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Determinants of Real Chinese GDP 1978-2014.

Abstract In 2014, the IMF reported that China became the largest economy in the world according to Purchasing Power Parity rates. This study aims to explain the Chinese economic miracle. It focuses on frequently suggested factors influencing China's real gross domestic product (GDP), such as export promotion, exchange rate policy, and foreign direct investment (FDI). The paper employs the Bounds test of the autoregressive distributed lag (ARDL) model to test for cointegration. Once cointegration is established. Granger Causality is investigated using the vector autoregressive model and the Toda and Yamamoto (1995) method. Two different combinations of the real macroeconomic variables exports, exchange rate, imports, and FDI were employed to examine Granger causal relationships. All explanatory variables, except for the exchange rate, were found to have plausible relationships with GDP. The exchange rate and GDP relationship was unexpected; a Renminbi appreciation was associated with an increase in GDP. To investigate this paradox, a third ARDL model was estimated with exports as the dependent variable and the exchange rate, world GDP, and FDI as the independent variables. In this model, we found evidence of cointegration and a plausible relationship between real exports and the real exchange rate. Exchange rate devaluation increased exports and thus indirectly increased GDP. Such findings help to resolve the unexpected results. Nonetheless, according to the Granger causality tests the established statistical evidence is rather weak. We found that both the exchange rate and FDI are no longer strong drivers of economic growth in China.

Keywords ARDL-bounds test * Granger causality * Cointegration * FDI * Exchange rate * Exports * Imports * Chinese GDP

JEL CIO * 010 * 050

Introduction

For almost four decades, China has experienced phenomenal economic growth, as demonstrated by the 28-fold increase in real Chinese gross domestic product (GDP) from 1978 to 2014. The growth period began in 1978, only two years after the passing of the long-time communist leader Mao Zedong. The successful transformation of China from a closed, planned, agrarian economy to an open market is mainly attributed to the Deng Xiaoping-led government, which launched radical economic reforms. Such reforms marked a turning point in the history of China that also radically affected the world economy.

The expanding foreign trade sector, after the opening of China to the world economy, is considered to be the most important contributing factor to the transformation of China. There are, however, indications that the phenomenal GDP growth period may already have reached its peak. More recently, the global financial crisis has had a negative impact on the Chinese economy. Starting with the international financial crisis in 2007, the Chinese economy began experiencing a drastic reduction of its exports.

A factor that may have played a crucial role in boosting Chinese exports is the exchange rate (ER). Since exports are a component of GDP, it is plausible that the ER affected GDP as well. In the past, China received much criticism for controlling or even manipulating the value of its currency, the "Ren Min Bi" Renminbi (Yuan), to boost its exports. (1) This study also examines the validity of this criticism.

Since the opening of the Chinese economy, continuous labor migration from rural to urban areas has been considered a major factor contributing to the rapid increase in Chinese GDP. Such migration provided cheap labor and contributed to large gains in labor productivity, as workers moved from agriculture to manufacturing. As a result, real labor productivity increased by an average annual growth rate of 3.4% from 1978 to 2014. Most economists believe that foreign direct investment (FDI) has contributed to the growth of GDP. After the opening of the Chinese economy to the

world in 1978, many foreign companies invested heavily in China. Such companies took advantage of the exceptionally low Chinese labor costs, and gained a comparative advantage. During the period 1978 to 2014, FDI increased at an exceptionally high annual rate. In addition to supplying physical and financial capital, FDI has also facilitated expansion of exports by providing the know-how of international business.

A few analysts have expressed concern that a slowdown of the Chinese economy may also have a negative impact on the global economy. Such analysts expect the Chinese economy to shift to a slower pace of economic growth if unfavorable external and/or domestic conditions develop. One such domestic concern is the possibility that the supply of migrant workers from rural to urban areas may dry up in the future. Such an event would cause labor shortages in the manufacturing sector. Another concern regarding China's future economic development is the environmental degradation that was an unintended side effect of intensive manufacturing. Environmental degradation could be a growth deterrent for China. In addition, the state of the financial and banking sectors of China, particularly the high level of debt held by state banks and state-owned enterprises, is a major problem regarding the sustainability of economic development. Moody's downgrade of China's public debt in May of 2017 and the IMF's warning are indicators of such concerns.

The paper contributes to the literature on China's transformation, because it employs a unique econometric approach to discover the causes of Chinese economic growth. There are no other studies that pay close attention to the exchange rate and GDP in a similar model framework, using recent data.

Literature Review

Many empirical studies have investigated causal relationships between international trade and economic growth. Most of the early contributions employed the vector autoregression (VAR) model, as well as the Johansen (1991, 1995) method of cointegration in conjunction with the vector error correction model (VECM). Such studies have investigated Granger causal relationships between trade and GDP growth for both developing and developed countries. Some authors found empirical evidence supporting causality from trade to GDP growth; whereas, others found evidence supporting causality from economic growth to trade. A few empirical studies, however, have found bidirectional Granger causality between GDP and trade (Zestos and Tao 2002; Zestos et al. 2016).

Several authors examined the relationship between Chinese economic growth and FDI. One of the earliest studies, by Liu et al. (2002), reported that China's real exports and real GDP during the period 1979-1997 grew at the exceptionally high rates of 15% and 9%, respectively. The authors also found evidence that export-promotion policies were successful in boosting Chinese economic growth. Yao (2006) also examined the relationship between economic growth, FDI, and exports, and found evidence that foreign invested enterprises (FIE) were crucial in boosting Chinese exports. To attract FIE, China launched major economic reforms. For example, China substantially devalued the Renminbi (RMB). Yao provided evidence that exports and FDI positively affected real Chinese GDP growth.

