The Impact of China?S Slowdown on the Asia Pacific Region: An Application of the Gvar Model

An export-oriented development strategy fostered the Asia Paci?c region?s economic success, making it the fastest growing region in the world. In recent years, despite waning demand from the crisis-hit Western economies, the accelerating demand from China boosted intraregional trade in Asia. Although China?s Asian trading partners bene?t from increasing exports to China, this stronger linkage with China has made them more vulnerable to the risk of a Chinese slowdown. This paper examines the impact of a negative Chinese gross domestic product (GDP) shock on Asian economies by employing the Global Vector Autoregressive (GVAR) model, using the dataset through the third quarter of 2014 for 33 countries. The analysis finds that a negative Chinese GDP shock impacts commodity exporters, such as Indonesia, to the greatest extent, re?ecting both demand and terms of trade shocks. Export-dependent countries in the East Asian production cycle, such as Japan, Malaysia, Singapore and Thailand, are also severely a?ected. The analysis also finds that a negative shock to China?s real GDP would not only have an adverse e?ect on the price of crude oil, as some previous studies have also shown, but also on the prices of metals and agricultural products. The study also investigates the impact of a potential negative shock to the real GDP of the United States on Asian countries, and determines that although the U.S. economy has a larger in?uence on Asian economies than China?s economy, the Asian countries are more exposed to China than ever through increased economic ties.

An export-oriented development strategy fostered the Asia Pacific region's economic success, making it the fastest growing region in the world. In recent years, despite waning demand from the crisis-hit Western economies, the accelerating demand from China boosted intraregional trade in Asia. Although China's Asian trading partners benefit from increasing exports to China, this stronger linkage with China has made them more vulnerable to the risk of a Chinese slowdown. This paper examines the impact of a negative Chinese gross domestic product (GDP) shock on Asian economies by employing the Global Vector Autoregressive (GVAR) model, using the dataset through the third quarter of 2014 for 33 countries. The analysis finds that a negative Chinese GDP shock impacts commodity exporters, such as Indonesia, to the greatest extent, reflecting both demand and terms of trade shocks. Export-dependent countries in the East Asian production cycle, such as Japan, Malaysia, Singapore and Thailand, are also severely affected. The analysis also finds that a negative shock to China's real GDP would not only have an adverse effect on the price of crude oil, as some previous studies have also shown, but also on the prices of metals and agricultural products. The study also investigates the impact of a potential negative shock to the real GDP of the United States on Asian countries, and determines that although the U.S. economy has a larger influence on Asian economies than China's economy, the Asian countries are more exposed to China than ever through increased economic ties.

