarizes the mean values of data in three sub-periods-1985-1997, 1998─2007, and 2008─2015. The period from 1985 to 1997 marks the pre-Asian financial crisis (AFC) period, 1998-2007 is the period between AFC and global financial crisis (GFC), and 2008-2015 is the post-GFC period. To compare the effect of fiscal policy in the three sub-periods, we also denoted the three sub-periods from economic structure reform perspective. The 3 sub-periods are domestic demand-oriented model, three-wheel-oriented (investment, consumption, and trade) model, and export-oriented model, and they track the evolution of China's economic structure. For the identification of the fiscal policy shocks, the variables in the first structural model-government expenditure model are central government expenditure, local government expenditure, net tax, fixed asset investment, and gross domestic product per capital (GDP per capital).
In the Cholesky decomposition approach, there are several methods for estimating the precision matrix. For example, the order can be selected thorough Investment in infrastructure is calculated by adding investment in management of water, conservancy, environment and public facilities; transport, storage and post; production and supply of electricity, heat, water and gas; services to households, repair and other services; and education; culture, sports and entertainment and public management, social security and social organizations, between 1991 and 2014 All variables were deflated by the consumer price index (2015 = 100 and transformed to natural log form. All data are converted into monthly data series through Eviews

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Fiscal policy and economic growth: some evidence from China comparison of the cross-correlation coefficients from the data, Granger causality verification, impact response function, or decomposition of expected error term (Chang & Tsay, 2010;Chen & Leng, 2015;Park, 2020;Wagaman & Levina, 2009). But in many applications, the variables often do not have a natural order. That is, the justifiable variable order is not available or the pre-determination of the variable order is not possible before the analysis (Xiaoning & Xinwei, 2020). When using structural VAR, one may order the variables with an economic rationale and in this case, the order would be specified by the author's own matrix (Ludvigson et al., 2020). According to de Castro Fernández & Hernández de Cos (2006), in the ordering between variables such as taxes and expenditure, it could be quite difficult to fully justify which one should come first. Nevertheless, this choice does not seem to substantially affect the main results, mainly due to the low and non-significant correlation between expenditure and net-tax shocks. In this regard, we decided to re-estimate under the alternative assumption that taxes or consumption come first. Since the residuals of reduced-form in the expenditure and net-tax equations showed low and non-significant correlation, the differences with the baseline VAR results, if any, were minimal. As a matter of fact, none of the variables under analysis showed different response profiles and the output multipliers were almost identical. Barro (1990) assumed that government expenditure is financed contemporaneously by a flat-rate income tax which is 0.25 for the Cobb-Douglas case. In our study, we removed the substitution effect between government expenditure and tax through applying 75% of tax as the original tax before regression. Then we follow Perotti (2002) to build up a model including net tax but without division of the government sector into central versus local government. Table 3 below shows the summary statistics of the main variables. The structural vector autoregression (SVAR) model can be formed as below: Perotti (2002) divides fiscal policy into discretionary measures and automatic stabilizers. The effectiveness of discretionary measures is quantified by the size of the multipliers while the effectiveness of the automatic stabilizer is measured by the magnitude of an exogenous shock that fiscal policy can smoothen out. The formula to calculate net tax is: where The orthogonalization matrix P s = A −1 B is then related to the error covariance matrix by Σ = P s P � s in the short-run SVAR model. The variables in the second structural model-the investment model-are investment in infrastructure, investment in manufacturing, investment in R&D, net tax, and GNI. We choose these three investment variables in light of the aggregate nature of the production functions. The exact contribution of infrastructure to productivity remains limited in the sense that the production function approach does not cover all welfare aspects of infrastructure investment. For example, the impact of infrastructure investments on consumers is not taken into account. Furthermore, the production function approach cannot give an ex-ante evaluation of specific investment projects. Industrial development plays an important role in the economic growth of developing countries such as China. Furthermore, manufacturing investment influences the productivity performance of these countries. Romer (1986) developed the endogenous growth model, in which technological innovation is created in a R&D sector that combines human capital and knowledge.
(1) The second structural model also share the Cobb-Douglas production function which is in line with Gramlich (1994) and Voss et al (2003). In this model, public capital is disaggregated into various components. This exercise is similar in spirit to Easterly and Rebelo (1993) which also examines whether particular sectors of public investment are important for economic growth. In China's case, investment in infrastructure is calculated by adding investment in management of water, conservancy, environment and public facilities; transport, storage and post; production and supply of electricity, heat, water and gas, services to households, repair and other services; and education; culture, sports and entertainment and public management, and social security and social organizations. Data are collected for 1985-2015 from various editions of the Statistical Yearbook of China from 2003 through 2016.
In the third structural model, external debt is divided into short-term and longterm debt. Other variables are government expenditure and government revenue. Favero and Giavazzi (2007) emphasized the importance of including the debt feedback effect when estimating the effects of fiscal policy shocks. The identified system is: where Y t = g e g r , which denote government expenditure and government revenue, d l,t is long-term debt to GDP ratio, d s,t is short-term debt to GDP ratio, and d * l and d * s are unconditional mean values. Generally speaking, in terms of impulse-response functions, fiscal multipliers reflect the impact of fiscal variables on GDP or GNI, or , where X is government expenditure or tax. However, Davig et al. (2010) point out that current fiscal policy will affect future fiscal policy, which means that ordinary impulse response cannot accurately capture the impact of fiscal policy on the economy. Therefore, Perotti (2004) applies the SVAR model to calculate cumulative impulse response and cumulative multipliers as , which can be interpreted as the ratio of the cumulative value of GDP or GNI to the cumulative value of government expenditure or tax. In addition, Mountford and Uhlig (2009) develop a new method assuming the discount rate as In our paper, we calculate the multipliers based on three models: which represent the multiplier, cumulative multiplier, and discounted cumulative multiplier.