Narayan (2006) examined the "nexus" between the Chinese trade balance and the exchange rate of RMB to United States (U.S.) dollar. He employed the Bounds test of the autoregressive distributed lag (ARDL) model to establish evidence of co-integration between the two variables, and provided evidence that RMB devaluation improved the trade balance. Jalil et al. (2010) found a strong and positive causal relationship between finance and growth. The authors concluded that financial development and international trade have both played a positive role in affecting real economic growth. Zhou (2010) claimed the miraculous economic growth of China is explained by the institutional reforms. Finally, Popescu (2013) and several other authors attribute the high Chinese economic growth to the development of the urban sector, which was supported by the continuous migration of workers from rural to urban areas. Popescu claims that economic growth was also favorably affected by fiscal decentralization.

A few other authors investigated the relationship between environmental degradation and Chinese growth. Zhang and Cheng (2009) employed VAR and error correction models (ECM) to study causal relationships between carbon dioxide emissions, energy consumption, and economic growth for the period between 1960 and 2007. They found economic growth depends on carbon dioxide emissions. Therefore, they recommend that Chinese authorities launch new environmental policies. More recent studies raise concerns about the long-term sustainability of Chinese economic growth. Zhang (2015) pointed out that since the global recession, growth of both Chinese exports and GDP began to slow down. Zhang claims that in response to these global challenges, the Chinese government began promoting domestic consumption.

Chen et al. (2015) claim that China would be able to maintain a high rate of growth if it undergoes major reforms of its financial and banking system. According to the authors, there is strong evidence that the government favors the state-owned enterprises (SOE) relative to private firms. Therefore the SOE, due to government favoritism, are inefficient. China has recently put forward initiatives to liberalize its economy and thus remove misallocation of resources by relying more on market pricing mechanisms.

Methodology

Two econometric models are employed to investigate causal relationships between two subsets of variables in relation to Chinese GDP. We use the ARDL model developed by Pesaran et al. (2001) to test for cointegration with the Bounds Test. In addition, the VAR model is employed to test for Granger causality using the Toda and Yamamoto (1995) method. The ARDL-Bounds Test complemented with the VAR model is considered superior to the previously employed two-step method by Engle and Granger (1987), and the Johansen method (1991, 1995) used in conjunction with the VECM.

The superiority of the ARDL model and the Bounds Test methodology lies in the fact that the ARDL model can be employed whether the time series variables are integrated of order zero 1(0), of order one I(1), or are mutually cointegrated. As long as the variables are not of order 1(2) or higher, the ARDL-Bounds Test procedure can be employed. The ARDL model includes lagged differences as right-hand side variables of optimum and varying order for each explanatory variable. (2) The Bounds Test is performed with a Wald F-statistic, which tests for joint-significance of all the one-period lagged levels of all variables included in the conditional unrestricted ECM. The two critical values of the lower and upper limits of the Bounds Test are derived for the case when all variables are stationary in levels 1(0) and also when all variables are stationary in the first differences 1(1).

The first ARDL model is denoted as Model A, and uses the variables: Y = real GDP, X = real exports, ER = real exchange rate, and M = real imports. (3) Real GDP is used as a proxy for real GDP growth in this study because the ARDL model requires all of the included variables to be in levels. Therefore, GDP and GDP growth are used interchangeably for the remainder of the study. The real GDP in both Models A and B is calculated by dividing the nominal GDP in RMB by the 2010 Chinese GDP deflator. (4) The real ER in both Models A and B is calculated by multiplying the nominal exchange rate (RMB/US dollar) by the ratio of the US GDP deflator over the Chinese GDP deflator. (5) All variables except for ER are expressed in real 2010 RMB and are divided by population, and therefore are expressed in per capita RMB terms. (6) Furthermore, all variables in both Models A and B are expressed in terms of their natural logarithms. Annual data were used in Model A, and the time series data set spans the period of 1978 to 2014, for a total of 37 observations.

In Eq. (1), we present the conditional unrestricted ARDL ECM for the variables ln[Y.sub.t], ln[X.sub.t], InE[R.sub.t] and In[M.sub.t]. The left-hand side variable, the dependent variable, is the first difference of the natural logarithm of the GDP, denoted as [DELTA]ln[Y.sub.t]. The right-hand side includes a number of optimum lagged differences of all the variables, Y X, ER and M of order r, s, k and p determined according to Schwarz information criterion (SIC). The right-hand side also includes the one-period lagged variables: in[Y.sub.t-1], in[X.sub.t-1], InE[R.sub.t-1] and In[M.sub.t-1].

[DELTA]ln[Y.sub.t] = [[alpha].sub.0] + [[summation].sup.r.sub.i=1] [[alpha].sub.1i] [DELTA]ln[Y.sub.t-1] + [[summation].sup.s.sub.i=0] [[alpha].sub.2i] [DELTA]ln[Y.sub.t-1] + [[summation].sup.k.sub.i=0] [[alpha].sub.3i] [DELTA]lnE[R.sub.t-1] = [[summation].sup.p.sub.i=0] [[alpha].sub.4i] [DELTA]ln[M.sub.t-1] + [[alpha].sub.5]ln[Y.sub.t-1] + [[alpha].sub.6]ln[X.sub.t-1] + [[alpha].sub.7]lnE[R.sub.t-1] + [[alpha].sub.8]ln[M.sub.t-1] + [[epsilon].sub.t]. (1)

where t = 1,2,3 ..., and [[alpha].sub.0], [[alpha].sub.1i], [[alpha].sub.2i], [[alpha].sub.3i], [[alpha].sub.4i], [[alpha].sub.5i], [[alpha].sub.6i], [[alpha].sub.7i], and are parameters to be estimated, and e, is assumed to be a white noise error. The Bounds test is performed using the estimated ARDL model by setting the coefficients of all the one-period lagged variables jointly equal to zero. The null and alternative hypotheses [H.sub.o] and [H.sub.a], respectively, of the Bounds test for cointegration are [H.sub.0] : [[alpha].sub.5] = [[alpha].sub.6] = [[alpha].sub.7] = [[alpha].sub.8] = 0 and [H.sub.a]: [[alpha].sub.5] [not equal to] [[alpha].sub.6] [not equal to] [[alpha].sub.7] [not equal to] [[alpha].sub.8] [not equal to] 0, or at least one of these four coefficients is different than zero.