Introduction
Global economic integration has expanded dramatically over the past two decades. Global trade surged to $37 trillion in 2014 from $6 trillion in 1990. Led by China, Asia Pacific countries' trade levels rose 18 times over this period, which is faster than any other regional country groups. 1 The export-oriented development strategy brought the Asia Pacific region economic success through rapid growth, making it the fastest growing region and the world's growth engine. On the other hand, increased integration and dependence on exports intensified the region's vulnerability to external shocks.
Since 2008, due to the anemic growth in the United States and the recession in the Eurozone, the advanced economies' demand for Asia Pacific exports has been waning. Nevertheless, thanks to surging Chinese demand, the rest of the Asia Pacific countries' ("Asia" henceforth) exports remained as a positive outlier. The Asian exports to China doubled over the last five years and China became the largest market for Asia after surpassing Japan in 2005 and the US in 2007. As China became the central point of the Asian supply chain, its demand has been supporting the region's production of goods ranging from raw materials to electronic components. 2 Despite the recent acceleration in the US economy, the advanced economies' overall growth expectations remain subdued; therefore, China's continuing role supporting the Asian economies remains critical. However, China's economy is slowing down from the rapid growth rates exceeding 10 percent over the past several decades. The real GDP growth in 2014 was 7.4 percent, which was the weakest in 24 years. Further slowdown is expected going forward, and some projections show growth rates dropping to about 6 percent by the end of the decade.
Against this background, we aim to examine and quantify the impact of a negative Chinese GDP shock on Asian economies by employing the Global Vector Autoregression (GVAR) model developed by Pesaran, Schuermann and Weiner (2004), and Dees, di Mauro, Pesaran, and Smith (2007). Through GVAR, we examine how and to what extent the Chinese economic growth affects Asian countries. The transmission mechanism of this slowdown may be diversified: in this paper we examine the shocks to the real economy based on trade linkages. For simplicity, the original GVAR model assumes a fixed trade weight for the sample period. However, considering the recent rapid expansion of Chinese trade volume, both in exports and imports, we find that the "fixed weight" assumption is not optimal. Thus, following Cesa-Bianchi, Pesaran, Rebucci, and Xu (2011;henceforth CPRX), we construct a model with time-varying trade relations. After estimating the GVAR model, we calculate a set of generalized impulse response functions (henceforth GIRFs) for four different timings 3 with different trade weights, and investigate the changes of the shock propagation mechanism from China to the Asian countries. 4 To the best of our knowledge, Han and Ng (2011) is the first study that focuses its analysis on Asia's economies using the GVAR methodology; however, its focus was on evaluating macroeconomic forecasts for the original ASEAN economies. Matsubayashi (2013) examined the impact of the financial crisis in the US and Eurozone on the East Asian countries using GVAR with a time-varying weight matrix. In light of structural change in world trade around 1995, Matsubayashi has also estimated the GVAR model using a sample up to 1994Q4, and compared its impulse response functions (henceforth IRFs) with the ones obtained from the entire sample period. Matsubayashi reported that the impact of the US and Eurozone on Asian countries, especially China, is becoming larger since the last half of 1990s, reflecting the tighter trade linkages between China and the US and Eurozone.
Several recent studies examined the impact of the Chinese slowdown employing various 3 As we discuss below, China's membership of the World Trade Organization in 2001 dramatically altered the outlook of global trade. Thus, we have investigated the effect of China at years 1985China at years , 1995China at years , 2005China at years , and 2013. Two of them are before joining, and two others are after joining the WTO. 4 The focus of CPRX was to investigate the effect of the Chinese economy on the Latin American countries.
techniques. The IMF's China Country Report (2011) 5 analyzed the spillover effects of domestic policies in China. Based on the work by Chen, Gray, N Diaye, Oura, and Tamirisa (2010), 6 the report assessed how the worsening credit quality of the Chinese corporates and banks negatively affects the rest of the world by using the GVAR. Ahuja and Nabar (2012), Ahuja and Myrvoda (2012)  China's slowdown also curbs its demand for commodities, and we investigated whether this translates into commodity price drops. Our GIRFs show that a negative shock to the real GDP of China not only reduces crude oil prices, as some previous studies have shown, but also metals and agricultural prices. We also ran our model to test the impact of a potential US real GDP shock, and confirms that although the US has a stronger influence on Asian economies than China, these countries are more exposed to China than ever through increased economic ties.
The rest of the paper is organized as follows. In Section 2, we analyze the historical transition of the Chinese trade volume using trade data. In Section 3, we explain the standard GVAR model following past studies, and introduce several modifications, such as the time-varying trade weights, increasing the number of commodities, and inclusion of the "shift in intercepts" dummy variables to control the outliers. In Section 4, we estimate the model. In Section 5, we calculate the GIRFs, and investigate the effect of a Chinese economic shock on the Asian countries by comparing the shapes of the GIRFs with various settings.
Section 6 summarizes our conclusions.

The transition of China's trade share
China's membership of the World Trade Organization in 2001 dramatically altered the outlook for global trade and became a turning point for the country's economic development. In the left panel of Figure 1, we see how the share of exports of Asian countries to China evolved over the past several decades. We observe a significant jump since 2001: particularly, exports of Australia, Japan and the Republic of Korea to China have expanded more than three-fold. Likewise, the Asian countries' imports from China have been rising considerably in recent years (see the right panel of Figure 1). In particular, Australia, Japan, the Republic of Korea, Malaysia and the Philippines saw the largest rise in their imports from China.
China's share of world trade rose from about 4 percent in 2000 to around 11 percent last year. Figure 2 shows the evolution of trade shares of each country in 1985, 1995, 2005, and 2013

Analytical tool: The GVAR model
Our main goal is to measure the impact of China's economic slowdown and in order to do so, we assume a scenario where China's real economic growth declines by one percent.
In the following section, we first review the structure of the standard GVAR model. Next, we explain several modifications, which are necessary to achieve our objectives.