Empirical results
In this section, we discuss and report the main findings of our empirical analysis, for both the full sample period of 1985─2015 as well as the three sub-periods. We use monthly data because approving and implementing new measures in response to innovations in the macroeconomic variables typically takes at least one month. Therefore, the use of monthly variables allows for setting the discretionary contemporaneous response of government expenditure or net taxes to GNI to zero. Preregression analysis shows the presence of co-integrating relations and hence a possible specification of a vector error correction model but the number of long-term equations shows no feasibilities. Blanchard and Perotti (2002) find no significant differences between estimated results obtained with and without taking the co-integrating relation into account. With regard to the choice of the interest rate, most existing studies use the short-term interest rate. For example, Chan et al. (1992) uses the onemonth US treasury bond yield, while Nowman (1997) uses the one-month LIBOR. 1 This study selects 7-day interbank interest rate as the discount rate. It should be pointed out that our sample period 1985 to 2015 coincides with a significant expansion of China's external debt in tandem with sustained rapid economic growth.

Test of Johansen cointegration
We use Johansen cointegration test to obtain preliminary evidence of cointegration relationships. The result provides evidence in favor of two cointegration relationship in Model 1. The lag length was chosen by final prediction error (FPE) to be 2. 2  Tables 4 and 5 show the results for Model 1 and Model 2, respectively.

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Fiscal policy and economic growth: some evidence from China In a similar way, the result of Johansen cointegration test for Model 2 shows evidence in favor of three cointegration relationship. The lag length was chosen by SBIC to be 1. 3

Test for unit roots
The structural vector autoregressive (SVAR) methodology requires that all variables be stationary. Therefore, a formal analysis of the stochastic properties of the series is needed. We make alternative assumptions about the deterministic components of the model. More specifically, before our econometric analysis, we (a) remove the different sample means from the series, and (b) remove the different fitted-trend lines from the raw series. The second issue concerns the presence of unit roots in the series, which is tested by the standard Dickey-Fuller and Phillips-Perron tests. The results are reported in Table 6 below. Both tests reject the null of unit root for the first differences of the log of the series. The t-statistic for the null hypothesis of a unit root is tested with 4 lags at 5% significance critical values. Since the t-statistic values are smaller than the critical values, we reject the null of unit root at conventional significance levels.

