key: cord-0978250-bg7133ye authors: Ouyang, Alice Y.; Rajan, Ramkishen S.; Willett, Thomas D. title: China as a reserve sink: The evidence from offset and sterilization coefficients date: 2010-01-04 journal: J Int Money Finance DOI: 10.1016/j.jimonfin.2009.12.006 sha: fbe0d057935e58f3ad14820b322d8b30941b89ee doc_id: 978250 cord_uid: bg7133ye China has been stockpiling international reserves at an extremely rapid pace since the late 1990s and has surpassed Japan to become the largest reserve holder in the world. This paper undertakes an empirical investigation to assess the extent of de facto sterilization and capital mobility using monthly data between mid 2000 and late 2008. We find that China has been able to successfully sterilize a large portion of these reserve increases thus making it a reserve sink such as Germany was under the Bretton Wood system. China has become the world's largest foreign exchange reserve holder, having amassed almost US$ 2 trillion of international reserves by the end of 2008 (Fig. 1) . 1 The rapid accumulation of reserves has generated several controversies. One concern is whether this continuing balance of payments surplus signals the need for a substantial revaluation or appreciation of the Chinese Yuan (CNY) to protect China both from the inflationary consequences of the liquidity buildup and a misallocation of resources 2 as well as to help ease global economic imbalances. An alternative view, particularly associated with Schnabl (2003a,b, 2004) , argues that a fixed exchange rate is an optimal policy for China and the larger Asian region both on the grounds of macroeconomic stability and rapid economic development. The global monetarist approach of McKinnon is based on the assumption of little or no sterilization of reserve accumulations, so that any payments imbalance is temporary. However, many other commentators have suggested that the Chinese government's concern with inflation has led the People's Bank of China (PBC) to heavily sterilize these reserve inflows. 3 Contrary to the wide spread concerns among many economists about the huge size of current global economic imbalances, Dooley et al. (2004) famously argued that mainstream economists have failed to recognize that we are now in a new informal version of the Bretton Woods system (BW2) and the global economy is therefore not in genuine disequilibrium. While there are clearly important analogies between the current international monetary system and Bretton Woods (BW1), the question is still open as to whether we are currently closer to the early or late days of BW1. 4 In the later days of BW1 much attention was given to the concept of countries as reserve sinks into which reserves flowed. Instead of stimulating adjustments, as assumed in global monetarist models, the reserves effectively disappear from the system (down the sink) and hence contributed to continuing disequilibrium. Germany was seen as the prototype of the reserves sink during the BW1 days. Today China appears to be playing that role. Thus investigating how China has reacted to its reserve increases is of international as well as national importance. 5 An intermediate view is that while China has sterilized most of its past reserve increases, continuing to do so is becoming increasingly difficult for China as its reserves continue to rise and capital controls 3 Note that one can still use a monetary approach to consider the implications of sterilization. Indeed, Mussa (2008) takes this approach and argues that stabilization is a major reason for China's continuing balance of payments surpluses. 4 On the issues see the analysis and references in Eichengreen (2006) and Bird and Willett (2008) . 5 See Willett (1980) for references to this literature. become more porous (Prasad, 2005; Prasad and Wei, 2005; Xie, 2006) . One of the reasons why there is so much disagreement is because, as Goodfriend and have noted, ''(t)he fraction of reserves sterilized by the central bank has varied over the last few years and it is not straightforward to assess exactly how much sterilization has taken place.'' This paper estimates the degree of recent sterilization in China, as well as the degree of capital mobility as measured by offset coefficients, i.e. the fraction of an autonomous change in the domestic monetary base that is offset by international capital flows. 6 In one sense, the level of sterilization can be observed from the degree to which the central bank takes action to offset the effects of increases in international reserves on the domestic base or other monetary aggregates. However, this can offer a misleading picture of the effectiveness of sterilization. If the central bank wants the base to increase anyway, then it would decide not to neutralize the reserve increases; this would not imply that it had lost control of the domestic monetary process. China's large balance of payments surplus in 2003 was accompanied by rapid domestic money and credit expansion which is consistent with an inability to effectively sterilize. It appears, however, that the primary cause of the rapid expansion of money and credit was the Chinese government's concern with maintaining rapid economic growth, not the inability of the PBC to control the domestic monetary base. 7 Thus, the PBC did not try to fully neutralize the domestic monetary effects of the reserve increases under government direction. To investigate the central bank's ability to control domestic monetary aggregates, it is necessary to estimate the extent to which international flows undercut its control. This in turn requires the estimation of the counterfactual of the desired rate of monetary growth, i.e. estimation of the central bank's monetary reaction function. There is no one correct theoretical