Structure of the standard GVAR model
The standard VAR of country i is a stand-alone model in the sense that it specifies the inter-temporal as well as inter-variable relation among a set of country i's macroeconomic variables, x it . The VAR(p) of country i, which includes p-th order lag of x it , is represented as follows: where a and Φ and the coefficient vectors. A vector of country-specific shocks, u it , is assumed to be distributed serially uncorrelated with zero mean and a nonsingular covariance With this specification, all variables of x it are assumed to be endogenous in general, thus interactively determined within its economy.
There are variables that are determined outside the country of interest. The price of crude oil, which largely reflects the demand and supply conditions in the world market, is one such example. For a small-open economy, it is more likely that the oil price is exogenously determined. Thus we expand the VAR model and add such global variables, d it , as follows: The GVAR model consists of a set of county-by-country VAR models that includes a set of "country-specific foreign variables" x * it , which is constructed by taking the weighted average across all the countries j of the corresponding variable as follows: where the weights satisfy ω ii = 0 and ∑ N j=1 ω ij = 1 for i = 1, . . . , N . Since this weight represents the closeness of the economic activities between the countries, the trade share, which is constructed by using the bi-directional trade flow data, is often used.
The VARX*(p, q, r) of country i, which includes p-th order lag of x it , q-th order lag of x * it and r-th order lag of d it , is represented as follows: where a, Φ, Λ, and Υ are the coefficient vectors. Since this specification includes the foreign variables ("star" variables) and the global variables, both of which are assumed to be weakly exogenous, the model is called VARX*.
When we estimate the country-specific VARX*, x * it are constructed directly from the data. However, for dynamic analysis such as calculating the impulse response functions, the value of x * it is calculated internally from the forecasted values of {x * jt } for i ̸ = j, which are obtained by solving the system of Equations (1) and (2). This is why the GVAR model can describe the interactions of variables not only within a country but also between countries.

Data and a related specification issue
In this paper, following CPRX, we have estimated 26 country-specific VARX* models. 8 Based on the dataset obtained from Centre for Financial Analysis & Policy, Judge Business School, University of Cambridge, 9 which covers the periods from 1979Q1 to 2011Q2, we have extended the dataset up to 2014Q3 in order to investigate the up-to-date impact of the Chinese economy on the world. The GDP of these 26 countries adds up to approximately 90% of the world GDP; therefore we claim that the model covers the world economy.
The standard elements of three variables in Equation (2) in the related literature are as follows. The domestic variables, x it , include the real GDP y it , the inflation rate π it , the real exchange rate e it − p it , the real equity prices q it , the short-term interest rate ρ S it , and the long-term interest rate ρ L it . Since q it , ρ S it , and ρ L it , are missing for some countries, they are included when available. 10 The foreign variables, x * it , are constructed as defined by Equation (1). As for the global variables, d it , the log of oil price index p O t is included in order to 8 Since one of the economies is the Eurozone, which consists of eight countries, i.e. Germany, France, Italy, Spain, Netherlands, Belgium, Austria, and Finland, the total number of countries in our data is 33. 9 We have downloaded GVAR Data 1979Q1-2011Q2 (2011 Vintage) from "The GVAR Toolbox" website at Centre for Financial Analysis & Policy, Judge Business School, University of Cambridge. URL is http://www.cfap.jbs.cam.ac.uk/research/gvartoolbox/download.html. The most updated dataset currently available is 2013 Vintage at "Global VAR Modelling" website created by Dr. L.Vanessa Smith. URL is https://sites.google.com/site/gvarmodelling/.
10 Specifically, the definitions of the variables are as follows: capture the influences from the international commodity market. 11 The dataset contains various types of countries. included in x US,t , and foreign financial variables, i.e. q * US,t , ρ S * US,t and ρ L * US,t , are excluded from 11 It is possible to include the global variables for some countries, but exclude them for the other countries. Thus we added country index "i" to its subscript.
x * US,t . This means that, for the US, the global variable d US,t is empty.
For the rest of the sample economies, it is assumed that both the international commodity markets and the foreign financial markets influence their economies. Thus for economy i, three commodity prices are included in d it , and three foreign financial variables are included Lastly, regarding the real exchange rate, we include e it − p it in x it for the remaining economies. However, conversely, it implies that the value of US currency is determined outside the US economy, and thus e * US,t − p * US,t is treated as a part of a "US-specific foreign" variable.

Several modifications
In order to appropriately measure the effect of China's emergence in the global economy, we introduce several modifications to the standard GVAR model. They are: 1. making the weight matrix ω ij time-varying 2. adding the metal price index p M t and the agricultural price index p A t to d it

detecting the structural breaks
The importance of these aspects will be discussed below.

