The US trade deficit and
China s exchange rate
regime
-
An empirical assessment of the impact of Yuan
appre-ciations on the US trade imbalance with China
Roman Bahr
Student ID: 10827331
Master’s thesis
M.Sc. Research Seminar International Economics & Globalisation
Universiteit van Amsterdam
2
ndof August 2015
E-mail: roman.bahr@student.uva.nl
Supervisor: Naomi Leefmans
Statement of Originality
This document is written by student Roman Bahr who declares to take
full responsibility for the contents of this document.
I declare that the text and the work presented in this document is
orig-inal and that no sources other than those mentioned in the text and its
references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the
su-pervision of completion of the work, not for the contents.
Table of contents
1.
Introduction………..4
2.
Literature Review………..7
2.1.
Literature on the Marshall-Lerner condition…………...………..8
2.2.
Literature on the J-Curve phenomenon………...…..9
2.3.
Literature on trade between the US and China………..10
3.
Theoretical background………..12
3.1.
China s Exchange Rate Regime……….12
3.1.1.
Historical evolution………12
3.1.2.
Mechanism of preserving the currency value………13
3.2.
The Marshall-Lerner condition………14
3.3.
The J-curve phenomenon...…….………15
4.
Empirical analysis.………..16
4.1.
Data and variables………16
4.2.
Methodology………19
4.2.1.
The ARDL-ECM………..20
4.2.1.1.
Step I: Bounds testing for cointegration………22
4.2.1.2.
Step II: Estimation of the ECM……….24
4.2.1.3.
Post-estimation tests……….26
5.
Regression results………..27
5.1.
Long-run estimations in the unrestricted ARDL-ECM…………...28
5.2.
Short-run dynamics in the restricted ARDL-ECM……….31
5.3.
Post-estimation tests………..32
6.
Conclusion………...34
7.
References………...36
-400 -350 -300 -250 -200 -150 -100 -50 0
US Trade-balance with China (Goods in billion US$)
1.
Introduction
During the last decades China s importance in international trade has been grow-ing steadily, such that it became the world s leadgrow-ing export nation. )ts major trad-ing partner is the United States, which accounted for 20% of Chinese exports in 2014 (OECD and US Census Bureau, . As China s rapid export-growth has been accompanied by increasing imbalances in bilateral trade with the US, i.e. US imports from China largely exceed exports to China, debates on policy measures to counteract the US trade deficit were fuelled internationally and especially in the US itself. In particular, claims of China preserving its trade advantage by keeping its currency below its actual value arose, therefore being to a great extent accountable for the overall US trade deficit. In fact, as displayed in figure 1, the US bilateral trade deficit in traded goods with China rose from US$ 29.5 billion in 1994 to US$ 342.6 billion in 2014.
Figure 1. Yearly bilateral US-China trade balance (goods in billion US$)
Data: US Census Bureau
Generally, a higher exchange rate, i.e. a higher level of domestic currency units for one unit of the foreign currency, enhances a country s trade competitiveness, since the relative price of exports to the foreign market decreases, therefore driving up foreign demand. In order to strengthen its competitiveness, China pegged its cur-rency, the Yuan or Renminbi (RMB), to the US$ in 1994. This fixed exchange rate
0 1 2 3 4 5 6 7 8 9 10 NER: Yuan/US$
regime has been kept for more than a decade. Meanwhile, estimates of the Yuan undervaluation went up to 50% in early 2005. (Goldstein and Lardy, 2008)
In the debates on the US trade deficit, the US as well as international organi-sations as for instance the IMF prevalently called for an adjustment of the Yuan-US$ exchange rate (Morrison, 2008). In July 2005, the People’s Bank of China (PBC) inclined to the pressure and appreciated the Yuan by 2% at once (Federal Reserve Bank of St. Louis, 2015). From that date on a managed float regime has been kept, with the Yuan tied to a basket of major currencies (Morrison, 2008). This enabled the currency to appreciate from its peg-value of 8.28 Yuan/US$ prior to the reform by 25% up to a value of 6.21 Yuan/US$ end of 2014. Due to a sharp decrease in demand for Chinese exports during the financial crisis, the PBC pegged the Yuan to the dollar again to retain its competitiveness in 2008 (see figure 2). After the eco-nomic situation appeared to recover in 2010, the managed float was re-established and thus the appreciation of the Yuan continued (Morrison, 2013). The evolution of China s exchange rate regime will be analysed more detailed in section 3.
Figure 2. Monthly nominal exchange rate (Yuan per US-Dollar)
Data: Federal Reserve Bank of St. Louis
The increased value of China s currency may have decreased the US trade deficit compared with the size it would have had absent of the Yuan appreciation. This thesis therefore aims at exposing the actual effect of the Yuan appreciations empir-ically. It frames the question: How has the revaluation of the Yuan affected the
bi-lateral US trade balance with China? )n particular, it is ought to reveal significance of the revaluation effect through the channel of the real exchange rate (RER).
Methodologically, an Autoregressive Distributed Lag – Error Correction Model (ARDL-ECM), an econometric procedure developed by Pesaran, Shin and Smith (2001), is adopted. It includes regression of the dependent variable in first-difference form on the independent variables, their lagged first-differences as well as lagged levels of all variables and is augmented with an error correction term, which reflects movement towards equilibrium. This approach has been increasing-ly applied in studies on trade balance effects in recent years, not onincreasing-ly as it allows for estimation of short- and long-run effects simultaneously, but also since it ena-bles usage of data integrated of different levels, i.e. stationary and non-stationary, in cointegration analysis (Bahmani-Oskooee and Brooks, 1999). Its properties as well as advantages will be discussed in detail in section 4.
Using this method, the impact of the RER on the trade balance will be esti-mated, controlling for domestic and foreign income, since an increase in a coun-try s income will raise import demand and therefore affect the trade balance. A time series analysis will be conducted, containing bilateral data on trade between the US and China. Monthly data on US exports and imports, forming the trade bal-ance, on the RER and income of the US as well as China from 2004:12 until 2014:11 will be used in order to investigate short- as well as long-run effects. Consequently, this analysis will also reveal, whether the so-called J-curve phenomenon – intro-duced by Magee (1973) – exists, i.e. whether an overall long-run improvement of the trade balance follows an initial deterioration after a currency depreciation. A detailed explanation of the latter will be found in section 3.3.
Consistent with findings of the existing literature on exchange rate effects on the trade balance, as displayed in section 2, rather weak, but significant1 effects of
the Yuan appreciations on the trade balance between the US and China are ex-pected. Moreover, there might be alternative causes for the bad trade performance of the US. As for instance McKinnon (2012) argues, it could well be the case that the US find its negative trade balance rather caused by relatively low savings.
In context of a large scope of literature, this thesis is ought to contribute an insight into the recent development of the RER effects on the trade balance
tween the US and China. As can be seen in section 2, several studies assessed RER effects on trade between the US and China, yet, to my knowledge, no analysis of the Yuan revaluation effect on the US trade deficit has been conducted on the particu-lar time-span after the Yuan has been de-pegged. Application of the ARDL-ECM model reflects the econometric evolution of the last two decades and seems to be an appropriate approach to examine short- and long-run dynamics of the recent Yuan appreciation.