The second ARDL model is denoted as Model B and includes the same variables as Model A, except that exports (X) were replaced by the variable FDI. (7) All variables except for ER are measured in real 2010 RMB and are divided by population; thus, they are expressed in per capita RMB terms. Equation (2) below presents the conditional unrestricted ARDL ECM. The variables used in Model B are reported as annual observations spanning the period 1982 to 2014, for a total of 33 observations:

[DELTA]ln[Y.sub.t] = [[beta].sub.0] + [[summation].sup.r.sub.i=1] [[beta].sub.1i] [DELTA]ln[Y.sub.t-1] + [[summation].sup.s.sub.i=0] [[beta].sub.2i] [DELTA]lnFD[I.sub.t-1] + [[summation].sup.k.sub.i=0] [[beta].sub.3i] [DELTA]lnE[R.sub.t-1] = [[summation].sup.p.sub.i=0] [DELTA][M.sub.t-1] + [[beta].sub.5]ln[Y.sub.t-1] + [[beta].sub.6]lnFD[I.sub.t-1] + [[beta].sub.7]lnE[R.sub.t-1] + [[alpha].sub.8]ln[M.sub.t-1] + [[epsilon].sub.t]. (2)

where t = 1,2,3 ..., and [[beta].sub.0], [[beta].sub.1i], [[beta].sub.2i], [[beta].sub.3i], [[beta].sub.4i], [[beta].sub.5], [[beta].sub.6], [[beta].sub.7], and [[beta].sub.8] are parameters to be estimated, and [[epsilon].sub.t] is a white noise error. The null and alternative hypothesis for the Bounds test are shown respectively as [H.sub.0]: [[beta].sub.5] = [[beta].sub.6] = [[beta].sub.7] = [[beta].sub.8] = 0 and [H.sub.a]: [[beta].sub.5] [not equal to] [[beta].sub.6] [not equal to] [[beta].sub.7] [not equal to] [[beta].sub.8] [not equal to] 0, or at least one of these four coefficients is different than zero.

Empirical Results

Before proceeding with the estimation of the models, we first investigated the dynamic properties of the time series variables. Thus, unit root tests were performed for all the variables. The most common unit root tests used for time series econometric studies, the augmented Dickey and Fuller (ADF) (1979) and the Phillips and Perron (PP) (1988) tests, have been criticized for being unreliable with small samples. Alimi (2014) and Dejong et al. (1992) both criticized these two tests because they tend to reject the null hypothesis too frequently when it is actually correct, and accept it when it is false. Consequently, in addition to the ADF and PP tests this study employed two relatively newer tests, the Dickey-Fuller generalized least squares (DF-GLS) test developed by Elliott et al. (1996) and the Ng and Perron (2001) test. (8) According to the four unit root tests, almost all of the variables were stationary in their first differences for both Models A and B. Therefore it is appropriate to proceed with the estimation of the ARDL models.

In Table 1, the estimated ARDL conditional unrestricted models of Eqs. (1) and (2) are presented respectively. Both Models A and B have the natural logarithm of real GDP per capita as the dependent variable. The independent variables for the two models appear in the fourth row of Table 1. Specific summary statistics and other information about the estimated models are also reported. The numbers in parentheses in the second row of Table 1 refer to the number of lagged differences included for each variable. The Schwarz information criterion (SIC) was employed to determine the optimum number of lagged differences for Model A, whereas, more than one information criterion were employed to determine the optimum number of lagged differences for Model B. (9) Several of the coefficients are statistically significant in each model, denoted by the number of asterisks. In both models the Durbin-Watson statistics are close to 2, indicating that the models are likely to be free of serial correlation.

Furthermore, to ensure that each model was free of serial correlation, the Breusch-Godfrey serial correlation Lagrange multiplier (LM) test was performed for each of the two models. The results of the LM Tests for the two models are reported in Table 5 of the online only supplemental appendix. According to the test results, both models pass this test at the 5% level of significance. We also examined the structural stability of Models A and B using the cumulative sum (CUSUM) and the CUSUM of squares. The graphs of these tests appear in the online only supplemental appendix as Figures 1 and 2, respectively. These tests were suggested by Pesaran and Shin (1999) to test the stability of the coefficients of the ARDL model. Since the graphs of the CUSUM and the CUSUM of squares tests remain within the 95% confidence intervals, this provides statistical evidence that the models do not have a structural break.

The ARDL model was used to test for cointegration among the variables. Table 2 reports the Bounds test results for Models A and B. The test statistic values are compared with the critical values of the Bounds test calculated by Pesaran et al. (2001). Because the sample sizes are relatively small (n = 37 and n = 33), we decided to also report the critical values of the Bounds Test calculated specifically for small sample sizes by Narayan (2005). The calculated F-statistics for Models A and B are 14.59 and 5.20 respectively. The F-statistic value for Model A is very large and above the 1% 1(1) critical values of both the Pesaran et al. (2001) and the Narayan (2005) upper bound values. The F-statistic value for Model B is above the 2.5% 1(1) critical upper value of the Pesaran et al. (2001) bounds and the 5% 1(1) critical value of the Narayan (2005) bounds. Therefore, we conclude that the null hypothesis of no cointegration is rejected in both models.