specification for central bank reaction function, but the literature has developed a standard set of variables to be considered within this function. This allows us -at least in principle -to breakdown the interrelationship between international reserve changes and the monetary base into those relating to autonomous changes in the monetary base (the offset coefficient) and those relating to autonomous changes in international reserve flows (the sterilization coefficient). We also make use of recursive estimation to investigate changes in offset coefficients and sterilization over time. While we find no evidence of the inability of the government to sterilize a high proportion of reserve accumulations, we do find substantial increases over time in our estimates of the offset coefficients, suggesting that sterilization is becoming increasingly difficult. The next section briefly explores the evolution of the balance of payments flows in China since 1999-2000, focusing on the magnitude and sources of reserve buildup as well as the reserve buildup's monetary consequences. It also briefly discusses the sterilization policy measures used in China (de jure sterilization). Section 3 offers a summary of the main empirical methodologies commonly used to estimate the de facto extent of sterilization. As will be discussed, the estimation procedure used in this paper is based on a set of simultaneous equations to estimate both the ''sterilization coefficient'' (i.e. how much domestic money creation responds to a change in international reserves) and the ''offset coefficient'' (i.e. how much balance of payments changes in response to a change in domestic money creation). Since the foreign exchange and the domestic monetary markets are interrelated, ignoring such interrelationships can lead to biased results. Section 4 discusses the data and definitions of variables to be used in the empirics and presents the empirical results of the sterilization and offset coefficients based on monthly data for the period from June 2000 to September 2008. This section also discusses a number of robustness checks. The results remain remarkably stable to the alternative estimation techniques used as well as to different proxies for exchange-rate expectations and for valuation changes in international reserves. We also present a recursive estimation which suggests that while remaining substantial, the degree of sterilization has fallen in recent years. The final section 6 After this paper was initiated, two other studies on sterilization in China by Burdekin and Siklos (2005) and He et al. (2005) became available. While using a different methodology, they reach broadly similar conclusions. These studies are considered in FN 40. 7 Lardy (2005) argues that the money expansion in 2003 was the government's mistaken overreaction to the potential adverse effect of severe acute respiratory syndrome (SARS) on economic growth. concludes with a brief discussion of the macroeconomic policy implications and tradeoffs facing China in the future. 2.1. Evolution of China's balance of payments 8 China has experienced large and growing surpluses on both the capital and current accounts since 2001, while even the errors and omissions balance (a broad proxy for capital flight by residents) turned positive (Fig. 2) . Thus, reserves increased markedly during this period. An interesting dynamic appears to have taken hold in China (as well as in many other Asian economies) during this period. Large reserves are viewed as a sign that the domestic currency will eventually appreciate. They also tend to be taken as an indication of ''strong fundamentals,'' hence leading to an upgrading of the country's credit ratings. This expectation of future capital gains and lower risk perceptions motivated large-scale capital inflows and added to the country's stock of reserves as central banks have mopped up excess US dollars. From Fig. 3 , it is apparent that the swelling of China's capital account surplus since 2003 was largely because of a surge in portfolio capital flows as well as ''other investments'' (i.e. short-term debt flows), most likely a reflection of mounting market expectations of an impending revaluation of the Chinese currency (i.e. speculation on the CNY as a one-way trade). As noted by Prasad and Wei (2005) , ''much of the recent increase in the pace of reserve accumulation is potentially related to 'hot money' rather than a rising trade surplus or capital flows such as FDI that are viewed as being driven by fundamentals'' 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 (p.8). 9 conclude, however, that even with hot money flows excluded, China faced a substantial payments disequilibrium and while in 2004 IMF reports expressed doubts about whether the RMB was fundamentally undervalued, by 2006 the growing trade surplus had convinced most observers including the IMF that the RMB was fundamentally undervalued. Estimates of the extent of undervaluation varied enormously, however. 10 The Chinese government finally loosened its strict US dollar peg and allowed for a small revaluation from 8.28 to 8.11 CNY per US dollar in July 21, 2005 and simultaneously announced that the currency would be pegged to a basket of currencies. 11 Interestingly, China has since experienced a sharp increase in its trade surplus relative to the capital account despite expectations of continued upward pressure on the CNY 12 (i.e. one logically would have expected to see an intensification of speculative inflows). On the one hand, the decline in the capital account surplus was partly policy-induced. The government has been promoting outward investments by Chinese corporates and domestic institutional investors and has loosened a number of restrictions on capital outflows to ease some appreciation pressures from huge 1990-2007. 