This thesis is structured as follows. The existing literature on exchange rate effects on international trade is discussed in section 2, finding a large extent of rel-evant studies, which overall show rather inconclusive results. A theoretical back-ground for the treated topic is provided in section 3. Next, in section 4, the empiri-cal approach based on the econometric model of Pesaran et al. (2001) is explained. Section 5 then reveals the estimated regression results as well as their analysis, before final conclusions are drawn in section 6.
2.
Literature review
This section reviews the existing relevant literature on exchange rate effects on international trade. Over the last decades different methodologies have evolved to assess exchange rate effects on trade. Thus there is a large and diverse amount of relevant empirical studies.
Theoretically, there are two basic mechanisms that have been examined in most of the literature. First, there is the Marshall-Lerner (M-L) condition referring to the exchange rate elasticities of exports and imports2 of a country. It requires
the sum of those elasticities to be greater than 1 in order to pass the effect of an exchange rate alteration through onto the trade balance, i.e. the differential of ex-ports and imex-ports of a country (Bahmani-Oskooee, Harvey and Hegerty, 2013). Sec-ond, there is the J-curve phenomenon, which describes short- and long-run dynam-ics of the trade balance as a consequence of an exchange rate movement. It pre-sumes that there is an initial negative trade balance effect of a currency devalua-tion in the short-run, followed by a positive long-run effect of larger extent
mani-Oskooee and Ratha, 2004). This is due to a delayed adjustment of trade vol-umes to the new relative price, the exchange rate. Both the M-L condition and J-Curve phenomenon will be explained more in detail in section 3.
Below at first the empirical literature testing the M-L condition will be dis-cussed. It typically involves the use of aggregate, i.e. multilateral, trade data. Thereafter those examinations elaborating the J-curve are presented, which pref-erably make use of bilateral trade data. This is said to reduce aggregation bias, i.e. positive trade balance effects of the exchange rate of one country might in aggre-gated view be offset by negative effects of another (Bahmani-Oskooee and Brooks, 1999). Several studies obtain ambiguous results with respect to both the M-L con-dition and predominantly the J-curve effect.
2.1. Literature on the Marshall-Lerner condition
One of the first studies to assess trade elasticities is Houthakker and Magee (1969). Using a simple model with reduced form equations, the relative world price as well as income and their long-run impact on exports and imports separately are exam-ined for several industrial countries. However, they do not formally address the M-L condition. Similarly, Wilson and Takacs (1979) conduct their study including the nominal exchange rate (NER) as explanatory variable for trade levels, yet not ob-taining a significant effect on trade.
Arize (1987), using a two stage least square model, finds the M-L condition to be satisfied for 7 out of 8 African countries also by applying price ratios, where-as Rose (1991) does not reveal any significant evidence. The latter uses cointegra-tion analysis introduced by Engle and Granger (1987) on 5 major OECD members to examine the effect of the exchange rate on the aggregate trade balance.
While the previous studies are based on aggregate trade data, Bahmani-Oskooee and Brooks (1999) apply bilateral trade data on the US and 6 trading part-ners. Integrating the real exchange rate (RER) in a cointegration model – see next paragraph – they find that trade with 4 of the 6 partners satisfies the M-L condi-tion. Sinha (2001) obtains evidence from Asian countries. In 4 out of 5 cases the M-L condition holds. A single equation cointegration model is adopted, which, accord-ing to Arize (1996), is claimed to be an adequate method to examine the M-L condi-tion.
2.2. Literature on the J-curve phenomenon
Literature that distinguishes between short- and long-run effects of the exchange rate on trade examines the existence of the J-curve phenomenon. The first study to mention in this context is the work by Magee (1973), as it introduces the J-curve effect empirically. Based on US trade data the trade balance is modelled as export-to-import ratio depending on home and foreign income (Y, Y*). It is concluded that there might be a J-curve effect, however no significant evidence is obtained. Simi-larly, Haynes and Stone (1982) only find mixed results, as well estimating exchange rate effects of the export-to-import ratio, on 41 countries using aggregate data. So does Himarios (1985), who applies OLS and includes the RER as a determinant of the trade balance, making use of a lag-structure. However, solely a significant long-run relationship is found.
Rosenzweig and Koch (1988) estimate separate equations for export and import levels for the US applying Granger-causality, i.e. testing if one time series can forecast another, and like Mahdavi and Sohrabian (1993) find a delayed J-curve, whereas Rose and Yellen (1989) neither find evidence of cointegration of the variables in the long run, nor for a J-Curve. The latter examine US trade data with the G7 states on a bilateral level. Defining the dependent variable, the trade bal-ance as differential of exports and imports reveals the weakness of not being a unit-free measure (Bahmani-Oskooee and Ratha, 2004).
Shirvani and Wilbratte (1997) estimate the export-to-import ratio on a bi-lateral level for the US and obtain a significantly positive long- as well as mid-term effect of a currency devaluation on the trade balance. Thus they rather find an L-curve instead of a J-L-curve (Bahmani-Oskooee and Ratha, 2004). Like several previ-ous studies, they apply Johansen cointegration on their estimation, which includes the RER and home respectively foreign income (Y, Y*) as explanatory variables.
Above-mentioned Bahmani-Oskooee and Brooks (1999) predominantly also examine the J-curve effect. They attribute Rose’s and Yellen’s (1989) failure to find evidence of cointegration or a J-curve to the fact that they neither incorporate an error correction model (ECM), which is claimed to be supportive in showing coin-tegration, in their autoregressive model, nor apply the Akaike Information Criterion (AIC) for the optimum number of lagged variables. Instead Bahmani-Oskooee and Brooks adopt a more advanced methodology, the Two-step Autoregressive
Distrib-uted Lag model, in a first version introduced by Pesaran and Shin (1995), which consists of an autoregressive distributed lag model amended by an error correc-tion term (ARDL-ECM). This approach enables examinacorrec-tion of short- and long-run dynamics as well as the use of time series data integrated at different levels, i.e. stationary at level or in first differences, in order to show cointegration, which is later on referred to as the bounds testing approach in the advanced model by Pe-saran, Shin and Smith (2001). It will be the foundation of this thesis examining ex-change rate effects on the bilateral trade balance between the US and China. How-ever, Bahmani-Oskooee and Brooks do not obtain any evidence of a J-curve, albeit they find the RER and trade balance cointegrated in the long run, which as well applies to Bahmani-Oskooee and Wang who investigate China s trade bal-ance with 13 countries via a VAR model. Estimates of the RER effect in the latter study range mostly close to, but below 1.
In a vast number of further studies, J-curve estimations mostly result in am-biguous findings, as for instance Bahmani-Oskooee and Ratha (2003) estimate US data with several trade partners, finding proof of it in approximately half of the cases.