Making the weight matrix ω ij time-varying
Previously, a set of "country-specific foreign variables" x * it was defined as Equation (1), which is constructed by using a constant weight matrix, ω ij . Now, it is modified as: so that the evolving between-countries closeness is measured by a sequence of time-varying weights, which satisfies ω ii (t) = 0 and ∑ N j=1 ω ij (t) = 1 for i = 1, . . . , N .
To our best knowledge, the first published application of a time-varying weight matrix was used by CPRX (2011), who investigated the impact of China's economic growth on the Latin American countries.
Since this weight represents the closeness of the economic activities between the countries, the ideal weights should properly reflect this magnitude. In the literature of GVAR, either one of two candidates is often used. One is the trade weight, which is constructed by using the bi-directional trade flow data. The other is the financial weight, which represents the flow of funds between the countries.
As we have examined in Section 2, China's trade linkages with the rest of the world have drastically increased after China joined the WTO in 2001. Although the financial linkages are deepening, the trade linkages continue to define China's economic impact. Besides, the quality of data used for constructing the trade weight is more reliable than that of financial weight, and these data are available from the 1980s. 12 Thus we construct ω ij (t) by using the three-year averages of bi-directional trade flow data, obtained from the IMF's Direction of Trade Statistics.

Adding two commodity price indices
In the literature, the standard GVAR models are estimated with only one global variable, i.e. the crude oil price, which is the representative of commodity "energy". According to Table 2, which reports the shares used for calculating the World Bank's Commodity Price Index, the share of crude oil in the energy index is 84.6%. The importance and the influence of crude oil price fluctuations on the macroeconomic variables of countries, such as the US, are reported by numerous researchers. Just to name a few, Hamilton (1983Hamilton ( , 1996Hamilton ( , 2003, Hooker (1996), and Cunado and de Gracia (2005).
The sum of "agriculture" and "metals and minerals" adds up to 96.5%. Since China is a major importer of metals and agricultural products, it is worth investigating the importance of including these indices in d it , which allows us to model the multiple channels of impact propagation through the international commodity markets. Table 3 summarizes the covariance analysis of three commodity prices (in log-differences).
The price of oil is the most volatile and the price of agricultural products is the least volatile.
In terms of the instantaneous correlation coefficients, Corr(∆p M   (3) is used. ***, **, *, represent 1 percent, 5 percent, and 10 percent significance levels, respectively. causality from the "agri" price. These results again contradict the view that "oil" is the foremost intermediate input, so that a hike of the oil price increases both agricultural and metal prices.
Given this preliminary analysis, we are now confident that the inclusion of agricultural and metal prices provides additional information, which is not revealed by inclusion of only oil prices.

Detecting the structural breaks with a difference-stationary VAR
As we formally report below, all the variables in our VARX* are the I(1) processes. Thus if they are co-integrated, the VARX* model can be transformed into a vector error correction model with exogenous variables. The previous papers in this field have mostly adopted this specification, which makes us impose any long-run relations that might exist in the economy, and increases the efficiency of parameter estimation.
However, as our sample covers the period between 1979Q1 and 2014Q3, it surely includes influential events such as the Asian Financial Crisis in 1997, the Lehman Shock in 2008, etc., which are likely to generate the structural breaks. The difficulty of detecting the structural break with the co-integrating VAR is reported by Hendry (2000).
A strand of research combines the Bayesian methods and the vector error correction models (henceforth VECM). Jockmann and Koop (2011), for instance, have incorporated the Markov switching into the VECM, which allows both the cointegrating vectors and the number of cointegrating relationships to change when the regime changes. Even though it is a fascinating approach, the computational burden outweighs the benefits when it is applied to the GVAR. 13 Besides, our aim is not forecasting but the historical evaluation of China's impact. Therefore, we treat the issue of structural breaks in a simpler manner.
First, the following "difference-stationary" VAR specification is used from now on: If it is correctly specified, the VECM is preferred to the difference-stationary VAR since the former generates more efficient estimates. However, the presence of unpredictable structural breaks hinders this task. Thus, we decided not to pursue the VECM specification.
Second, we have sequentially searched for one and only one significant "shift in intercept" event for each equation, which is one form of a structural break, by t-test. For this purpose, first, we search for the most significant intercept-shifts for each equation, by trimming the both 20% edges of the sample period. After detecting the most significant intercept-shifts, we add the intercept-shift dummy variables if and only if the intercept dummy is statistically significant at a 5% level, to the model in order to control the effect of possible structural breaks.