9 Three caveats should be noted. First of all, part of the change in reserves is also because of a valuation effect as a portion of reserves that was invested in non-US dollars (gold, euros, etc) has changed in US dollar terms (while most central banks including the PBC do not disclose the composition of assets in which reserves are being invested, it is generally suggested that a large part has been invested into dollar-denominated assets like Treasury securities). Prasad and Wei (2005) offer some ''guess-timates'' on the possible valuation effects. Secondly, there was a one-off fall in reserves in China in 2004. This was because since 2003 the government transferred US$ 60 billion to three state-owned banks, Bank of China (US$ 22.5 billion), China Construction Bank (US$ 22.5 billion), and Industrial and Commercial Bank of China (US$ 15 billion) to aid in their recapitalization (see Ma, 2007 for details). And lastly, while China has not yet become fully convertible on the capital account, a large number of so-called ''qualified foreign investment institutions'' or QFIIs received approval by the China Securities Regulatory Commission to increase their investments to China which in turn has fuelled large-scale portfolio capital inflows (see Hu, 2005 for details). 10 On these issues see the analysis and references in Goldstein and Lardy (2008) . 11 The CNY has been on a very gradual appreciating path since reserves accumulation, while simultaneously tightening some restrictions on capital inflows such as imposing a quota in July 2004 on offshore borrowing by foreign banks operating in China. On the other hand, the sharp increase in the country's current account balance is somewhat harder to rationalize. 13 It has been suggested by some observers that the current account surplus has been partly driven by overinvoicing of exports and under-invoicing of imports. As noted by one market commentator: The massive flip-over between the financial account and trade account. in 2005.raises the possibility that capital flow for.(CNY).speculation masqueraded as a trade surplus last year due to improving capital account control. This is important in understanding the nature of China's BoP surplus. 2005 BoP data suggest that capital account flows accounted for one-third of the BoP surplus, while 2004 data suggest that this was three-quarters. If 2004 data are more accurate, the appreciating pressure appears to be mainly a speculative phenomenon (Xie, 2006) . 14 What are the monetary consequences of this huge reserve buildup in China? Our analysis from here onwards (including the empirical analysis in Section 4) focuses on data from mid 2000 to late 2008 for which monthly data are available. Fig. 4 shows that, since December 2002, domestic high-powered money creation proxied by the growth in broadly defined net domestic assets (NDA) 15 has remained rather low if not negative. This 13 Prasad and Wei (2005) and Liu and Otani (2005) detail the steps taken to deregulate China's capital account transactions. 14 Also see the discussions in Goldstein and Lardy (2008) and Ma and McCauley (2005) who state that a large part of the overall current account surplus in China (40 percent) was also due to net income transfers. They further note that the Chinese government required banks to report ''unusually large'' (US$ 10 000) remittance inflows and related dollar sales. 15 Broadly defined net domestic assets (NDAs) equals monetary base (MB) minus net foreign assets (NFAs). helped moderate the increase in the domestic monetary base (MB) and overall money supply (M2) (Fig. 5) , suggesting that the PBC was actively neutralizing the impact of the reserves buildup using various policies and instruments. Two conventional sterilization policies frequently used by the PBC are open market operations (OMOs) and raising reserve requirements (He et al., 2005) . While the PBC initially used treasury bonds or securities as the sterilization tools, since September 2002 it has replaced all outstanding securities with central bank bills (CBCs) for use in the OMOs. Fig. 6 reveals the sharp growth in PBC issuances in the last five years. Apart from OMOs, the PBC has raised the reserve requirement ratio continuously since 2007, from 9 percent to 16.5 percent over the period under consideration. 3. Estimating the extent of sterilization: methodological and empirical issues Most current studies which estimate the extent of sterilization can be classified into three groups. The first group assumes that capital flows are exogenously determined and typically estimate sterilization coefficients by running simple OLS on the monetary reaction function such as the one below: where DNDA t and DNFA t represent the change in net domestic assets (a proxy for domestic money creation) and net foreign assets (a proxy for international reserves), respectively, and X represents other explanatory variables that might influence a monetary authority's reaction. The coefficient of c 1 ¼ À1 represents full monetary sterilization, while c 1 ¼ 0 implies no sterilization. In some instances (such as Burdekin and Siklos, 2005) , DMB t or DM2 t is used instead of DNDA t . If this is the case then c 1 ¼ 0 represents full sterilization since a rise of international reserves does not affect the monetary base (or broad money). The second group uses a VAR model to estimate the lagged effects of NDAs and NFAs. The standard form of a VAR model is as follows: Some papers within this group include additional variables in the model such as the domestic interest rate, price level, or exchange rate (for instance, see Cavoli and Rajan, 2006; Christensen, 2004; He et al., 2005; Moreno, 1996) . 