2.3. Literature on trade between the US and China
Lastly, the more recent literature assessing trade specificially between the US and China, thus being directly linked to the research question in this thesis, is re-viewed. Whereas in earlier studies separate equations for exports and imports or equations differencing both are employed, the more recent literature uses ratios of exports over imports or vice versa.
First to mention are Bahmani-Oskooee and Wang (2008), who divide trade between the US and China from 1978 to 2002 by 88 industries, which is claimed to avoid aggregation bias, i.e. effects on one trade sector equalising effects on another sector leading to insignificant results, and examine the impact of a depreciated Yu-an on the trade balYu-ance. By application of the ARDL-ECM method, including data on the RER, home and foreign income, the US trade balance of 34 industries appears to be significantly negatively affected in the long run, among which 22 reveal a J-curve. Contrarily, Zhang and Sato (2009) estimate only a weak link between the RER and the bilateral trade balance of China and the US between 1994 and 2007
via an Vector Autoregressive model, which extents the AR model to multivariate time series. They examine impulse responses of China s trade balance dependent on the RER, home and foreign income. Moreover, they find China s trade balance as well as the RER accountable for the variability in US income.
Zhang, Fung and Kummer (2006) make use of a computable general equilib-rium (CGE) model, which is based on Walrasian law, i.e. labor and capital market clearing as well as perfect competition. Simulations are run for different possible levels of Yuan revaluation, where short-run effects on the US trade deficit are found to be mostly insignificant. This is claimed to be due to the inelasticity in US demand for Chinese exports. Only in case of larger Yuan appreciations of 12%, the US trade balance improves, while China s worsens. This in turn is found to have an adverse effect on the world market.
Zhang (2012) applies a macro-econometric model by Fair in order to fore-cast the effect of a 25% Yuan revaluation on multiple macroeconomic variables as well as income- and price elasticities. He fails to reveal significant changes in the trade imbalance between the US and China.
Concluding, several studies assessed exchange rate effects on the bilateral trade balance between the US and China so far. However, e.g. Bahmani-Oskooee and Wang (2008) examined said effect disaggregated by sectors for a time-span well before the Yuan moved to a managed float, whereas above mentioned Zhang et al. (2006) only use forecasts for the appreciation effect. The research capturing the most recent time period in the literature, up to 2 years after de-pegging the Yuan, is Zhang and Sato (2009). Nevertheless, their focus rather lies on China and the consequences it bears from the reformed exchange rate regime. Also, analysing the appreciation effect only until 2007 might not be sufficiently representative for the purpose of showing the long-run impact the revaluated Yuan has. Therefore, this thesis extends the underlying period to 2014, focussing on the US as well as its trade imbalance with China and employing the most recent technique in interna-tional trade analysis, the ARDL-ECM approach by Pesaran et al. (2001).
3.
Theoretical background
This section provides the theoretical background on the major mechanisms in the context of the analysis in this thesis. In particular, China s exchange rate regime is examined as well as the mechanisms of the M-L condition and the J-curve phenom-enon are explained.
3.1. China’s exchange rate regime 3.1.1. Historical evolution
The Chinese exchange rate system experienced several changes, which were driv-en by economic and political factors. In the following, the major changes in the re-gime from mid-twentieth century until today will be revealed.
Between 1949 and 1952, the exchange rate was highly volatile and the economy was recovering from World War II. In order to advance recovery, the PBC aimed at export encouragement, while constraining imports, which should fuel domestic production. Furthermore, a system of multiple exchange rates was united to one. Later on, the PBC moved to a policy more balancing between exports and imports.
From 1953 until 1972, a fixed exchange rate system was kept erasing the possibility of using the exchange rate as policy tool, i.e. enhance the economy via a currency depreciation. From 1973 on the Yuan then was pegged to a currency bas-ket and fluctuated continuously. By the end of that period, in 1983, the Yuan was highly overvalued.
Between 1983 and 1992, the Chinese economy was in transition. A dual ex-change rate regime was pursued, which consisted of the official rate and the inter-nal settlement rate (ISR). The latter was applied for trade transactions only and enabled exporting firms to sell their foreign earnings at foreign exchange swap centers. With 2.8 Yuan/US$ it was almost double the official rate. Between 1985 and 1993 the Yuan depreciated sharply and the dual exchange rate system was gradually abandoned towards a regime, where the exchange rate is determined by demand and supply in the foreign exchange markets. By 1993 the dual rate spread reached from 5.77 Yuan/US$, the official rate, to 8.70 Yuan/US$ in the swap mar-ket.
In 1994, the Yuan then was pegged to the US Dollar in a managed floating exchange rate regime, accompanied by a further sharp depreciation at once to a value slight-ly above 8 Yuan/US$. The daislight-ly band of fluctuation was set at 0.3%. This peg also remained in place during the Asian Financial Crisis 1997-1998, providing stability to the Asian region (Cui, 2014).
Under pressure from the US government and international bodies, among others the IMF, which claimed an undervaluation of the Yuan between 12 and 50% (Morrison, 2013), the PBC released the US-dollar-peg in July 2005. Instead a man-aged float, which tied the Yuan to major currencies, among others the US Dollar, the Euro, the Japanese Yen and the Korean Won, with different, not publicly re-vealed weights for each currency was installed. The band of daily fluctuation was widened to 0.5%. This provided space for the Yuan to appreciate continuously, which it did against all major currencies in the basket until 2008, when the PBC returned to the dollar-peg in order to stabilise its export sector during the global financial crisis. In 2010, the managed float superseded the fixed regime. The daily fluctuation band was widened to 1% in 2012 and 2% in 2014. Consequently the Yuan appreciated to a value of 6.21/US$ by the end of 2014.
3.1.2. Mechanism of preserving the currency value
The PBC preserved the dollar-peg while the fixed exchange rate regime was in place despite appreciative pressure, which was caused by China s large exports and the accompanying foreign exchange inflows. Since implementation of the man-aged float, the PBC still operates in a similar manner, except it aims at moderating the pace of Yuan appreciation instead.
To achieve its target, the PBC intervenes in the currency market by absorb-ing foreign capital, i.e. mostly US Dollars, which Chinese exporters gain in the for-eign market, and buying it in exchange for Yuan. Furthermore, via strict capital controls, in- and outflows of foreign capital are restricted and therefore fluctua-tions in demand and supply of foreign capital are kept on a low level. This in turn stabilises the exchange rate.