The estimated ARDL models reported in Table 1 complement the Bounds test by using a t-test on the coefficient of the one-period lagged dependent variable, [Y.sub.t-1]. The estimated t-values of these coefficients are -4.84 and--1.33 for Models A and B, respectively, although the t-values are not reported in Table 1. Since the t-value of Model A is above the 1 % 1(1) critical value of the t-limiting distribution in the Pesaran et al. (2001) Table CI (iii) case iii, this provides further evidence supporting cointegration for Model A. The t-statistic for Model B is insignificant, weakening support for cointegration.

Table 3 below presents the estimated long run ECM of ARDL Models A and B. The main additional feature of the long run ECM is the inclusion of the one-period lagged error correction term (E[C.sub.t-1]) from the cointegrating equations. As displayed below, the coefficients of ECM are highly significant and negative in both models. This implies that when the variables are not at their long-run equilibrium values, there will be a quick adjustment for the variables to return to their long-run equilibrium values. In model A, more than 17% of the adjustment would take place within the first year. The adjustment will be much slower in the second model, as only 6.3% of the error would be corrected within the first year.

Another important feature of the long-run ECM ARDL model is that the model also generates the cointegrating equation:

Model A : ln[Y.sub.t] = 0.568ln[X.sub.t] - 0.897lnE[R.sub.t] + 0.761ln[M.sub.t] p-value (0.04) (0.00) (0.00), (3)

Model B: ln[Y.sub.t] = 0.016lnFD[I.sub.t] - 0683lnE[R.sub.t] + 1.618ln[M.sub.t] p-value (0.93) (0.04) (0.03). (4)

Equations 3 and 4 above are the cointegration equations of Models A and B, respectively. The coefficients of the right-hand side variables are the long-run elasticities of Y with respect to each variable. (10) In Eq. (3) for Model A, all three independent variables are statistically significant. Both Xand M have positive coefficients indicating that an increase in X or M, assuming everything else held constant, will increase Y. The elasticity of Y with respect to M, [E.sub.Y.M] - 0.76, is higher than the elasticity of Y with respect to X, [E.sub.Y,X] = 0.57. This indicates that imports are more important than exports in affecting Y. It is highly likely that China's imports include many capital goods, which have a long-run multiplier effect in the economy. On the other hand, increases in real exports constitute a simple addition to Y. The coefficient of the exchange rate is negative in both models, implying that as the RMB devalues (depreciates), Y decreases, but this is unexpected. (11)

The cointegrating Eq. (4) of Model B shows that the relationship of Y with FDI and M is positive. The elasticity of Y with respect to M, [E.sub.Y,M], is 1.62 and much larger than the elasticity of Y with respect to FDI, [E.sub.YFDI], which is 0.02; furthermore, FDI is statistically insignificant. This result is unexpected, since it is widely believed that FDI is one of the most important determinants of Chinese economic growth. China facilitated FDI by adopting several policies that helped foreign enterprises gain comparative advantage in many industries.

To investigate the unexpected relationship between Y and ER, we re-estimated both models after replacing the variable InE[R.sub.t] in the two equations with a nonlinear quadratic trinomial of ER, as the graph of the exchange rate is parabolic. Such a reformulation of the model, however, did not improve the empirical results. Therefore, the relationship between ER and Y will be further investigated.

Resolving the Exchange Rate Puzzle

Historical Review of the Chinese Exchange Rate Policy

During the communist era, the exchange rate played virtually no role in influencing international trade; however, this changed with the opening of China to the world economy. As of 1978, China employed a dual-exchange rate system, with the official exchange rate pegged to the U.S. dollar. Because the official Renminbi rate was overvalued, an informal internal settlement exchange rate evolved. This internal settlement exchange rate reflected the number of Renminbi needed to earn one dollar from Chinese exports. From 1978 to 1984, that rate was about 280 RMB to 1 U.S. dollar. By 1985, the official exchange rate, after a sequence of gradual devaluations, converged to the internal settlement rate. Since then China has fully liberalized the Renminbi for transactions involving the current account, but not for the capital account. Particularly, China kept restrictions on short-term capital movements. The RMB, prior to 1994, was continuously depreciating as a result of a rising price level in the country (Xu 2000).

In 1994, China ended the dual exchange rate system after first devaluing (overnight) its official rate by 33% from 5.8 to 8.7 RMB to the dollar. The national foreign exchange market was established in April 1994, and during the next two years the Renminbi gained strength versus the dollar from 8.7 to 8.28 RMB per dollar. China kept the RMB exchange rate stable during the Asian crisis in 1997-1999. This was done through the Chinese Central Bank, or the People's Bank of China (PBC), which frequently intervened to maintain the exchange rate at 8.28 RMB per dollar (Kawai and Pontines 2014).

In July 2005, China abandoned the peg of the RMB to the U.S. dollar and switched to a managed floating system vis-a-vis an undisclosed basket of currencies. This happened only after the announcement of a 2.1% revaluation of the Renminbi versus the dollar. The Chinese government made this decision in response to mounting pressure from the U.S. Following the 2005 foreign exchange reforms announced by the Chinese Prime Minister Wen Jiabao, the Renminbi appreciated versus the U.S. dollar during the next three years (Kawai and Pontines 2014). (12)

During the global financial crisis that started in 2007, the Chinese government re-pegged the Renminbi to the U.S. dollar at the rate of 6.87 RMB. This decision triggered new criticism from the U.S. A weak currency contributed to the creation of large trade surpluses that were accompanied by massive capital inflows. To keep inflation at bay, the PBC kept sterilizing such capital inflows. The commitment of the PBC to support the exchange rate fluctuation within a daily narrow band of .3%, however, resulted in the loss of the PBC's independent monetary policy. (13)

On June 19, 2010, the PBC announced that it was abandoning its peg to the U.S. dollar, and resumed a managed floating exchange rate regime. In April 2012, the PBC widened the exchange rate band to 1 % daily. To achieve its commitment and keep the Renminbi from further appreciation, the PBC intervened in the foreign exchange market. Consequently this contributed to the accumulation of a vast amount of foreign reserves. These reserves reached $3.2 trillion in 2012, $3.8 in 2013, and approximately $4 trillion in 2014 (Prasad and Zhang 2014). Since then purchases and sales of reserves were employed to direct the exchange rate in what the Chinese authorities consider an appropriate rate. It is now widely recognized that Chinese exchange rate policy is gradually becoming more flexible and market oriented. This is something which is in line with the internationalization of the Renminbi, particularly since it became one of the five reserve currencies comprising the IMF's basket currency, the Special Drawing Rights (SDR). Thus, the China's exchange rate policy has recently become more balanced, pursuing either devaluation or revaluation according to what Chinese authorities deem appropriate.