16 The advantage of a VAR approach is that it allows one to trace out the time path of the various shocks on the variables contained in the VAR system (i.e. the impulse response function). If a shock from foreign assets (say an unexpected increase in foreign assets) is associated with an offsetting decrease in domestic money creation, it can be concluded that the sterilization is significant. An important limitation of the VAR approach is that it tends to treat all variables as symmetrically endogenous. As equations (2a) and (2b) show, a standard form of the VAR model only yields the estimated values of lagged NDAs and NFAs due to the issue of identification. Consequently, the model cannot estimate the contemporary effect of variables without restrictions. The third group of studies -including this paper -estimates the contemporaneous relationship between NDAs and NFAs using a set of simultaneous equations. Although the studies in the first group ignore the simultaneous bias by assuming capital flows are exogenously determined (see Kwack, 2001) , it is important to note that domestic monetary conditions are affected by changes in international capital flows and foreign reserves. Concurrently, international capital flows respond to a change in domestic monetary conditions (e.g. higher domestic interest rates would, ceteris paribus, lead to greater 16 Takagi and Esaka (1999) argue that it is inappropriate to use this approach to measure the effectiveness of sterilization given the variety policy instruments used in sterilization in addition to OMOs. Consequently, the authors use the change of DM1 t (orDM2t ) rather thanDNDAt ; full sterilization is said to exist if an unexpected increase in foreign assets is not associated with a corresponding increase in overall money supply. capital inflows). 17 Some early studies, such as Argy and Kouri (1974) and Herring and Marston (1977) , have suggested using a simultaneous system to overcome the problem of simultaneity. The typical model specification for a set of simultaneous equations is: where X 1 and X 2 are the vectors of controls in the balance of payment function and monetary reaction function, respectively. Eqs. (3a) and (3b) are the balance of payments and the monetary reaction functions, respectively. The former estimates the ''offset coefficient''. The expected value of the offset coefficient is bound by 0 in the event of no capital mobility and À1 in the event of perfect capital mobility. 18 The latter measures the sterilization coefficient. The expected value of the sterilization coefficient is À1 if reserve buildup is perfectly sterilized and 0 if the central bank does not sterilize at all. In general, the greater the degree of capital mobility, the less effective is monetary sterilization; a small offset coefficient and a large sterilization coefficient generally imply that the central bank has a fairly high degree of monetary policy independence to neutralize the impact of capital flows effectively on a sustained basis. One concern with all of the above approaches is the lack of explicit micro foundations for inclusion or exclusion of control variables. There is of course a large literature on the determinants of monetary reaction functions, but to our knowledge Brissimis-Gibson-Tsakalotos (BGT) (2002) is the only instance in which the simultaneous equations used to estimate the NFAs and NDAs are explicitly derived from a theoretical framework (minimization of a simple loss function of the monetary authority subject to a number of constraints that reflect the workings of the economy). Ouyang et al. (2008) modify the BGT framework in a number of ways and apply it to several Asian economies (see Appendix 1). However, the modified framework cannot be applied directly to China which maintained a fixed peg to the US dollar until July 2005. Nevertheless, the vector of controls we use in the simultaneous model is informed by the modified BGT model and from existing empirical work in this area (for instance, see Celasun et al., 1999; Fry, 1993; Kim, 1995; Nyatepe-Coo, 1995; Sarjito, 1996; Rooskareni, 1998) . We specify a set of simultaneous equations as follows: where DNFA t * ¼ The annualized monthly change in the adjusted net foreign assets scaled by the GDP (adjustments to be discussed in Section 4.4); DNDA t * ¼ The annualized monthly change in the adjusted net domestic asset scaled by the GDP (adjustments to be discussed in Section 4.4); Dmm t ¼ The annualized monthly change in money multiplier for M2 19 ; Dp t ¼ The annualized monthly change in consumer price index; y c,t ¼ Cyclical income 20 ; DG t ¼ Cyclical fiscal deficit scaled by GDP; DREER t ¼ The annualized monthly change in the real effective exchange rate (REER); D(r t * þ E t e tþ1 ) ¼ The annualized monthly change in foreign interest rate plus the expected nominal exchange rate (CNY/US$) 21 ; e t ¼ Nominal exchange rate (CNY per US$). As can be seen from equations (4) and (5), the balance of payments function (Eq. (4)) consists of five control variables encompassing both ''push'' and ''pull'' factors as well as monetary policy responses, i.e. factors that motivate capital flows into specific recipient countries. We expect these variables to influence the balance of payments function in the following ways: First, a rise in the M2 money multiplier increases broad money and pushes the interest rate down, hence reducing capital inflows. In addition, a rising multiplier might be capturing an overall tightening credit policy, including a more restrictive policy towards capital inflows. 22 Second, higher inflation perpetuates concerns about exchange-rate depreciation, interest rate hikes and capital losses thereof, hence causing a reduction of capital inflows. 