The PBC can sterilise its interventions, i.e. revert the effect on the amount of money circulating, by selling government bonds. On one hand, this alleviates the inflationary pressure arising from non-sterilised interventions. On the other hand
it raises government debt, which in general negatively influences the budgetary sustainability. In case of China the latter is not a severe problem due to its rapid economic growth over the last decades. (Yongnian and Yi, 2007) In fact, China sterilised 80% of its foreign exchange market interventions between 2000 and 2006. (Lavigne, 2008)
However, interventions result in accumulation of foreign exchange reserves. By this means, China accumulated reserves of approximately US$ 50 billion in 1994 to a peak of US$ 4 trillion in 2014 (World Bank, 2015), which ranks top posi-tion in the world. It is estimated that 70% of those reserves are foreign reserve assets denominated in US Dollars. (Morrison, 2013)
Concerns on behalf of the US government were expressed that those huge US Dollar reserves could destabilise the US Dollar itself and if sold, US interest rates. Contrarily, it is also argued that even a large-scale sale of China s Dollar re-serves would not significantly affect US interest rates or the Dollar value due to the size and sufficient liquidity of the global financial market. (Salitan, 2010)
In addition to inflationary pressure and accumulation of debt, huge foreign exchange reserves bear opportunity costs for China. China s Dollar reserves are invested in foreign reserve assets, as for example US treasury bills or bonds, which generate interest. However, the interest rate on those investments is by far lower than the interest rate China pays on inward foreign investment. Therefore, the ex-porters bringing foreign reserves into China could invest it at much higher yields, than the PBC does after absorbing it. (Yongnian and Yi, 2007)
3.2. The Marshall-Lerner condition
As this study examines the effect of exchange rate changes on the trade balance, determination of the long-term relationship between those two will also reveal, whether the Marshall-Lerner condition is met or not.
The Marshall-Lerner condition, which is named after Alfred Marshall and Abba Lerner, in general terms states that a currency devaluation improves a coun-try s trade balance in the long run under one condition only: the absolute sum of exchange rate elasticities of export and import demands has to equal or be greater than 1.
The trade balance of a country can be described by the following equation: � = − � = ∗ �− � ∗ ∗∗ �,
where X and M represent the value of exports and imports respectively measured in domestic currency, P and P* the domestic and foreign price levels, � and � the export and import quantities and ER the nominal exchange rate.
A depreciation of the currency then affects the trade balance through two channels. Firstly, there is a negative cost effect, since the increased exchange rate raises the import value M as well as it decreases export revenues. Secondly, there is a positive quantity effect. The lower currency value, i.e. higher exchange rate, causes a price decline of exports in the foreign market and thus increases demand and �. Furthermore imports become more expensive, which in turn decreases import demand and �.
For the devaluation to be positively effective on the trade balance export and import quantity responses need to be sufficient to offset the price effects. In this context, elastic export demand, i.e. demand for exports increases proportional-ly more than the price decreases, causes total export revenues to increase. Analo-gously, elastic import demand causes total import expenditures to decrease.
Summarising, if the bilateral US trade balance with China is found to be sig-nificantly affected by changes in the Yuan-US$ exchange rate in the long run, i.e. the exchange rate elasticity of the trade balance is found significant, the M-L condi-tion is met. (Bahmani-Oskooee, Harvey and Hegerty, 2013)
3.3. The J-curve phenomenon
This thesis will analyse the post-reform dynamics of the exchange rate effects on the bilateral US trade balance with China in the short as well as the long run. Therefore, the J-curve phenomenon, explained in this section, will take a central role in investigation.
Assuming a depreciation of the home currency, which in the case of a bilat-eral exchange rate is equal to an appreciation of the foreign currency, following Magee (1973) the post-change path can be divided into two periods, short and long run. As indicated in the last section, there are two effects on the trade balance.
In the short run, the price effect, also cost effect, arises from inelastic de-mand and affects the trade balance negatively. Trade volumes show only delayed
adjustment to the new relative price of exports to imports, e.g. due to contracts on produced or purchased quantities to be fulfilled. The trade balance thus tends to deteriorate in the short run due to a lower ratio of export to import value.
In the long run, the quantity effect arises from the increased competitive-ness in trade due to the new relative price, which improves the trade balance. Over time foreign as well as domestic buyers switch to the domestically produced goods, which now are less expensive, raising export and decreasing import volumes. Con-sequently, the movement of the trade balance, increasing in the long run after ini-tially decreasing, describes the letter J.
In case of the bilateral US trade balance with China, appreciation of the Yuan against the US-Dollar, meaning a depreciation of the domestic currency for the US, should lead to a short-run deterioration followed by an improvement of greater extent in the long run.
4.
Empirical analysis
In this section, the empirical model and its application are discussed. First, the data as well as the variables of the model are revealed. This is followed by a detailed examination of the methodology, containing the two-step approach of the ARDL-ECM by Pesaran et al. (2001), which is used for estimation of the RER effects on the bilateral trade balance between the US and China. Ultimately, several post-estimation tests are explained.
4.1. Data and variables
This section presents the data and variables, used in the empirical analysis. Time series data are employed on a monthly base from December 2004 until November 2014, which accumulates to 120 observations. Regression analysis thus starts right before the fixed Yuan-Dollar exchange rate was released in 2005. The data are dis-aggregated from other countries, i.e. bilateral, and overall not seasonally adjusted.
The dependent variable is the bilateral US Trade balance with China. It will be represented by the ratio of US exports to China over US imports from China. This provides a unit-free measure, which is commonly used in the trade literature, as for instance employed by Bahmani-Oskooee and Wang (2008). A higher ratio, i.e.
10,00 11,00 12,00 13,00 14,00 15,00 16,00 17,00 18,00 19,00 20,00 RER: Yuan/US$
exports relatively increasing to imports, therefore reflects an improvement of the trade balance, since the revenue to expenditure ratio increases. The data on US exports and imports are obtained from the US Census Bureau. As it can be seen in figure 1, the bilateral US trade balance with China continues to worsen from 2004 on, with only a small outlier during the world financial crisis in 2008.
The first explanatory variable of interest is the Real Exchange Rate. It is de-fined by � =� ∗�����
���� , with ER being the nominal exchange rate, i.e. the amount
of Yuan per US-Dollar, � and � the consumer price indices for the US and China. In case of a Yuan appreciation, the RER therefore declines. In figure 3, it can be seen that after abandoning the fixed exchange rate regime, the Yuan appreciat-ed in real terms over time, yet not immappreciat-ediately. Data on the nominal exchange rate as well as consumer price indices are extracted from the Federal Reserve Bank of St. Louis.
Figure 3. Monthly real exchange rate (Yuan per US-Dollar)
Data: Federal Reserve Bank of St. Louis
Furthermore, US and China National Income are included in the model. Due to the unavailability of monthly GDP data, the industrial production indices, � and
�, serve as indicators for national income in order to keep the monthly
frequen-cy of the data. Industrial production reflects the output volume of the industrial sector and thus seems to properly indicate the trend of national income, which accordingly rises with higher (industrial) output. Adequacy of this proxy is
sup-80 85 90 95 100 105 110 115 120 125 130
IPI China IPI US
ported by correlation coefficients of 0.92 and 0.61 between annual IPI and GDP for the US and China, respectively. However, due to unavailability of data for the whole period observed in this thesis, those coefficients are taken from the time span be-tween 1999 and 2008.