Exchange Rate, Exports, and GDP Relationships

In Fig. 1 we examine the two time series variables X and ER. On the left-hand vertical axis of Fig. 1, the exchange rate is shown; whereas, the right-hand vertical axis shows the Chinese exports. It is clear from Fig. 1 that Chinese exports followed an uninterrupted upward trend until 2007, the year the international crisis begun. Since then, exports have been decreasing. The exchange rate had an upward trend until 1994, at which point it reversed direction and followed a downward trend. According to the data of the two time series variables, exports have been increasing even during periods of Renminbi revaluation (appreciation) and during periods when the Renminbi remained stable. The data indicate that the Renminbi had an upward trend, i.e. was depreciating, for only the first 17 of the 37 years in our sample. This suggests that the Renminbi was becoming a stronger currency after 1994.

The exchange rate turned out to be the most troublesome variable in this study. The unexpected estimated sign of the ER in the first two estimated ARDL models led us to further scrutinize its relationship with GDP.

Further Empirical Results: Model C

To investigate the unexpected result of the relationship between GDP (Y) and the ER, we estimate a third ARDL, named Model C. This new model utilizes exports (X) as the dependent variable, and the World GDP ([Y.sub.w]), ER, and FDI as the three right-hand variables. The real world GDP excludes the Chinese GDP. To calculate [Y.sub.w] we transformed the current U.S. dollar world GDP into real 2010 U.S. dollars. (14) Real Chinese exports expressed in RMB were transformed into real 2010 U.S. dollars using the real ER defined in Models A and B. The FDI variable is expressed in real 2010 U.S. dollars. (15) Unlike Models A and B, none of the variables in Model C are expressed in per capita terms. Model C was estimated in the natural logarithms of the variables. Furthermore, the sample size for Model C spans from 1982 to 2014, for a total of 33 observations. (16)

The four variables are cointegrated and the F-statistic for the Bounds test is 9.53, which is large and highly significant. A break, BREAK93, was also included as a right-hand variable in the estimated model to improve the fit.

The estimated ARDL Model C passes both the serial correlation and the structural stability tests. (17) According to Table 4, the one-period lagged error correction term is highly significant and negative. This implies that 42.5% of the adjustment takes place within the first year. The cointegrating equation is reported in Eq. (5). The coefficients of the three right-hand side variables, [Y.sub.w] ER, and the FDI, are highly significant in this model and have the expected signs:

Model C : In[X.sub.t] = 2A52lnW[Y.sub.t] + 1.433lnE[R.sub.t] + 0.206lnFD[I.sub.t] 0.328BREAK93 p-value (0.00) (0.00) (0.00) (0.00). (5)

The coefficients of the independent variables are the long-run elasticities of X with respect to each independent variable. The elasticity of X with respect to [Y.sub.w] is the highest of the three elasticities as [E.sub.X,Yw] = 2.45, which implies that a one percentage increase in [Y.sub.w] would increase X by 2.45%. Similarly, the elasticity of X with respect to ER, [E.sub.X.ER], is 1.43, and the elasticity of X with respect to FDI, [E.sub.X.FDI], is 0.206. The fact that the export elasticity with respect to the ER and to the FDI are high and positive implies that the two variables are also related to Chinese GDP. Thus, Model C complements the estimated results of Models A and B, since exports are a component of GDP. Such a relationship is plausible, therefore a Renminbi devaluation (depreciation) is associated with increases in Chinese GDP as expected, and this resolves the puzzle of Models A and B. Similarly, an increase in FDI indirectly increases Chinese GDP.

Granger Causality Tests for Models A, B, and C

Since the study established cointegration among the variables in each of the three models, Granger causality tests were performed. The innovative work by Pesaran et al. (2001) for cointegration of time series variables of differing integrating orders is complemented in this paper by the Toda and Yamamoto (1995) methodology. (18) As a result, we perform Granger causality tests for Models A, B and C within the framework of the estimated VAR model.

The same data used to estimate ARDL Models A, B, and C were also employed to estimate three corresponding VAR models named A', B', and C' respectively. Prior to performing the Granger causality tests, we investigated for the presence of serial correlation in the three VAR models. Thus, we performed the Breusch-Godfrey Lagrange Multiplier LM Test. According to these tests, there is no evidence of serial correlation at the 95% confidence level. (19) We also present the inverse roots of the autoregressive (AR) characteristic graphs of each VAR model to test the dynamic stability of the models. Since the inverse roots of the AR characteristic polynomials remain within the unit circle, it is concluded that the three models are characterized by dynamic stability. The tests (graphs) for dynamic stability and the results of the Breusch-Godfrey LM test for serial correlation for the three VAR models are reported in the online only supplemental appendix. The Granger causality tests for Model A' are presented below; whereas, the Granger causality tests for Models B' and C' are reported in the online only supplemental appendix. (20)

In Table 5 below the Granger causality test results for model A' are reported. The four variables of this model are: ln[Y.sub.t], ln[X.sub.t], lnE[R.sub.t], and ln[M.sub.t]. Eviews produces block exogeneity joint Wald tests for each of the four endogenous variables testing whether the three right-hand side variables jointly Granger cause the left-hand side variable. Also, a t-test is performed for each right-hand side variable. The first test shows that the three right-hand side variables, In[X.sub.t], lnE[R.sub.t] and ln[M.sub.t], jointly Granger cause In [Y.sub.t] since together they are highly significant. This was expected, since it is in line with the high F-test value of the Bounds test for cointegration. Interestingly, the only independent variable that is individually statistically significant in this test is X. This result supports the hypothesis that ER indirectly causes Y via exports. As for the remaining three joint block exogeneity tests in Table 5, they all support Granger causality at very high significance levels.