Estimation and testing
We proceed with the following analysis: 1. Testing the unit root 2. Detecting the structural breaks 3. Selecting the final specification of the models 4. Diagnostic tests

Testing the unit root
We begin by investigating the order of integration of each variable by using the Augmented Dickey-Fuller Tests. The Akaike information criterion is used for selecting the optimal lag length. The results indicate that most of the variables in levels contain a unit root, but are stationary after a first differencing.

Detecting the structural breaks
The One remedy is to add an intercept-shift dummy variable, which is supposed to explain a hidden dominant change of the data, if any. However, finding a good reason for adding such dummies is also controversial. Besides, given a large number of equations, it is almost an impossible task to examine such validities. Thus, ideally, we would like to detect and remove intercept-shifts automatically.
More specifically, we have adopted the following steps to detect and remove the interceptsshifts. 3. Choose the most significant step-indicator coefficient for each equation. If the t-value is significant at a 5% level, then add the step-indicator dummy to the GVAR model.
This algorithm was run equation-by-equation with all the lag combination of p, q, and r, and seven combinations of three commodity prices. In order to reduce the total number of parameters, we restrict the maximum lag length of foreign variables, q, to two, and that of global variables, r, to one. Further, we restrict the maximum lag lengths of domestic variables, p, to three. The list of the detected outliers is stored, and used for selecting the final specification for each country in the next step.

Selecting the final specification of the models
As the final step, adding the detected intercept dummy variable for each equation, we re-estimate the country-specific VARX*(p, q, r) models. Given these estimates, we search for the optimal lag lengths as well as the optimal combination of commodity prices for each country by using the AIC. The results are shown in the left half of Table 5. Note: Please refer to Table A1 in the Appendix for a glossary of acronyms. The specification used is Equation (4), where p=lag length of domestic variables (maximum lag is three), q=lag length of foreign variables (maximum lag is two), and r=lag length of global variables(maximum lag is one). AIC = logL -(number of parameters). Each model includes at most one automatically detected intercept-shift dummy, at the significance level of 5 percent. A column labelled "selected" reports the set of commodity prices included in the final version of VARX* models, where O, A, and M means the oil, agriculture, and metal prices, respectively. For the US, the commodity prices are treated as its endogenous variables, thus the value of r is not available (na).

Diagnostic tests
The country-specific VARX*, Equation (4), includes the contemporaneous values of x * it and d it , on its right hand side. We investigate two issues relating to them in this subsection.
One is about the weak dependence of the idiosyncratic shocks, which is a key assumption for the estimation of Equation (4). The second issue concerns the contemporaneous impact of foreign variables on the domestic counterparts.
In the literature of GVAR, it is a common practice that the country-specific VARX* models, Equation (4), i.e. the equations of x it , are estimated on a country-by-country basis.
As listed in  (3). Practically, this enables us to reduce the number of parameters significantly, and make us construct the world model.
Three justifications for this estimation procedure are given by Pesaran, Schuermann, and Weiner (2004). They are: 1) stability of the system; 2) smallness of weights ω ij (t); and 3) the weak dependence of the idiosyncratic shocks. 14 Here, we examine the weak dependence of the idiosyncratic shocks. Table 6 reports the average pair-wise cross-section correlations for the levels and first differences of x it , as well as the associated VARX* residuals.
Generally speaking, the average pair-wise cross-section correlations are high for the "Levels", but they drop drastically as differenced. The correlations further decline as their dynamics are modeled by VARX*. A closer look reveals that the VARX* model with the contemporaneous "star" variables (Type-2) generally yields much weaker dependence of idiosyncratic shocks than that without the contemporaneous "star" variables (Type-1). This is consistent with the idea that the contemporaneous "star" variables function as proxies for the common global factors. Thus, once country-specific models are formulated as being 14 The stability of the system is numerically confirmed when the impulse response analysis is examined in the latter section. The smallness of weights calculated from the trade flow data is reported elsewhere, thus we do not repeat it. Concerning the weak dependence, see Appendix for additional discussion.
conditional on foreign variables, the remaining shocks across countries becomes weak, as expected.
Next we examine the contemporaneous effects of foreign variables on their domestic counterparts. Because the data are either log-differenced (for the real GDP, inflation, real equity prices, and the exchange rate) or differenced (for two kinds of interest rates), one can interpret the estimate as impact elasticity. Table 7 reports these estimates. The number of asterisks indicates the level of statistical significance.
As for the statistically significant coefficients, all coefficients for short-term interest rates are positive, as expected. For real output, the Asian countries are relatively less sensitive to foreign demand since none of the coefficients is statistically significant even at a 10% level. Concerning inflation, the significant foreign effects on Australia, China, Malaysia, New Zealand and Singapore are observed. This might reflect the degree of openness of these economies, however further investigation is needed. Noticeably, all the coefficients of equity prices are positive and significant at the one percent level. For two interest rates, similar phenomena are observed. The fact that the impact elasticities of equity prices and the long-term interest rates exhibit highly significant coefficients might reflect the degree of financial integration. On the other hand, the insensitivity of short-term interest rates for several countries is due to their monetary policies. Except for Australia, New Zealand and Singapore, the elasticities of short-term interest are insignificant for all the Asian countries.