Figure 4 displays the development of the indices of both countries. In the case of the US the series first follows a growing path, before it abruptly collapses around September 2008, when the financial crisis burst. After a few months of downturn, it then started to steadily increase again in June 2009. The Chinese in-dex on the other hand seemed to move around a horizontal line until it experi-enced a downturn as a consequence of the financial crisis between June and No-vember 2008. After recovering to the former level until NoNo-vember 2009, it fol-lowed a slightly downward slope.
Figure 4. Monthly Industrial production indices
Data: OECD Database
Data on the industrial production indices are obtained from the OECD Database. Since monthly data on the industrial production of China are not provided contin-uously, values for the month January from 2006 until 2014 had to be interpolated by taking the average of the previous and the subsequent month.
4.2. Methodology
This thesis aims at revealing the effect of an exchange rate change on the bilateral US trade balance with China empirically, following the approach applied by Bah-mani-Oskooee and Brooks (1999) and developed by Pesaran et al. (2001). Hence, the following base regression is formulated:
ln� �� ,� = + ln � �+ ln �� + ln ��+ ��, (1)
where the bilateral trade balance between the US and China in period t is denoted by � �� ,�, the dependent variable, whereas � � is the variable of interest repre-senting the Yuan-US-Dollar RER in period t. Its coefficient – according to economic theory – is expected to have a negative sign, since appreciation of the Yuan lowers the RER, which in turn should improve the US trade balance.
Furthermore, the national income of the US and China in period t are in-cluded as controls, denoted by �� and ��, where the coefficient of the former is expected to have a negative sign, since a higher US income is associated with higher imports to the US and thus a worsening of the trade balance. Analogously, the coefficient of the latter is expected to be positive, reflecting that a higher for-eign income increases absorption of domestic exports and therefore improves the US trade balance.
All variables are employed in logarithms, which is possible, since none of the values can become zero or smaller, in which case logarithms would not be ap-plicable. The regression coefficients of the log variables are elasticities, i.e. per-centage values, which is a useful feature for the later analysis. Additionally, it con-tributes to preventing heteroscedasticity, as will be explained in section 4.2.1.3. (Gujarati, 2004)
In particular, this study will examine the appreciation effect in the short- as well as long-term, i.e. investigate the existence of a J-curve. However, reduced form equation (1) only estimates the long-run effects. It is a static model, i.e. includes no lagged values of the variables, and therefore reveals the immediate and complete effect of a change in the independent variable on the dependent variable within the same period. In order to obtain long- as well as short-run effects an error correc-tion model is used.
Pesaran et al. (2001) evolved one such model, first introduced in Pesaran and Shin (1995), namely the Autoregressive Distributed Lag – Error Correction Model (ARDL-ECM). It is commonly used in the more recent literature on international trade, among others Bahmani-Oskooee and Brooks (1999) apply it investigating the effect of exchange rate changes on the bilateral US trade balance with 6 trading partners. The ARDL-ECM is advantageous in application on trade balance effects, since it allows for simultaneous short- and long-term analysis. It therefore enables investigation of the existence of a J-curve and perfectly fits the analysis of the Yuan appreciation and the concomitant elasticity of the bilateral US trade balance with China.
Estimations employing this model consist of two steps. First, the bounds test approach is applied to test for cointegration of the variables, i.e. establish a long-run relationship. The model allows for variables of different integration lev-els, which can be I(0) or I(1). That is, the variables can be stationary in levels as well as in first differences proving cointegration. Second, the short-run dynamics are examined using an error correction model. Both steps will be explained in de-tail in section 4.2.1.
4.2.1.
The Autoregressive Distributed Lag – Error Correction ModelThis paragraph will reveal the two-step procedure of the ARDL-ECM. Beforehand, both the ARDL model and the ECM will be explained sequentially in a general ap-proach.
In order to elaborate the Autoregressive Distributed Lag (ARDL) model, its meaning is explained first. Autoregressive refers to the fact that the model con-tains lagged values of the dependent variable, i.e. it is regressed on its own values and therefore past values can have influence on follow-up values of the dependent variable. Distributed states that, besides the present value, also lagged values of the independent variable are included in the model, which implies the influence of the explanatory variable on the dependent variable to be immediately or delayed.
Formally, the common ARDL model with multiple lags can be described by the following equation:
The lag structure makes the ARDL a dynamic model, which reflects the adjustment between different equilibria over multiple periods. In case of stationary time series data, the model consistently estimates – as explained in section 4.2.1.3 – the long-run relationship of the variables via OLS, determined by the coefficients of the lagged variable.
If time series data are non-stationary, OLS estimation can bear spurious re-lations, i.e. estimation results are significant only due to common time components in the data of different variables. In this case, cointegration analysis can be applied – conditional on the variables being integrated to the same order – in order to con-sistently estimate the long-run relationship by OLS. According to Stock and Watson (2007) cointegration is defined as follows. Two non-stationary variables X and Y, which are both I(1), can be formulated in a linear combination �− � �, which is stationary (I(0)), since � offsets the common time components.
However, for the purpose of this study different levels of integration of the variables need to be allowed in cointegration analysis of the long-run relationship. The approach by Pesaran et al. (2001), the ARDL augmented by an error correction term, satisfies the requirements of this analysis.
The ARDL-ECM can be evolved based on the conventional ARDL (1,1) in equation (3), where the numbers in brackets denote the number of lagged values of dependent and independent variable respectively included in the model.
� = + �+ �− + �− + � (3)
Differencing both the dependent and independent variable, and forming a linear combination, the following specification is obtained:
∆ � = + ∆ �− �− − � − � �− + � (4)
Equation (4) is stationary, since the common time components in the two time se-ries are de-trended. The term �− − � − � �− is the error correction term, which is only then a stationary linear combination of the non-stationary variables, if cointegration exists between the time series. Therefore the bounds-testing ap-proach for cointegration – see section 4.2.1.1 – is applied.
In case of cointegration being proven, short- and long-run effects of X on Y can be consistently estimated. The effects on Y arise from multiple sources. First, the coef-ficient of the current change in X, , reflects the short-run response of Y. Second, the error correction term indicates the adjustment of Y to its long-run equilibrium value. In particular, determines the speed of adjustment from the previous dise-quilibrium. A smaller coefficient indicates a smaller error and thus a quicker at-tainment of the new equilibrium. Additionally, the coefficient on the lagged value of X, � , is called the long-run multiplier, as it reflects the long-run effect of X on Y within the error correction term. (Stock and Watson, 2007)
4.2.1.1. Step I: Bounds testing for cointegration
Following Pesaran et al. (2001), the first step in estimating exchange rate effects on the bilateral trade balance is the bounds testing for cointegration and formation of the unrestricted ARDL-ECM. It is ought to show whether a cointegrating relation-ship exists among the variables of the model, which is a necessary condition for a consistent estimation of the model.