According to Granger causality tests based on model B', ln[Y.sub.t] is Granger caused by the three independent variables lnFD[I.sub.t], lnE[R.sub.t] and In[M.sub.t], at a very high level of significance. In addition to the Granger causality supported by the block exogeneity joint test, every one of the individual right-hand side variables is Granger causing ln[Y.sub.t]. These results are based on the individual t-test of each right-hand variable.

According to Granger causality tests based on model C', real Chinese exports ln[X.sub.t] are jointly Granger caused by ln[Y.sub.wt], lnE[R.sub.t] and the lnFD[I.sub.t]. This joint Granger causality test result is not strongly supported, however, as the p-value is 0.09. Similarly, individual Granger causality from lnE[R.sub.t] to ln[X.sub.t] is not strongly supported, as the t-test is hardly significant with a 0.10 p-value. Finally, according to the individual t-test lnFD[I.sub.t], is strongly Granger causing In[X.sub.t] since its p-value is 0.02.

Concluding Comments

This study investigates factors determining real Chinese GDP from 1978 to 2014. Real exports and imports were found to directly affect and Granger cause China's GDP. The real exchange rate and the FDI, however, were only indirectly related to the Chinese GDP. These two variables, together with world GDP, were found to be cointegrated with real Chinese exports. In addition, the three variables jointly Granger caused real exports; therefore, they indirectly affected real GDP as exports are a component of GDP. This relationship, however, was not strongly supported by the Granger causality tests.

According to these empirical results, the exchange rate was not a powerful policy variable influencing the Chinese trade balance and GDP. A main reason for this is that long ago, Chinese prices began converging with world prices (Xu 2000). As a result, changes in the exchange rate did not have substantial effects on the terms of trade, and therefore did not drastically affect China's trade balance. Furthermore, even if exchange rate changes do affect the terms of trade, the effects do not last long because price adjustments quickly remove any created comparative advantage. Similarly, the empirical results suggest the importance of FDI may have begun to wane, and the Chinese economy may have experienced diminishing returns to capital.

We recommend that China focus more on its domestic economy, and this is something it has been doing the last few years. The trade balance has been gradually becoming less important for the Chinese economy. Chinese consumption has been steadily increasing for many years; however, it did not keep pace with other components of GDP. This was the result of an extraordinarily high Chinese saving rate, one of the highest in the world. Although it is difficult for governmental policies to boost consumption substantially and quickly, it is very likely that the development of reliable pension plans would reduce the strong incentive for families to save. Additionally, government investment in infrastructure and human capital should continue, in order to enhance efficiency in the Chinese economy.

It is plausible that China is in a position to move gradually towards allowing the RMB to freely float. This will free the BOC to apply an independent monetary policy, which will in turn enable it to cope with both internal and external shocks. Another source of growth is a policy allowing and encouraging rural workers to seek employment in urban areas, mainly near the coastal cities. The Chinese government has recently announced that they will pursue such policies in the future. Eventually, such policies should end, in order to avoid further congestion and pollution. An alternative could be for the government to promote decentralization and economic development of rural areas where an excess labor supply exists. This could be done by building appropriate infrastructure and by offering firms incentives to move to such areas. Such decentralization policies would enable Chinese citizens to remain in their ancestral homes, and would keep families together.

Furthermore, the government must adopt policies to reduce chronic state capitalism, which prevails as a result of subsidization. In addition, China must adopt policies to reduce income inequality, which in recent years has been rising alarmingly. An economically strengthened middle class will contribute to sustainable economic growth. Ultimately, a stronger domestic economy would lead to a more democratic system that would ensure sustainable growth. Finally, China has no other alternative but to drastically reduce environmental degradation. Government policies should strategically address this issue and develop ambitious plans to protect the environment.

Acknowledgements We express our gratitude to Hunter Simons for excellent research assistance. We also thank Christopher Newport University and the chair of the Department of Economics, Dr. Robert Winder. Particularly we thank the Dean of Social Sciences, Dr. Robert Colvin, for his continuous support. Finally, we thank Dr. Roark Mulligan for his constructive criticism.

https://doi.org/10.1007/s11293-018-9580-z

Published online: 14 June 2018

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11293-0189580-z) contains supplementary material, which is available to authorized users.

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(1) Rein Ming Bi (RMB) translates to "the People's Currency."

(2) The optimal lag length of each variable of the ARDL model is found by estimating: [(p + 1).sup.k] regressions, where k is the number of right-hand variables in the estimated equation and p is the maximum number of lags included for each variable in the single equation ARDL model.

(3) For both Model A and Model B. data for imports and exports come from the China Statistical Yearbook (2015).

(4) The nominal GDP data ate from the China Statistical Yearbook (2015), and the GDP deflator index is from the International Monetary Fund (2016) International Financial Statistics database.

(5) Data for the nominal exchange rate come from the Organization of Economic Cooperation and Development statistics (2015), the US GDP deflator comes from the Federal Reserve Economic Database (2016) of Saint Louis, and the Chinese GDP deflator comes from the World Bank (2016).

(6) The data for population in both Model A and Model B comes from Worldometers (2015).

(7) Data for FDI in real 2010 US dollars come from the World Bank (2016), and are transformed into real 2010 RMB by multiplying by the real ER. We employed the same ER used in Models A and B.

(8) The results of the unit root tests are included in Tables 1 through 4 of the online only supplemental appendix.