Test for variables order
Considering the importance of variable order on VAR/SVAR results, we carried out Granger causality Wald tests for different VAR/SVAR results in order to find the most robust variable order. In model 1, the Granger causality Wald tests results with the best variable order are shown in Table 7. The same tests of Model 2 and Model 3 prove our model fits the best as well. The Granger causality tests show that there is a significant bidirectional causality from net taxes, central government expenditures, local government expenditures, consumption, and trade balance to GDP in China. This means that the maximum of the five variables Granger-causes the other variables and GDP, and GDP Granger-cause each of the five variables. This suggests that each of the five variables contributed to the progress of the Chinese economy.

Government expenditure model
In terms of fiscal policy, China's government expenditure is determined primarily by the central government. The central government's fiscal decisions substantially affect the local government's fiscal decisions. We identified fiscal policy shocks using vector error correction model (VECM) model with 6 variables. We set the variable sequence as GDP per capita ( y ), net tax ( t ), central government expenditure ( c ), local government expenditure ( l ), consumption (a) and trade balance (b) during calculation. According to Barro (1990), under the assumption of constant returns to scale, government expenditure can change the steady growth rate. Fiscal decentralization leads to greater autonomy of local government. Zhang and Zou (1998) used the ratio of provincial government expenditure to central government expenditure as the measure of fiscal decentralization and found that decentralization affects provincial economic growth. The results of the government expenditure model are shown in Table 8.
The impulse response results are reported in Tables 9, 10, and 11 along with Appendix Fig. 1. A number of interesting patterns emerge. First, the overall trend for the full sample period indicates that the growth of both central government expenditure and local government expenditure, as discretionary fiscal policy tools, had positive effect on output growth except during the first quarter of central government expenditure. The response of output to net tax increase also appeared to be positive. Comparing the multipliers of other two impulse shocks, local government expenditure increase was more effective than central government expenditure in both short term and long term. In the first month, net tax increase had a bigger impact than local government expenditure increase.
Second, before the Asian Financial Crisis, central government expenditure increase had the biggest short-term impact on output growth, but the three fiscal variables all became permanently positive in terms long-term effects. Nevertheless, the cumulative multiplier of local government expenditure growth was larger than the cumulative multiplier of the other two fiscal variables.
Third, after the Asian Financial Crisis, the multiplier of central government expenditure was still bigger than the multiplier of local government expenditure. The multiplier of net tax growth tends to be negative after 20 quarters.
Fourth, during 2008-2015, local government expenditure increase had a significant impact on output growth, with a much larger multiplier than central government expenditure or net taxes. Its effect was positive and significant, implying that fiscal decentralization benefits economic growth.
The impulse response functions for the government expenditure model yields the following findings. For one, they provide strong evidence that fiscal policy multipliers may change over the business cycle-i.e. they tend to be larger during recessions than expansions (Woodford, 2010). Such evidence supports Keynesian arguments for using discretionary government expenditure during downturns to stimulate aggregate demand. Both Blanchard and Perotti (2002) and Mountfourd and Uhlig (2009) find that tax multipliers are smaller than spending multipliers in the short-term, which is plausible since theory predicts that part of the higher disposable income stemming from tax cuts is saved.
Our analysis shows that during 1998-2007, net tax multipliers show negative value, which implies that tax cuts stimulate output. During 1985-2015, central government and local government expenditure multipliers were 4.267 and 4.420, respectively, after one month. On the other hand, net tax growth multiplier was 0.508, which was smaller than central government expenditure multiplier, but it became bigger from 10th quarter onward. According to conventional wisdom, the 1 3 Fiscal policy and economic growth: some evidence from China Table 8 The results of government expenditure VEC model. Source: Authors' calculations Standard errors in parentheses, *p < .05; **p < .01; ***p < .001 Long-term variables

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Fiscal policy and economic growth: some evidence from China multiplier should be larger during recessions. It is noteworthy that the effect of local government expenditure was significant, with a post-GFC discounted multiplier of 1.2778 after 20 months. Interestingly, the impact of central government expenditure on output did not change visibly after AFC. Before 1997, the cumulative multiplier of both government expenditure and net tax declined steadily after 5 months, but the former is much larger than the latter. During 1998-2007, the cumulative multiplier of government expenditure increased from a negative value, whereas that of net tax decreased progressively. The value of government expenditure multiplier increased during 2008-2015. However, during the whole period of 1985-2015, the cumulative multiplier declined to 1.272 after 5 months. This amount is still larger than the cumulative net tax multiplier, which increased during the whole period.