The bounds testing approach bears an advantage in cointegration analysis: time series data on the variables can be of different integration order. That means, they can be stationary or non-stationary (Bahmani-Oskooee and Brooks, 1999). In particular, the model allows for series, which are I(0), I(1) or a mix of both, which is in favour of this analysis, since for instance data on the industrial production index can be stationary, whereas the exchange rate or trade balance can be non-stationary. Furthermore, it assesses weaknesses of other cointegration tests. As to name the two most commonly used, the Johansen cointegration test is limited, as it only allows variables of the same integration order (Bahmani-Oskooee and Wang, 2006), whereas the two-step Engle-Granger test cannot be applied on short sam-ples or if there are structural breaks in the data (Bahmani-Oskooee and Brooks, 1999). Especially, elimination of the latter shortcoming suits the data in this model. The observation period comprises the time-span around the financial crisis begin-ning 2008, which seems to have affected the path of some of the variables time series – as can be seen in 4.1 – and thus indicates a structural break.
However, the bounds test is not applicable for non-stationary time series of higher order, i.e. I(2) or more, since in that case the critical bound values computed by Pesaran et al. (2001) do not have validity. Therefore, in a first step a unit root
test, the Augmented Dickey Fuller (ADF) test, needs to be conducted in order to de-termine the order of integration of each time series. The ADF test formulates the Null hypothesis ( ) of an existing unit root, i.e. non-stationarity. The alternative ( ) states that there is no unit root, i.e. the data are stationary. The optimal lag length for this test is determined by the Akaike Information Criterion (AIC), which displays the lag combination with the least loss of information on the time series. (Stock and Watson, 2007)
In case, all time series are either I(0) or I(1), in the next step the unrestrict-ed ARDL-ECM can be constructunrestrict-ed, which constitutes the foundation for the bounds test for cointegration:
∆ln� �� ,� = + ∑ ∆ln � �− + ∑ ∆ln �−� + ∑ ∆ln �−� + ∑ ∆ln� �−� ,� + � ln � �− + � ln �−� + � ln �−� + � ln� �−� ,� + ��. (5)
Equation (5) contains (lagged) first difference values of the independent variables, ∆ln � �− to ∆ln �−� . It further includes the lagged values, ∆ln� �−� ,�, of the
de-pendent variable, which is the first differenced trade balance, ∆ln� �� ,�. Addition-ally, the first lagged level values of each variable are represented by ln � �− to ln� �−� ,�. The coefficients on the first differences, to , refer to the short-run dynamics – explained in step II – as they only describe changes within two periods, whereas the coefficients on the lagged level values, � to � , represent the long-run multipliers. The latter ones underlie the bounds test for a long-run cointegrating relationship among the variables, which is conducted in form of a F-test for joint significance of the coefficients. The linear combination of (� ln � �− + � ln �−� + � ln �−� + � ln� �−� ,�) can be seen as the error correction term in this unre-stricted version of the ARDL-ECM, which can be concluded from the error correc-tion term of the generally formulated equacorrec-tion (4).
In order to apply the bounds test, equation (5) is estimated via OLS first. The AIC is again used to determine the optimal lag length, which is especially im-portant, since the F-test is sensitive to the lag-length (Bahmani-Oskooee and Brooks, 1999). According to Pesaran et al. (2001), choosing the optimal lag length is a trade-off between sufficient lags in order to avoid serial correlation and a moderate amount of lags in order to prevent over-parameterization.
Testing for a cointegrating relationship, the F-test follows the of not existent cointegration, which is revealed by the long-run multipliers � to � jointly being zero. This is opposed by the of existent cointegration. The critical values of the F-statistic, which are non-standard distributed, are developed by Pesaran et al. (2001) and consist of a lower and upper bound. The lower bound is based on the hypothesis that all variables are I(0), whereas for the upper bound all variables are I(1). Hence, there are three possible outcomes of the F-test. First, if the F-statistic exceeds the upper bound, the of no cointegrating relationship can be rejected, thus proving existence of cointegration. Second, if the F-statistic falls below the lower bound, cannot be rejected, i.e. no cointegration is found. Third, if it lies between bounds, the outcome does not allow any conclusion. In the latter case, the result can be supplemented by the t-statistic on the coefficient of the independent variable of interest, the RER, for which Pesaran et al. provide non-standard critical values. Additionally, the error correction term in the restricted ARDL-ECM, as ex-plained in the next section, will provide proof for a long-run cointegrating relation-ship. (Bahmani-Oskooee and Brooks, 1999)
Once a cointegrating long-run relationship is established, extraction of the long-run effects, i.e. the long-run elasticities of the trade balance, is enabled, which are obtained from the coefficients of the lagged level values. This is due to the fact that in the long-run equilibrium the first difference values of all variables are zero, ∆ln� �� ,� = ∆ln � �= ∆ln �� = ∆ln �� = 0. After rearranging equation (5)
the effects of each independent variable on the dependent variable then is received by dividing the respective coefficient by the coefficient of the dependent variable. More specifically, − � /� states the effect of the RER, − � /� the effect of US industrial production and – � /� the effect of China industrial production on the trade balance in the long run. A significant coefficient on the RER – as indicated in section 3.2 – will also reveal, if the M-L condition is met. However, consistent with the existing literature (e.g. Bahmani-Oskooee and Wang, 2006), a rather weak im-pact of the exchange rate on the trade balance is expected.
4.2.1.2. Step II: Estimation of the Error Correction Model
Proving a cointegrating long-run relationship among the variables in the first step allows proceeding to step II, the estimation of the error correction model.
There-build upon the residuals of the equilibrium model from equation (1) and reveals the short-run dynamics of the trade balance after a change in the exchange rate.
The following specification describes the restricted version of the ARDL-ECM:
∆ln� �� ,� = + ∑ ∆ln � �− + ∑ ∆ln �−� + ∑ ∆ln �−�
+ ∑ ∆ln� �−� ,� + �� ��− + ��. (6)
Equation (6) is build similar to equation (5), as it regresses the first difference of the trade balance on (lagged) first difference values of the independent variables as well as its own lags. However, contrary to the unrestricted version it contains the lag of the error correction term, � ��− . It is obtained using the residual of equation (1), ln� �� ,�− − ln � �− ln �� − ln �� = �, and is deducted from the general error correction term in equation (4). Since � ��− is taken after the coefficients in the equilibrium model are estimated via OLS, it is called the re-stricted ARDL-ECM. This is in contrast to step I, where no pre-estimation is con-ducted and thus all coefficients are unrestricted.
As indicated in the previous section, the coefficients to represent the short-run effects on the trade balance. On regard of the focus of this thesis, espe-cially the coefficient on the lagged difference of the RER, , is of importance. Fol-lowing chapter 3.3, a negative sign on consecutive initial coefficients would, in combination with a positive long-run coefficient, support the existence of a J-curve. Furthermore, the coefficient on the lagged error correction term reflects ad-justment of the independent and dependent variables to the long-run equilibrium values. However, this can only be deducted, if the coefficient is significantly nega-tive and between 0 and -1. Otherwise the estimation on the error correction term would be inconclusive. Its magnitude then indicates, to which extent disequilibri-um of the previous period is reduced within one month. The coefficient therefore shows the speed of adjustment after a shock. As mentioned before, the error cor-rection term moreover supports the existence of cointegration, which as well only is the case, if the coefficient bears a negative sign. Cointegration causes the gap to equilibrium to diminish over time.