23 Third, higher real output could worsen the current account (due to the income effect), reducing foreign reserve accumulation. However, this variable is a double-edged sword in the sense that a domestic boom could perpetuate capital inflows directly (i.e. pull factor). Fourth, foreign reserves will be decumulated due to a decrease in the current account if the REER is positive (price effect). 24 Fifth, a fall in either the change in foreign interest rates or in the expected exchange-rate depreciation could lead to increased capital inflows from the country. 25 The monetary policy function (Eq. (5)) also consists of five control variables that are considered important factors influencing monetary policy actions. The monetary authority generally implements a contractionary monetary policy in response to a rise in inflation (for obvious reasons), an increase in the money multiplier (to curb overall money supply growth), or an expected exchangerate depreciation (either for its own sake or because of pass-through concerns). The expected coefficient for each of these variables should therefore be negative. In addition, the monetary authority tends to adopt a countercyclical monetary policy to contract domestic money creation when there is a rise in real GDP growth rate above the trend (i.e. a domestic economic boom) or a more expansionary fiscal deficit, implying a negative expected coefficient again. 26 We are least certain about the last variable as it is subject to a number of caveats. During an economic downturn there could be simultaneous use of expansionary monetary and fiscal policies and vice versa during an upturn in economic activity. It is also important to consider the context of expansionary fiscal policy. If done in the event of an economic downturn, the impact may not be the same as when output is at or above trend. 19 We also tried the M1 money multiplier but the results were not substantially changed. 20 Gerlach and Peng (2006) discuss various ways of measuring the output gap in a fast-growing and developing country, like China, that is undergoing significant structural changes. They find that various output gap measures, including estimates derived from the HP-filter rule, are quite highly correlated. 21 The exchange rate is in logarithms. As discussed in Section 4, we use three different assumptions for expected nominal exchange rate: perfect foresight, static expectations, and forward rates based on the NDF market for CNY. These all yield similar results. 22 It is plausible that a change in capital flows causes a concomitant change in the money multiplier (for instance, see Rajan, 2007) . More generally, one might think about specifying a separate equation endogenizing the money multiplier (Jha and Rath, 2001) . 23 Additionally, higher inflation could engender greater uncertainty, leading to reduced capital flows. 24 Ideally one needs to use a measure of real exchange-rate misalignment rather than its change. Short of estimating the ''equilibrium'' REER we tried the deviation of the REER from its trend, but the results did not improve. See Section 4.3 for other robustness checks undertaken. 25 Two caveats should be noted. First, we use only foreign interest rates rather than interest rate differentials as the domestic interest rates are already captured in the DNDA t term. Second, there are two other potentially important push factors causing increased capital flows into China, viz. a fall in risk premium and rise in foreign wealth. The other push factor, viz. industrial country growth, is likely highly correlated with domestic country cyclical growth which is already included in the equation. Dasgupta and Ratha (2000) and Montiel and Reinhart (2000) discuss the determinants of capital flows into developing countries. 26 More precisely, one would want to use a measure of broader fiscal stance, viz. full employment primary fiscal balance. Our estimations are based on monthly observations over the sample period from June, 2000 to September, 2008. All the data are from the IMF-IFS or TEJ Great China database 27 (except the three month CNY non-deliverable forward (NDF) rate which is from Bloomberg, and the change in consumer price index is taken from GTA database). Table 1 summarizes the definitions and sources of the various data used in the estimating equations. The relevant variables, such as the annualized monthly change in the ''adjusted'' DNFA à t , DNDA à t and DG t fiscal deficit are scaled by GDP. 28 To check for stationarity we 28 Three caveats should be noted. One, the manner of ''adjustment'' of the NFAs for revaluation effects is discussed in Section 4.2. Two, for the monthly data, the variables are scaled by ''monthly GDP'', which is measured by distributing quarterly GDP into corresponding three months weighted by the industrial production ratio. Three, we tried the regressions without scaling by GDP (since we are using first differences), but the coefficient on some variables, like the money multiplier, turned out to be far too large to make any economic sense. applied the standard ADF unit root test to each of the variables and found all variables to be stationary at the 10 percent significant levels with the exception of the money multiplier, inflation, and the exchange rate adjusted foreign interest rates (see Table 2 ). 29 Both dependent variables are stationary. 