Investment model
Three cointegration equation could be constructed via Johansen cointegraion tests. The results suggest that R&D investment has long-term positive impact on GNI, net tax, and infrastructure while manufacturing investment shows the opposite impact. Table 12 shows the results. However, this result does not provide any evidence regarding the temporal stability of the parameters of the relationship. The paper constructs a 5-variable SVAR model which estimates the responses of GNI to total investment (Model 2). For convenience, the variables' names are shortened as follows-GNI to y , net tax to t, investment in infrastructure to i , investment in manufacturing to m , and investment in R&D to r . The coefficients corresponding to the uncorrelated structural shocks t t , i t , m t , r t , y t can be obtained in Eq. (5) below.

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Fiscal policy and economic growth: some evidence from China Our results show that the coefficient signs from investment increases in infrastructure and manufacturing are negative, but they are statistically insignificant. Another interesting finding was that during the 1985-2015 time period, 1% increase of investment in manufacturing led to 0.11% decrease of GNI. On the other hand, 1% increase of R&D investment generated 0.03% increase in GNI, which is significant and positive compared to the other variables.
The results are reported in Tables 13, 14, and 15 along with Appendix Fig. 2. First, the response of GNI growth to manufacturing investment growth decreased in the first quarter and then recovered slightly from 2nd quarter onward. For investment growth in infrastructure and R&D, there was a positive initial impact. The responses were relatively large in the 1st quarter and peaks at 8th quarter. Until the 8th quarter, the response of GNI to R&D shock was the largest, with a discounted cumulative multiplier of 0.0078, followed by infrastructure at 0.0067. The manufacturing investment growth multiplier was only 0.0016. Second, before the AFC, GNI growth reacted negatively to increase in both infrastructure and R&D investment. During the same period, the output growth multiplier of manufacturing investment shock was positive and much higher than the other two sectors. Third, after the AFC, the discounted cumulative multiplier of manufacturing investment was much larger than that for infrastructure and R&D investment.
The impulse response functions generate a number of findings. The government was a main driver of manufacturing investment in the PRC. Due to the low efficiency of government investment and crowding out of private investment, a negative impact cannot be ruled out. Furthermore, some previous studies have shown that R&D investment can have a negative effect on economic growth. Technological progress may cause higher unemployment rate and in addition, strengthening of intellectual property rights protection may impede diffusion of new knowledge. Furthermore, infrastructure investment may promote economic growth in the long term by raising the productivity of all firms and industries. This explains why, upon the increase of infrastructure investment, the output growth multiplier increases from 0.0471 to 0.0680 during 8 quarters in 1985-2015 and from 0.2149 to 0.6375 after the AFC. The increase in the R&D multiplier after 1998 reflects China's gradual shift from an input-based economy to a knowledge-and innovation-based economy.
For infrastructure, the cumulative multiplier reached the highest value after 10 months during 1985-1997 and 2008-2015, and even in the whole time periods except for 1998-2007. For manufacturing factor, during 1998-2017, the highest cumulative multiplier appears after 3 months, but before 1997, the value decreases as the times goes on. At last, for R&D sector, the highest value usually appeared after 3 months except before 1997.