As for the procedure of step II, equation (1) is estimated via OLS first. After the AIC is used to determine the optimal lag length, equation (6) is estimated with the er-ror correction term extracted from the residuals of (1).
4.2.1.3. Post-estimation tests
In a last step, several post-estimation tests are conducted in order to examine, whether the results obtained in steps I and II are unbiased and efficient. Therefore, the stability of the applied ARDL-ECM is tested first, followed by diagnostic tests checking for autocorrelation and heteroscedasticity, as well as a normal distribu-tion of the residuals and misspecificadistribu-tion of the model.
In estimations of linear regression models via OLS method a few assump-tions, which are closely related to each other, need to be fulfilled for the results to be representative. First, the error terms of regression should be independent of each other, i.e. not be correlated and thus random. Second, the error terms should be independent of the independent variables, i.e. have a mean of zero and the same variance unconditionally on the value of the independent variables. Third, all error terms should vary equally and therefore be identically distributed. (Stock and Wat-son, 2007)
The first assumption refers to autocorrelation, the occurrence of which can have several causes. On the one hand, there can be measurement errors in the ob-servations, influencing the dynamics of time series. On the other hand it can be due to omitted variable bias (OVB), i.e. variable, which would well contribute in expla-nation of the dependent variable, are left out. More general, autocorrelation can be evoked by any misspecification of the model. In consequence of correlating error terms, the variance of coefficients might be underestimated and the coefficient of determination, , which indicates the goodness of fit of the model, might be over-estimated. Hence, the OLS estimates might be biased. Testing for the existence of autocorrelation, the Breusch-Godfrey Lagrange Multiplier test (LM-test) is applied. It is based on the � - statistic on the regression residuals, examining the of no autocorrelation against the of autocorrelation.
The second assumption is on homoscedasticity. If the error terms depend on the independent variables, and thus their mean and variance, they are called het-eroscedastic. Heteroscedasticity originates from similar causes as autocorrelation
does. Consequently, estimations via OLS are less efficient. It is tested via the Breusch-Pagan-Godfrey (BPG) test on the variance of the residuals as well using the � - statistic to test the of homoscedasticity against the of heteroscedasticity. The third assumption is normality of the residuals. In case, the error terms are non-normally distributed, determination of the coefficients significantly different from zero may be problematic. For instance, large outliers in the data might distort the distribution, which then could disproportionally influence estimation of the coeffi-cients. Hence, the Jarque-Bera (JB) test is conducted, which is complementary to the test on the residuals variance and measures actual skewness and kurtosis of the residuals compared to the normal distribution using an adjusted � - statistic. It assumes the of normality of the residuals against the of non-normality.
As mentioned before, misspecification of the regression model can violate the OLS assumptions. Accounting for possible non-linear combinations of the inde-pendent variables, which could explain the deinde-pendent variable more exact and powerful, the Ramsey regression equation specification error term (RESET) test is performed. It uses a F-statistic for the joint significance of the coefficients of these alternative, non-linear combinations. The states that the coefficients are zero and thus there is no misspecification, whereas for the significance of the coeffi-cients is assumed. (Gujarati, 2004)
Finally, the stability of the regression model needs to be tested. In particu-lar, stability of the coefficients is examined, i.e. if these are constant over time. In-stability would imply that the coefficients are inconsistently estimated. Therefore, the joint test of the cumulative sum (CUSUM) and the cumulative sum of squares (CUSUMQ) is conducted in order to detect structural changes within the estimated model. It is applicable on linear regression model containing non-stationary data and tests the cumulative sum of the recursive regression residuals to constantly stay within a critical bound of 5%. The of stability is rejected, if the critical bound is transcended in any the two parts of the test. (Harvey, 1990)
5.
Regression results
This thesis aims to reveal the effect of a change in the Yuan-US$ exchange rate on the bilateral trade balance between the US and China. Applying the ARDL-ECM ap-proach by Pesaran et al., this effect is investigated both in the short and in the long
run. Based on that, as well the existence of a J-curve is examined. Therefore in this section, the outcomes of the regression estimations on the empirical model are presented and discussed, which are divided into the long-run results from the un-restricted ARDL-ECM, short-run results from the un-restricted ARDL-ECM and finally the tests on the diagnostic analysis and stability of the model.
5.1. Long-run estimations in the unrestricted ARDL-ECM
In the first step of the ARDL-ECM approach by Pesaran et al., the unrestricted ver-sion of the model is constructed. It is used to test for a cointegrating relationship among the variables via the bounds testing approach. If proof is found, it reveals the long-run effects of the independent variables, namely the RER and IPI of the US as well as China, on the US-China bilateral trade balance.
In order to enable the bounds test for cointegration, the order of integration of each time series is determined via an ADF test. The optimal lag lengths for the test is obtained from the AIC, which shows a structure of 12 lags of the first differ-ences for the trade balance, 2 for the RER, for the US )P) and for China s )P). The results of the ADF-statistic are displayed in table 1 and show that the bilateral US trade balance is non-stationary in levels, but in first differences at 5% significance, it thus is integrated of order 1, I(1). Equally, the RER and the IPI of China are found to be I(1) at 1% significance.
Table 1. Augmented Dickey Fuller Test
Variable Level First Difference Integration
Order Constant Constant
and Trend Constant
Constant and Trend ln� � ,�(12) -1.625 -1.808 -3.476** -3.669** I(1) ln � (2) -0.652 -2.587 -5.458*** -5.471*** I(1) ln � (5) -1.897 -2.068 -2.181 -2.366 ? ln � (3) -1.504 -2.777 -5.839*** -5.848*** I(1) Notes: 1. ***, **, * imply significance at 1%, 5%, 10%.
2. The numbers within parentheses of the variables represent the lag length of the dependent variable used, selected by Akaike Information Criterion (AIC).
Contrarily, the IPI of the US is neither in level, nor in first differences found to be stationary, which would determine it as I(2) or higher and therefore result in ineli-gibility for the bounds test. A possible reason for the latter finding is the financial crisis beginning in 2008, which strongly affected the income of the US. In particu-lar, US IPI experienced a severe downturn, starting around September 2008 and
lasting for several months, which provides the data with multiple outliers. In order to account for this structural break, an extended version of the ADF test is per-formed, the Augmented Dickey Fuller Additive Outlier (ADFAO) test, – see table 2 in the appendix – which allows for one structural break in the series (Vogelsang, 1999). It declares US IPI as I(1) at 1% significance.
Furthermore, since the income of China seems to experience a similar downturn during said period, the test is also run on the IPI of China, finding it to be I(0) at 1% significance. Summarising, all independent variables at first appear to be I(1), yet leaving the result on China s )P) vague, i.e. it is either ) or ) . (ence, the bounds testing approach, which allows for both integration orders, is perfectly suitable.