30 We used the Hodrick-Prescott (HP) method to measure the trends of real output and fiscal deficit. We do not have a direct measure of exchange-rate expectations so following the literature we consider three different proxies for how agents form expectations about the exchange rate. If economic agents have perfect foresight then the annual change of the actual nominal exchange rate at the next period might be the appropriate proxy for the expected exchange-rate depreciation for the next period. If agents have static expectations then the annual change of exchange rate at the current period is used as the proxy. Finally, the three month CNY NDF rate is also used as a proxy for the expected exchange rate for the next period. We find similar results with the three measures. Table 3 provides the summary statistics of the various variables used in the model. A typical balance sheet of the monetary authority is as follows: Since the changes of both NDA and NFA are based on the monetary authority's balance sheet, care must be taken in accounting for non-policy related changes in the variables such as the revaluation effects due Note: (*) Significant at more than 10 percent; (**) Significant at more than 5 percent; (***) Significant at more than 1 percent. Summary statistics of variables used in empirical study (June, 2000 -September, 2008 Siklos (2000) pointed out a similar problem with the Hungarian-German interest rate differential and has argued that interest rates should not be difference stationary. Brissimis et al. (2002) also found that the deviation of DM/French franc exchange rate from its target, expected change in the US composite variable and German consumer price inflation are not stationary in their estimation. to gold value and exchange-rate fluctuations. 31 In order to exclude monetary gold from the foreign assets we use the product of foreign reserves denominated in US dollars and the exchange rate (domestic currency/US$) to proxy foreign assets. The net foreign assets without the revaluation effect are as follows: where R t is foreign reserves denominated in US$ and e t is the RMB exchange rate against the US$. We use (R  e) rather than the actual FA in the PBC balance sheet as there are some differences between the two in the case of China, particularly in early 2002 when the latter declined sharply for an unknown reason. The problem with using (R  e) is that reserve values could change because of currency fluctuations. However, these valuation effects will not change the domestic currency value of the money base and we therefore need to exclude these effects from the book value of NFA before estimation. Ideally if we had the currency composition of reserves we could adjust for the valuation changes. Given that such data is not available, the best we can do is assume that all reserves are held in US$ and adjust the reserves for changes in the CNY/US$ bilateral rate. However we also tried different currency compositions of reserves holdings as do Prasad and Wei (2005) . Results are fairly robust and discussed in Section 4.3. Since the revaluation effect is the change of NFAs due to exchange-rate fluctuations, it can be measured as follows. In general, the monetary authority recognizes the end-year revaluation of foreign currency liabilities and assets in the Profit and Loss account of the income statement. Since the endyear income statement balance will be included in the equity (K) account of the balance sheet, the change of net foreign assets due to the revaluation effect can be offset by the change of equity so that the domestic monetary base will be the same. In other words, if NFAs rises because of an increase in e t , then Therefore, the revised change of net foreign assets ¼ DNFA t * ¼ NFA t À NFA tÀ1 (e t /e tÀ1 ). The adjusted variable excludes the price or valuation effect, which as noted, should have no direct impact on liquidity. The adjusted NFA t * is derived as a residual component: This effectively implies that DNFA t * and DNDA t * will be used as the dependent variables in eqs. (4) and (5) respectively. We start by estimating the simultaneous eqs. (4) and (5) using two-stage least squares (2SLS). We apply autocorrelation, autoregressive conditional heteroskedasticity (ARCH), and heteroskedasticity tests on the residuals from the estimated equations. 32 Newey-West heteroskedasticity and autocorrelation consistent (HAC) covariance estimates are used if there is a problem. 33 To correct for serial correlation problems, AR terms from 1 through 3 are also included in both regressions. The Log-31 Other factors include interest earnings earned from foreign reserves accumulation. Given the low interest rates in China as well as the fact that the majority of its capital inflows relate to the private financial account, we ignore these factors. 32 The Breusch-Godfrey serial correlation Lagrange multiplier (LM) test is used to check for the autocorrelation, while White's heteroskedasticity test is used to test the heteroskedasticity in the residuals. ARCH LM test is used to test for ARCH in the residuals. 33 Newey and West (1987) have derived a consistent covariance matrix estimator in the presence of both heteroskedasticity and autocorrelation. Since we use the Newey-West HAC estimates we do not need to include lagged dependent terms as done by Brissimis et al. (2002) and others. likelihood ratio test is applied to lag length selection. Table 4 summarizes the results of the estimating equations. We have three sets of estimations depending on whether we assume perfect foresight, static expectations, or forward-looking expectations. Forward-looking expectations are captured using the three month forward rate (the one-month forward rate unfortunately being unavailable). The estimated offset coefficients are around 0.5 and are statistically significant, indicating a moderate degree of capital mobility and a degree of porousness of China's capital controls. The estimated sterilization coefficients are also highly statistically significantly significant at around 1, 34 suggesting that the PBC has heavily sterilized its reserve accumulations in the last nine years. The money multiplier is statistically and economically significant across all the estimations with the correct sign. Cyclical