The Chinese impact
In this section, we estimate the GIRFs using the estimated GVAR model. The concept of GIRFs was proposed by Koop, Pesaran, and Potter (1996) and has been applied to VAR analysis by Pesaran and Shin (1998). Note: Please refer to Table A1 in the Appendix for a glossary of acronyms. VARX* Res (Type-2) refers to residuals from country-specific VARX* models. The specification is given as Equation (4). VARX* Res (Type-1) are obtained after re-estimating the model without the contemporaneous "star" variables. Note: Please refer to Table A1 in the Appendix for a glossary of acronyms. White's heteroskedasticity robust standard error is used. ***, **, *, represent 1 percent, 5 percent, and 10 percent significance levels, respectively.
Mathematically, it is defined as where σ ii,ℓℓ is the corresponding diagonal element of the residuals' variance-covariance matrix Σ u ; Ω t−1 is the information set at time t − 1.
GIRFs are different from the standard IRFs proposed by Sims (1980), which assumes orthogonal shocks. The standard IRFs are calculated using the Cholesky decomposition of the covariance matrix of reduced-form errors. Thus, if we calculate the IRFs using different orders of variables, the shape of the IRFs will be different. If a VAR contains two or three variables, we might be able to use the standard IRFs by assuming a relation between the variables inferred from economic theory. However, the same approach is not useful for the GVAR model since it contains a large number of variables. This means that we cannot list a set of variables with a reasonable order that reflects economic theory. Therefore, instead of using the standard IRFs proposed by Sims (1980), we use the GIRFs, which produce shock response profiles that do not vary for different orders of variables.
We will investigate how a negative real GDP shock in China transmits to the Asian countries as well as major developed economies based on the trade weights of 1985, 1995, 2005, and 2013. As explained in Section 2, as the trade linkages strengthen, we see a Our focus is on seeing how the change of trade relations affects the propagation of shock.
First, we will examine the impact of a one percent drop in China's real GDP growth rate on the developed nations of the United States, the Eurozone, and Japan, see the first row of Figure 3. The first panel shows the evolution of the Chinese GDP growth rate after a one percent decline. Possibly due to the feedback effect, a one percent decline in the GDP growth rate results in 1.6% reduction of the real GDP in levels after 20 quarters for China.
For the United States, the Eurozone, and Japan, the impact of a negative shock on Chinese GDP is increasingly negative as we use more recent trade weights. However, the GIRFs have a negative shape when using the trade weight matrices of 1985 and 1995, and these lines are near zero. Therefore, it may imply that a negative Chinese shock would have had minimal or nonexistent effect on these economies in 1985 and 1995.
In terms of the magnitude, we notice that the US experiences the most pronounced impact compared to the Eurozone and Japan both in the short-term as well as the long-term. In the long-term, the size of US GDP drops by 0.07%. On the other hand, for the Eurozone and Japan, the size drops by approximately 0.05%. In terms of scale, the recent impact is approximately 12 times bigger than that of 1985 for the US and the Eurozone. For Japan, it is about 20 times bigger. Thus, we conclude that, over three decades, the US and Eurozone exhibit similar responses both qualitatively and quantitatively. We will test the significance of the negative impact in the next section.
The second to fourth rows of Figure 3 show the GIRFs for a one percent decline in China's growth on our set of Asian countries. As in the developed countries' case, the impact of a negative shock has become progressively negative on the Asian economies using more recent trade weight structures. The Republic of Korea, Malaysia and Singapore had a nearly nonexistent impact with 1985 trade weight. Similar phenomena, but a slightly negative impact, are observed for other countries.
Under more recent trade structures, every country except the Philippines experiences a negative shock either in the short term or in the long term; however, the level and extent of the shocks differ greatly. Indonesia is by far the most negatively impacted country both in the short term as well as the long term. It is followed by Thailand (-0.095% in the long term), the Republic of Korea (-0.070%), Singapore (-0.050%), Malaysia (-0.050%), and Australia (-0.045%). The impact of a negative Chinese real GDP shock is less marked for India (-0.018%). Interestingly, for the Philippines, the impact of a negative Chinese shock is positive.
In the last three panels of Figure 3, we display the GIRFs for a one percent decline in China's GDP on three commodity price indices. China's increasingly commodity-intensive growth path manifests itself in the increasingly negative impact of Chinese negative growth shock on commodity prices. Similar to the GIRFs observed above, the impact of Chinese negative GDP shock is considerably more visible under the 2013 trade matrix structure.
China is the world's largest consumer of industrial metals (-1.33% drop in a long term) and the second-largest consumer of oil (-1.14%). China's impact on agricultural prices rose significantly after year 2000, although the impact on prices in both the short-term and the long-term is much more muted compared to the impact on oil and metal prices. Figure 4 shows the GIRFs for a one percent decline in China's real GDP growth rate using the trade weights of 2013 at a 68% confidence interval using a bootstrapping method.
The figures show that the GIRFs of US, Euro, Japan, Indonesia, the Republic of Korea, Malaysia, Singapore and Thailand are significant at a 68% confidence interval.  Table 8.
Lastly, we also note that oil, metal and agricultural price indices are consistently all negatively significant.
What is the response of other domestic variables? Figures 6 and 7 report the GIRFs of three other variables, Dp (rate of inflation), eq (real equity price), and reer (real effective  Table A1 in the Appendix for a glossary of acronyms. The lines correspond to the paths of standard GIRF(blue), median(red line), and 16th and 84th percentiles (red long dash) of the distribution.
exchange rate). To make the figures concise and easier to understand, we have shortened the horizontal axis from 21 quarters (five years) to 13 quarters (three years), and added two vertical lines, corresponding to four quarters and eight quarters after the shock.
For the rate of inflation, it drops after a negative Chinese shock for all the countries, except Indonesia. For the equity price, the markets of most countries are negatively impacted, although there are notable differences. New Zealand is the only exception whose equity market positively responds to a negative Chinese shock. As we have obtained a positive response path for its real GDP, this might be the reason. Lastly, for the real effective exchange rate, all countries experience depreciation.