After finding all variables to meet the condition for the bounds test, the un-restricted ARDL-ECM is constructed. The AIC suggests a lag structure of (12, 0, 4, 3) in the same order of variables as before. Estimation outcomes of equation (5) are displayed in table 3, whereas the full regression output can be seen in table 4 in the appendix.
Table 3. Lagged Variables Output Equation (5) – unrestricted ARDL (12,0,4,3) (Dependent Variable: ∆ln� �� ,�)
Variable Coefficient Std.Error t-Statistic Prob. �� � �− -1.476594*** 0.3316591 -4.45 0.000
������− -0.418108** 0.1771778 -2.36 0.021
������− 1.324869** 0.5837722 2.27 0.026
�� �−, -1.114637*** 0.261755 -4.26 0.000
Note: ***, **, * imply significance at 1%, 5%, 10%.
The F-test for joint significance, i.e. cointegration among the variables, of the coef-ficients on the lagged level variables uses the bound critical values provided by Pesaran et al. Again, only exceeding the upper bound allows the conclusion of coin-tegration, whereas falling between bounds leads to an inconclusive result and fall-ing below the lower bound forecloses cointegration. The test shows a result ex-ceeding the upper bound critical value at 1% significance and thus rejecting the of all coefficients being zero. Supplementary to that, the t-statistics on the coeffi-cients of the trade balance lag and the RER lag as well exceed the upper bound at
1% supporting the finding of cointegration. The outcomes of both tests are shown in table 5.
Table 5. F- and t-statistic on Equation (5) for long-run cointegrating relationship
Statistic Value Significance Level Critical Values I(0) I(1) F-test 6.33*** 1% 5% 10% 4.29 3.23 2.72 5.61 4.35 3.77 t-test ln� �− � ,� -4.26*** 1% 5% 10% -3.43 -2.86 -2.57 -3.43 -2.86 -2.57 ln � �− -4.45***
Note: ***, **, * imply significance at 1%, 5%, 10%.
Since a cointegrating long-run relationship among the variables is proven, the long-run multipliers can be extracted from the estimation results of the unrestrict-ed ARDL-ECM in table 3. As shown in section 4.2.1.1, the long-run RER elasticity of the trade balance is calculated by the ratio -(� /� ), which amounts to a value of -1.33. Both coefficients are highly significant, at 1%, which allows the conclusion that every 1% decrease in the RER causes a 1.33% increase in the trade balance. This result is conform with the expectation of an improvement of the bilateral US trade balance with China in consequence of an appreciation of the Yuan, consider-ing that the bilateral US trade balance is defined as exports over imports and an appreciation of the Yuan implying a decrease in the RER variable. It also proves that the M-L condition is fulfilled.
Additionally, the elasticity on US income can be received from the ratio -(� /� ) = -0.38. This result is significant at 5% and shows that the bilateral US trade balance experiences a decline of 0.38% for every 1% increase in US income, which is consistent with economic theory. A higher income of the US is assumed to raise demand for imports deteriorating the trade balance. Analogously, the elastici-ty on China s income equals the ratio -(� /� ) = 1.19, which is found at 5% signifi-cance. According to this value, a 1% increase in China s income causes a . % in-crease in the bilateral US trade balance. Theoretically, a higher income of China raises demand for US exports, thus improving its trade balance with China, which is consistent with the latter finding.
From the time series data it can be seen that the RER appreciated by 30.8% during the observation period. Based on the estimated long-run coefficient of -1.33 between the RER and the trade balance, consequently the bilateral US trade
bal-ance with China, i.e. the ratio of exports over imports, would have experienced an improvement of 40.96% accountable to the RER.
5.2. Short-run dynamics in the restricted ARDL-ECM
The second step in the two-step approach by Pesaran et al. comprises formation of the restricted ARDL-ECM and estimation of the short-run dynamics, particularly between the RER and the bilateral US trade balance with China. After step I proved a positive long-run relationship between an appreciated Yuan and the bilateral US trade balance, existence of a negative short-run relationship would be evidential for the J-curve phenomenon.
Before the restricted equation is estimated, the error correction term has to be formed. As explained in section 4.2.1.2, it is derived from the residuals of the equilibrium model estimation. Hence, equation (1) is estimated first; its results are displayed in table 6. It reveals that a decrease of 1% in the RER provokes a 1.6% increase of the trade balance as immediate response. Furthermore, an increase of 1% in China s income causes a 2.14% increase in the trade balance. Both outcomes are significant at 1%. The coefficient on the US income on the other hand is not significant.
Table 6. Output Equation (1) – Equilibrium Model (Dependent Variable: ln� �� ,�)
Variable Coefficient Std. Error t-Statistic Prob.
�� � � -1.599*** 0.130597 -12.25 0.000
������ -0.296 0.226814 -1.31 0.194
������ 2.139*** 0.520337 4.11 0.000
Note: ***, **, * imply significance at 1%, 5%, 10%.
The residuals of the equilibrium model estimations, representing the gap between equilibrium and actual values, are then used to create the error correction term in the restricted ARDL-ECM. In order to estimate the latter efficiently, the AIC once more determines the optimal lag structure, which is (12, 2, 1, 3) in the same order as before. The complete regression results are shown in table 8 in the appendix. Table 7 reflects only those, which are of importance for investigation.
Examining the existence of a J-curve, given the long-run effects already fulfilling the needed condition, the coefficients on all of the displayed consecutive lags on the first differenced RER should be significantly positive (Bahmani-Oskooee and Brooks). However, the results reveal, that none of the coefficients is significant, with the first and third being positive interrupted by a negative coefficient on the second value. Thus, no J-curve can be found for the Yuan appreciation effect on the bilateral US trade balance with China.
Table 7. Selected Output Equation (6) - restricted ARDL (12,2,1,3) (Dependent variable: ∆ln� �−� ,�)
Variable Coefficient Std. Error t-Statistic Prob.
� �− -0.916*** 0.216616 -4.23 0.000
∆�� � � 1.707 1.295705 1.32 0.191
∆�� � �− -1.307 1.462151 -0.89 0.374
∆�� � �− 1.296 1.364830 0.95 0.345
Note: ***, **, * imply significance at 1%, 5%, 10%.
Conclusions on the coefficient on the lagged error correction term are only valid, if it is significant and falls between -1 and 0. It then reflects the adjustment of all var-iables to its long-run equilibrium values. With a value of -0.92 and a significance level of 1%, it fulfills all those conditions. Its magnitude indicates the speed of ad-justment after a shock. Therefore, it can be concluded that 92% of a previous dise-quilibrium diminishes within one month. Additionally, existence of a long-run coin-tegrating relationship among the variables is supported.
5.3. Post-estimation tests
This section is ought to reveal the results of testing the assumptions for unbiased and efficient estimations via OLS. The tests are conducted on all three estimated regression models post-estimation and regard the model diagnosis and stability. Their outcomes are shown in table 9.
First, the LM test is performed to test for autocorrelation. In case of the equilibrium model in equation (1), the test significantly rejects the null hypothesis of no autocorrelation at 1% with a �2-statistic of 12.57. This might be due to the