output is statistically significant and negative across all the estimations, which suggests that the income effect leading to a worsening of the current account may be greater than the direct impact that positive cyclical income has on attracting capital inflows. This again is consistent with international capital mobility for China being moderate rather than high. The lagged inflation term is statistically significant with negative (correct) signs across all regressions. The exchange rate adjusted foreign interest rate coefficients have the incorrect sign though they are generally statistically insignificant. Both the lagged REER and the cyclical fiscal deficit are statistically insignificant in balance of payments function and monetary reaction function, respectively. There is evidence of persistence in both reactions functions. As a robustness check, we re-estimated the regressions above using three-stage least squares (3SLS) (see Table 5 ). The results are highly robust, though the offset and sterilization coefficients (in absolute terms) are somewhat larger using 3SLSL. It is worth noting that the correlation coefficient between the residuals of the two equations is about 0.55, suggesting no serious correlation problem exists. Due to the small sample size and no notable improvement of estimation using 3SLS our focus remains on the 2SLS estimation in the following analysis. We undertook a number of other robustness checks, but for sake of parsimony the estimated equations are not included in the paper. 35 One of the potentially more important checks involved trying various currency compositions of reserves. With the assumption of 90 percent US$ assets and 10 percent Euro assets, the estimated offset coefficients vary from 0.54 to 0.56 (depending on different ways of forming expected exchange-rate depreciation), while the estimated sterilization coefficients move around 1.04. With the assumption of 70 percent US$ assets, 20 percent Euro assets and 10 percent Japanese Yen assets, the estimated offset coefficients vary from 0.57 to 0.58, while the estimated sterilization coefficients vary from 1.07 to 1.09 (Table 6 ). Overall the empirical results are robust across different scenarios and assumptions. We therefore maintained the assumption of 100 percent US$ assets for simplicity. We also applied the rolling (forward) recursive estimation on monthly data to estimate the dynamic change of offset and sterilization coefficients (see Fig. 7 ). 36 This is done by deriving the initial estimates by using the sample from 2000:M6 to 2006:M1 and then adding an observation (after 2006:M1) and excluding the first observation (after 2000:M6) each time, so that each estimation uses the same size of observations. The recursive offset coefficient remained fairly stable between early 2005 and mid 2006 at around 0.55, dropped slightly to around 0.45 till late 2007, before rising very gradually since then to average around 0.5 over 2008. With regard to the recursive sterilization coefficients, while sterilization peaked in early 2005, it has been declining ever since, reaching around 0.7 by late 2007 and has remained stable ever since. This suggests sterilization has been quite heavy but not complete in recent years. This contrasts with the estimates of complete sterilization in the initial estimates and illustrates the value of recursive estimation. According to the judgments of a number of economists China's capital controls have been becoming increasingly less binding. 37 This is consistent with the fact that we find China's offset coefficient to have been around 0.5 between 2000 and 2008. However, insofar as the de facto capital 35 We also replaced the lagged REER with the trade balance, and replaced the change in REER with the deviation of REER from trend (as ideally one needs to use a measure of real exchange-rate misalignment rather than change). In all of the cases the results were largely unchanged. Detailed regression results are available from authors on request. 36 Table 6 only reports the robustness check under the assumption of perfect foresight expectation. The estimation results for other exchange-rate expectations are available from the authors on request. 37 See for example Lardy (2005) and Prasad and Wei (2005) . mobility is imperfect, sterilization can be effective. As China has been sterilizing capital inflows fairly aggressively. We estimate that the PBC has typically sterilized around 90 percent of the reserve inflows, which is similar to those obtained by Burdekin and Siklos (2005) and He et al. (2005) . While Burdekin and Siklos (2005) suggest the PBC has over-sterilized the foreign reserves, they find the PBC has not done so sufficiently to prevent M2 (broader money supply) from increasing. 38 He et al. (2005) find that the PBC has fully sterilized the capital inflows, and most of the responses finish in a month. Our rolling recursive estimates suggest that while sterilization in China was virtually complete until early 2007, it has been partial -but still high at around 0.7 -between late 2007 and late 2008. This is consistent with views that as the large payments surpluses have continued, sterilization has become increasingly difficult. Our estimates of high sterilization over the period of China's recent huge buildup in reserves support the view that China has operated as a reserve sink, much as Germany and Japan did during the later stages of the Bretton Wood system. While Dooley et al. (2004) have suggested the current global economic imbalances are much less worrisome than most economists have suggested, the chaotic end of the Bretton Woods exchange-rate regime in the early 1970s is but one of many examples that large prolonged international payments imbalances seldom lead to happy