The impact of a potential US GDP shock
For comparison with the impact of a potential Chinese real GDP shock, analyzed in the previous section, we will now investigate the impact of a one percent drop in US real GDP on other countries. First, we review the GIRFs of China, the Eurozone, and Japan in Figure   8. Although the response of China with the trade weights of 2013 is found to be entirely positive, which is quite counter-intuitive, the effect of the US on China becomes weaker over the sample period.
On the other hand, for the Eurozone and Japan, we note that, although the impact is negative, the level and shape does not change across different trade matrices, which was the case for China given its growing presence in the global economy. Figure 8 shows that a decline of the US real GDP growth rate has a negative impact on Asian countries, including New Zealand and the Philippines, which both showed a more muted response to a Chinese shock. By comparing Figure 8 with Figure 3, it is easy to infer that although the impact of a US shock will be considerably larger than a Chinese shock, the magnitude of response progressively increases reflecting China's increased economic ties and influence on Asian economies.
In Figure 9, we calculated the 68% confidence interval using a bootstrapping method contrasting the GIRFs of 2013 and 1985. The impacts on the Republic of Korea and Singapore are statistically significant at 68% confidence interval when using a trade weight matrix in 1985 and 2013. With the more recent trade structure, the response of Australia, Malaysia, the Philippines, and Thailand also becomes statistically significant. For New Zealand, the significant effect of the US is observed for four quarters after the shock. However, some of the remaining countries show a borderline statistical significance, while others are not statistically significant. In general, the distribution of GIRFs with respect to a one percent decline in US s growth rate remains the same over the last three decades for the Asian countries. This finding contrasts with the effect of a Chinese shock. Although the US has a stronger influence on Asian economies than China, these countries are more exposed to China than ever through increased economic ties. Note: Please refer to Table A1 in the Appendix for a glossary of acronyms. The lines correspond to the path of median (blue), 16th and 84th percentiles (red dash) of the distribution. The horizontal axis is now shortened to three years, and two vertical lines correspond to four quarters and eight quarters after the shock, respectively. For China's equations, the real equity price is not included due to data unavailability. Thus the corresponding GIRFs are not calculated..