(9) The SIC is known to select fewer lagged differences than any of the other criteria, and as a result, it picks the most parsimonious model. This is desirable for this study, as the sizes of the two samples of Models A and B are relatively small.

(10) This is because all the variables in both models arc expressed in terms of their natural logarithms.

(11) Although China has had a fixed exchange rate regime vis-a-vis the U.S. It almost always maintained a fluctuation band, thus It is appropriate to state that the exchange rate devalues or depreciates as both arc possible under the Chinese foreign exchange regime.

(12) Within this period the nominal exchange rate appreciated by 17.5% whereas the real exchange rate by 15%.

(13) This was a big setback for policy stabilization purposes, because monetary policy constitutes a powerful tool to cope with shocks in the economy.

(14) The nominal world GDP in US dollars, and the nominal Chinese GDP in U.S. dollars, comes from the World Bank. The GDP deflator index used to transform World GDP into real 2010 U.S. dollars is from the IMF IFS database.

(15) The export data come from the China Statistical Yearbook. The FDI data come from the World Bank. The ER used in Model C is the same as defined in Models A and B.

(16) Unit roots for Model C are available in the only supplementary appendix.

(17) To save space we only report the long-run ECM ARDL model and accompanying cointegration equation.

(18) Toda and Yamamoto showed that even if a set of level variables arc of different order of integration, the standard asymptotic theory is still valid, provided the order of integration docs not exceed the lag length of the VAR model.

(19) This is the case because none of the probability values are below 0.05.

(20) The tests were carried out with the software EViews and arc referred to as: "Granger Causality/Block Exogeneity tests." in Eviews.

George K. Zestos [1], Wei Guo [2], Ryan Patnode [1]

[mail] George K. Zestos

gzestos@enu.edu

[1] Department of Economics, Christopher Newport University, 1 Avenue of the Arts, Newport News, VA 23606, USA

[2] Department of Economics, Harbin Finance University, Haping Liudao Street 6, Harbin, Heilongjiang, China

Caption: Fig. 1 Real Chinese exports and real Chinese exchange rate (RMB/USD)
Table 1 Estimated conditional unrestricted ARDL models A and B

Model A (1,3,4,2)        [DELTA]ln[Y.sub.t]
Sample: 1978-2014        [DELTA]ln[X.sub.t],
Dependent variable       [DELTA]lnE[R.sub.t],
Independent variables    [DELTA]ln[M.sub.t]

C                        0.15
[DELTA]ln[X.sub.t]       -0.02
[DELTA]ln[X.sub.t-1]     -0.05
[DELTA]ln[X.sub.t-2]     -0.08 **
[DELTA]lnE[R.sub.t]      0.04
[DELTA]lnE[R.sub.t-1]    0 22 ***
[DELTA]lnE[R.sub.t-2]    0.25 ***
[DELTA]lnE[R.sub.t-3]    0.15 ***
[DELTA]ln[M.sub.t]       0.12 ***
[DELTA]ln[M.sub.t-1]     -0.07 *

ln[X.sub.t-1]            0.09 ***
lnE[R.sub.t-1]           -0.01 ***
ln[M.sub.t-1]            0.131 **
ln[Y.sub.t-1]            -0.17 ***
[R.sup.2]                0.82
[[bar.R].sup.2]          0.70
S.E.                     0.013
D.W.                     2.10
F                        6.83
SIC                      -4.88

Model B (1,3,3,3)        [DELTA]ln[Y.sub.t]
Sample: 1982-2014        [DELTA]lnFD[I.sub.t],
Dependent variable       [DELTA]lnE[R.sub.t],
Independent variables    [DELTA]ln[M.sub.t]

C                        -0.08
[DELTA]lnFD[I.sub.t]     0.02
[DELTA]lnFD[I.sub.t-1]   0.03 **
[DELTA]lnFD[I.sub.t-2]   0.00
[DELTA]lnE[R.sub.t]      0.01
[DELTA]lnE[R.sub.t-1]    0.16 ***
[DELTA]lnE[R.sub.t-2]    0.12 **

[DELTA]ln[M.sub.t]       0.06 *
[DELTA]ln[M.sub.t-1]     -0.08 **
[DELTA]ln[M.sub.t-2]     -0.01
InFD[I.sub.t-1]          0.00
InE[R.sub.t-1]           0.10
In[M.sub.t-1]            -0.04 **
In[Y.sub.t-1]            -0.06
[R.sup.2]                0.80
[[bar.R].sup.2]          0.64
S.E.                     0.01
D.W.                     1.71
F                        4.98
SIC                      -4.67

*, **, *** represent the significance levels
of .10, .05, .01, respectively

Source: Export and import data come from the China
Statistical Yearbook (2015). FDI data come from the World
Bank Database (2016). The exchange rate is calculated using
data from the Organization for Economic Cooperation and
Development (2017), the World Bank, and the Federal Reserve
Economic Database (FRED) of Saint Louis (Federal Reserve
Economic Data 2016). Real GDP is calculated using data from
the China Statistical Yearbook (2015) and the International
Monetary Fund (2016) International Financial Statistics (IFS)
database. Exports, imports, FDI, and GDP are transformed into
per capita terms using data from Worldomcters statistics (2015)

Table 2 Critical values for bounds test

Estimated statistics

Model          F-statistic   Degrees of
                             freedom

A              14.59         36
B              5.20          32

Bounds calcuated by Pesaran and Narayan

               Pesaran et al. (2001)      Narayan (2005)

Significance   1(0) Bound    1(1) Bound   1(0) Bound   1(1) Bound
level

10%            2.72          3.77         2.96         4.10
5%             3.23          4.35         3.62         4.91
2.5%           3.69          4.89         --           --
1%             4.29          5.61         5.20         6.85