External debt model
In the third model, we consider the potential debt feedback following Bohn (1998), who developed a fiscal reaction function in which d * is the unconditional mean of 1 3 Fiscal policy and economic growth: some evidence from China the debt-to-GDP ratio as shown in formula (2). Following Favero and Giavazzi (2007), we build a 3-variable SVAR model which includes the government expenditure to GDP ratio and the government revenue to GDP ratio, and then examine the response of the two variables to the debt-to-GDP ratio.
In Table 16, we report the coefficients and the standard errors from the estimation for the full sample period and sub-sample periods.
The debt-to-GDP ratio has significant positive effect on both government revenue and expenditure ratios for the full period, but the effect differs across sub-periods. After the Asian financial crisis, the ratio of short-term debt to GDP has a significant effect on government revenues but an insignificant effect on government expenditure. Both government expenditure and revenue respond significantly to the ratio of long-term debt to GDP for the full sample period but there is no significant effect before the Asian financial crisis. Both long-term and short-term debt have a more significant effect on government revenues than government expenditures. This suggests that the debt level helps to stabilize government budget balance primarily through the response of government revenues to deviations of actual debt level from the target level. It is noticeable that after GFC, both of the long-term debt and short-term debt have no significant impact on government expenditure. During 2007-2008, external debt outflow, which sustained at around 16%, is much faster than inflow. Comparing to 4 trillion fiscal stimulus, paying external debt interests have little impact on government expenditure, simultaneously this means Chinese government expenditure had smaller degree of dependence on external debt.

Conclusion
Sustained rapid growth since the initiation of market-oriented reforms in 1978 transformed China into the world's second largest economy. However, China's growth has slowed down visibly since the global financial crisis, primarily due to long-term structural factors. Furthermore, the COVID-19 highlights the need for more sustainable growth which protects the environment and benefits the broader population, including the poor. China's positive experience with countercyclical fiscal policy during the global financial crisis highlights the potential of fiscal policy as an important tool for supporting the country's growth. A massive fiscal stimulus staved off recession and the economy weathered the global financial crisis remarkably well. In addition, fiscal policy can help China build back better after COVID-19-e.g. public investments in clean energy. China's experiences are generally consistent with a large literature that suggests that fiscal policy can have a significant and positive effect on economic growth. In this paper, we empirically examine the relationship between fiscal policy and economic growth in China. To do so, we use empirical methods which distinguish automatic fiscal policy from discretionary fiscal policy (e.g. Perroti, 2002). Our econometric analysis yields a number of interesting findings. Our evidence suggests that local government expenditures have a larger impact on output growth than central government expenditures or net taxes. However, net taxes become progressively more influential in the long run. In addition, both government expenditure and net tax multipliers seem to change depending on the phase of the business cycle. During the initial stages of market liberalization in 1990s, manufacturing investment contributed the most to output growth but in recent periods, public investment in R&D made a substantial contribution. In addition, our evidence indicates that long-term debt has a significant influence on China's key fiscal variables, especially government revenues.
Overall, our analysis provides cautious grounds for optimism that fiscal policy can help Chinese policymakers engineer a gradual and smooth transition toward a more sustainable growth paradigm while maintaining healthy growth rates. Fiscal policy, especially government spending, seems to have a significant and positive effect on output in both short and long run. Since local government spending in particular seems to affect output, there is an urgent need to induce local governments to take sound and efficient fiscal decisions so that their expenditures can contribute to sustainable growth beyond the short term.
Samuelson emphasized the prominent position of consumption and technology in a market-oriented economy. In this connection, future research may consider adding total factor productivity as a proxy for technology shock to further enrich the model. In our analysis of China, we find that in recent years the effect of R&D investment on output exceeds the effect of infrastructure investment. It is consistent with the conventional wisdom that in order to sustain growth China has to shift from a growth strategy based on more capital and labor to one that is based on productivity and innovation. In fact, this shift has already been occurring for some time. Finally, the significant effect of long-term public debt on the fiscal balance, especially through fiscal revenues, suggests a need for China to monitor debt as an indicator of fiscal sustainability.

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Fiscal policy and economic growth: some evidence from China . Notes: IRFs depict the GNI response to a 1% shock in investment in infrastructure, investment in manufacturing and investment in R&D. The grey shadow area in the SVAR panels show 95% upper and lower confidence bands. Source: Authors' estimation