The shock propagations through metals and agricultural prices
Lastly, we re-examine the implication of adding two commodities to the standard GVAR model. As we briefly discussed, in terms of AIC, we found the benefit of selecting the best combinations out of three commodities over the oil-only model for all 26 economies. 15 Here, instead, we compare the shapes of the GIRFs using the year 2013 trade weights. See Figure   15 We thank comments from Joseph Zveglich and Renee Fry-McKibbin on the treatment of this issue.    Note: Please refer to Table A1 in the Appendix for a glossary of acronyms. The lines correspond to the path of median (blue), 16th and 84th percentiles (red dash) of the distribution. The horizontal axis is now shortened to three years, and two vertical lines correspond to four quarters and eight quarters after the shock, respectively. For Indonesia's equations, the real equity price is not included due to data unavailability. Thus the corresponding GIRFs are not calculated.

16
The responses of the "oil-only" model appear to overestimate the impact of China's slowdown for the US, Australia, New Zealand, the Philippines, and Singapore. For example, the response of Australia was significant with the "oil-only" model, which now becomes marginally insignificant with three-commodity model. According to Table 5, the VARX* model of Australia includes all three commodity prices. This suggests the usefulness of adding two commodity prices to the GVAR model. On the other hand, for Indonesia, the three commodities model suggests a larger negative impact in the long-term. Although the magnitude is much smaller than that of Indonesia, the negative impact of a Chinese shock on Malaysia and Thailand are also larger with three commodity models. These results indicate the usefulness of including the multiple commodity prices in order to capture the different channels of shock transmission.

Conclusions and remarks
In this paper, following CPRX, we estimated a GVAR model using a time-varying trade weight matrix. China's economy has been growing fast and its presence in the global economy  1985, 1995, 2005, and 2013 in order to compare the size and timing of the shock propagations.
We also calculated the 68% and 90% confidence intervals using the bootstrapping method and tested whether the estimated impacts are statistically significant.  Table A1 in the Appendix for a glossary of acronyms. The lines correspond to the 16th and 84th percentiles of the "oil-only" case(red dots) and the "optimal combination of multiple commodities" case (blue line) the most, reflecting both demand and terms of trade shocks. Export-dependent countries on the East Asian production cycle, such as Japan, Singapore, Malaysia and Thailand, are also severely affected.
A shock to the Chinese real GDP also has an impact on the international prices of not only the crude oil market but also metals and agricultural markets, showing the degree of influence of China on the global terms of trade.
With regard to the future research, we consider improvement of the trade weight matrix to be the key. In this paper, following CPRX, we used the trade weight matrix representing the linkages to different countries. However, capital inflows and outflows significantly affect economies. Since the measurement of closeness of countries is key for the GVAR model, we should also consider using foreign direct investment data. If we can capture the financial linkages between countries, we can, for example, analyze the impact of monetary policy changes in advanced economies on developing countries.

On the weak exogeneity
This subsection follows the example by Fisher (1993) with a slight modification. For simplicity, let both x t and x * t be scalars, and consider the VAR* model for a country (without country index i) One can reparameterize Equation (6) in terms of conditional and marginal models as: The error term of the conditional model becomes: where Ω = Σ 11 − Σ 12 Σ −1 22 Σ 21 with Σs being the corresponding covariance elements of (u ′ 1t , u ′ 2t ) ′ . Then, the parameters in Equations (6), (7), and (8) are related as: The short-run dynamic stability of the conditional model requires θ 2 in Equation (7) to be |θ 2 | < 1. If this restriction is not imposed, the parameters of the conditional distribution λ 1 = (θ 0 , θ 1 , θ 2 , θ 3 , Ω) and marginal distributions λ 2 = (a 2 , Γ 21 , Γ 22 , Σ 22 ) define a sequential cut between the conditional and the marginal models. Hence, weak exogeneity holds. If the short-run dynamic stability is imposed, on the other hand, it implies |Γ 11 −θ 1 Γ 21 | < 1 due to cross-equation restrictions. Under this circumstance, λ 1 and λ 2 are no longer variation free. However, if Γ 21 is zero, weak exogeneity still holds.
Following this insight, we have investigated the weak dependence of idiosyncratic shocks, and confirmed that pair-wise cross-section correlations of shocks are actually very weak.