Source: Export and import data come from the China Statistical
Yearbook (2015). FDI data come from the World Bank Database (2016).
The exchange rate is calculated using data from the OECD (2017),
the World Bank Database (2016) and the FRED of Saint Louis
(Federal Reserve Economic Data 2016). Real GDP is calculated using
data from the China Statistical Yearbook (2015) and the IMF (2016)
IFS database. Exports, imports, FDI, and GDP are transformed into
per capita terms using data from Worldomctcrs statistics (2015)
The bounds calculated by Pesaran et al. (2001) comc from
Table C1(iii) case (iii)--unrestricted intercept and no trend.
The bounds calculated by Narayan (2005) come from the Appendix,
page 1988, Case III unrestricted: interval and no trend for
degrees of freedom n = 35

Table 3 Estimated long-run ECM of ARDL models A and B

Model A (1,3,4,2)         [DELTA]ln[Y.sub.t]
Sample: 1978-2014         [DELTA]lnX,
Dependent variable        [DELTA]lnER,
Independent variables     [DELTA]lnM

C                         0.15 ***
[DELTA]ln[X.sub.t]        -0.02
[DELTA]ln[X.sub.t-1]      -0.05 *
[DELTA]ln[X.sub.t-2]      -0.08 ***
[DELTA]lnE[R.sub.t]       0.04
[DELTA]lnE[R.sub.t-1]     0.22 ***
[DELTA]lnE[R.sub.t-2]     0.25***
[DELTA]lnE[R.sub.t-3]     0
[DELTA]ln[M.sub.t]        0.12 ***
[DELTA]ln[M.sub.t-1]      -0.07 ***
E[C.sub.t-1]              -0.17 ***

Model B (1,3,3,3)         [DELTA]ln[Y.sub.t]
Sample: 1982-2014         [DELTA]FDI,
Dependent variable        [DELTA]lnER,
Independent variables     [DELTA]lnM

C                         -0.08 **
[DELTA]lnFD[I.sub.t]      0.02 *
[DELTA]lnFD[I.sub.t-1]    0.03 ***
[DELTA]lnFD[I.sub.t-2]    0.01
[DELTA]lnE[R.sub.t]       0.01
[DELTA]lnE[R.sub.t-1]     0.16 ***
[DELTA]lnE[R.sub.t-2]     0.12 **

[DELTA]ln[M.sub.t]        0.06 **
[DELTA]ln[M.sub.t-1]      -0.08 ***
[DELTA]ln[M.sub.t-2]      -0.01
E[C.sub.t-1]              -0.06 ***

*, **, *** represent the significance
levels of .10, .05, .01 respectively

Source: Export and import data come from the China
Statistical Yearbook (2015). FDI data come from the
World Bank Database (2016). The exchange rate is calculated
using data from the OECD (2017), the World Bank Database (2016)
and the FRED of Saint Louis (Federal Reserve Economic Data 2016).
Real GDP is calculated using data from the China Statistical
Yearbook (2015) and the IMF (2016) IFS database. Exports,
imports, FDI. and GDP arc transformed into per capita terms
using data from Worldomcters statistics (2015)

Table 4 Estimated long-run ECM ARDL model C

Model C (1,1,4,0)        [DELTA]ln[X.sub.t]
Sample: 1982-2014        [DELTA]ln[Y.sub.t],
Dependent variable       [DELTA]lnE[R.sub.t],
Independent variables    [DELTA]lnFD[I.sub.t]

C                        -14.83 ***
[DELTA]ln[Y.sub.w]       2.29 ***
[DELTA]lnE[R.sub.t]      1.17 ***
[DELTA]lnE[R.sub.t-1]    0.014 ***
[DELTA]lnE[R.sub.t-2]    -0.1688
[DELTA]lnE[R.sub.t-3]    0.40 ***
[DELTA]lnFD[I.sub.t]     0.12
BREAK93                  0.15 ***
E[C.sub.t-1]             -0.42 ***

*, **, *** represent the significance
levels of .10, .05, .01 respectively

Source: Export data comes from the China Statistical
Yearbook (2015). FDI data comes from the World Bank Database
(2016). The exchange rate is calculated using data from the
OECD (2017), the World Bank Database (2016), and the FRED of
Saint Louis (Federal Reserve Economic Data 2016). World GDP
is calculated using data from the World Bank Database (2016)
and the IMF (2016) IFS database

Table 5 Granger causality tests for model A'

Excluded             [chi square]   df             Probability

Dependent variable                  In[Y.sub.t]
In[X.sub.t]          9.76           5              0.08
InE[R.sub.t]         4.64           5              0.46
In[M.sub.t]          8.86           5              0.11
All                  31.09          15             0.00

Dependent variable                  InE[R.sub.t]

In[Y.sub.t]          66.29          5              0.00
In[X.sub.t]          47.30          5              0.00
In[M.sub.t]          55.23          5              0.00
All                  233.49         15             0.00

Excluded             [chi square]   df             Probability

Dependent variable                  In[X.sub.t]
In[Y.sub.t]          14.83          5              0.01
In[X.sub.t]          9.54           5              0.08
InE[R.sub.t]         19.69          5              0.00
All                  55.55          15             0.00

Dependent variable                  In[X.sub.t]

In[Y.sub.t]          33.76          5              0.00
In[X.sub.t]          10.78          5              0.05
InE[R.sub.t]         5.63           5              0.34
All                  60.73          15             0.00

Source: Export and import data come from the China
Statistical Yearbook (2015). The exchange rate is calculated
using data from the OECD (2017), the World Bank Database (2016),
and the FRED of Saint Louis (Federal Reserve Economic Data 2016).
Real GDP is calculated using data from the China Statistical
Yearbook (2015) and the IMF (2016) IFS database. Exports,
imports, and GDP are transformed into per capita terms
using data from Worldomotors statistics (2015)
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Date:Jun 1, 2018
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