endings. Finally, the high level of sterilization we found is not consistent with the strong form of the monetary approach that assumes no sterilization and raises questions about arguments that China's pegged exchange rate has been an important source of discipline over domestic inflation (see, Schnabl, 2003a,b, 2004) . Indeed, in recent years with the absence of sterilization, China's peg would have been a source of substantial inflationary pressure. Going forward, the Chinese authorities would do well to continue to relax the management of the exchange rate, in addition to taking further steps towards deregulation of capital outflows in a judicious manner. Less management of the exchange rate in turn should provide the PBC greater opportunities to use interest rate policy to manage domestic liquidity conditions and pressures. The monetary authority's loss function is determined by the change in the logarithm of the price level and cyclical income (Y c,t ). All the parameters are assumed to be positive. The evolution of key variables including inflation and cyclical income is discussed below. The evolution of inflation can be written as follows: where:p 1 > 0; 0 < p 2 < 1; p 3 > 0, MB t is the monetary base and mm t is the money multiplier. Eq. (A1) states that inflation is a monetary phenomenon with a lagged effect. In addition, depreciation of the nominal exchange rate (rise in s t ) could increase inflationary pressures due to increased prices of tradable goods. The evolution of cyclical income can be written as follows: Y c;t ¼ 4 1 ½ðDNFA t þ DNDA t Þmm t þ MB t Dmm t þ 4 2 Y c;tÀ1 þ 4 3 DG t (A3) 4 1 > 0; 0 < 4 2 < 1; 4 3 > 0 where: G t is the government expenditure. We assume that both expansionary fiscal and monetary policies can boost cyclical output. The balance of payments is defined as usual (ignoring errors and omissions): where: CA is the current account balance and DNK t is the net capital inflow in time t. The current account in turn is assumed to depend simply on both cyclical output and the lagged real effective exchange rate (to capture inertial effects) in a linear manner: CA t ¼ a 0 þ a 1 Y c;t þ a 2 DREER tÀ1 ; a 1 < 0; a 2 < 0 (A5) where: REER is the real effective exchange rate (rise implies a currency appreciation). The net capital inflow is assumed to depend imperfectly on the uncovered interest differentials: where: s t is the current exchange rate (logarithm); E t s tþ1 is the current expectation of the exchange rate at time t þ 1; r t is the domestic interest rate; r t * is the foreign interest rate; and c represents the degree of substitutability between domestic and foreign assets, i.e. the degree of international capital mobility. This in turn is affected by the extent of capital controls. The interest rate is determined by the change in money supply: Dr t ¼ Àj 1 ½ðDNDA t þ DNFA t Þmm t þ MB t Dmm t ; j 1 > 0 (A7) After substituting eq. (A3) to (A7) into (A1) we derive: Dp t ¼ ðp 1 mm t þcp 3 þp 3 ca 1 4 1 mm t þp 3 j 1 mm t ÞDNFA t þðp 1 mm t þp 3 ca 1 4 1 mm t þp 3 j 1 mm t Þ DNDA t þðp 1 MB t þp 3 ca 1 4 1 MB t þp 3 j 1 MB t ÞDmm t þðp 3 ca 1 4 2 ÞY c;tÀ1 þðp 2 ÞDp tÀ1 þðp 3 ca 1 4 3 ÞDG t þðp 3 ca 2 ÞDREER tÀ1 þðp 3 ÞD À r à t þE t s tþ1 Á (A8) Given this we can solve for vL t =vDNDA t ¼ 0 landvL t =vDNFA t ¼ 0, and after substituting the constraints into the loss function, we derive two reduced-form equations: DNFA t ¼ À nh bcp 3 ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t þbðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þ 2 mm 2 t þ r4 2 1 mm 2 t i. u 1 o DNDA t À nh bcp 3 ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 ÞMB t þ bðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þ 2 mm t MB t þ r4 2 1 mm t MB t i. u 1 o Dmm t Àf½bp 2 ðp 3 c þ ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t Þ=u 1 gDp tÀ1 Àf½bca 1 4 2 p 3 ðp 3 c þ ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t Þ þ r4 1 4 2 mm t =u 1 gY c;tÀ1 Àf½bca 1 4 3 p 3 ðp 3 c þ ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t Þ þ r4 1 4 3 mm t =u 1 gDG t Àf½bca 2 p 3 ðp 3 c þ ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t Þ=u 1 gDREER tÀ1 Àf½bp 3 ðp 3 c þ ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t Þ=u 1 gD where:u 1 ¼ b½p 3 c þ ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t 2 þ r4 2 1 mm 2 t þ 32 2 ðd 2 À 1Þ 2 > 0. DNDA t ¼ À nh bcp 3 ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t þ bðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þ 2 mm 2 t þr4 2 1 mm 2 t i. u 2 o DNFA t À nh bðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þ 2 mm t MB t þ r4 2 1 mm t MB t i. u 2 o Dmm t Àf½bp 2 ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t =u 2 gDp tÀ1 Àf½bca 1 4 2 p 3 ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t þ r4 1 4 2 mm t =u 2 gY c;tÀ1 Àf½bca 1 4 3 p 3 ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t þ r4 1 4 3 mm t =u 2 gDG t Àf½bca 2 p 3 ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t =u 2 gDREER tÀ1 Àf½bp 3 ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t =u 2 gD À r à t þ E t s tþ1 Á (A10) where:u 2 ¼ b½ðp 1 þ p 3 j 1 þ ca 1 4 1 p 3 Þmm t 2 þ r4 2 1 mm 2 t þ dq 2 ðd 1 À 1Þ 2 > 0. To ensure identification of eqs. (A9) and (A10), we drop DG from the former and REER from the latter (discussed in Section 3.2). Eqs. (A9) and (A10) are the estimating equations used in the paper (eqs. (4) and (5) in Section 3.2). 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The views expressed in this paper are those of the authors and do not necessarily reflect those of the HKIMR, its Council of Advisors, or the Board of Directors. Comments on earlier versions from an anonymous referee of this journal, Richard Burdekin, Leroy Laney, and Pierre Siklos are appreciated as is financial support from the Freeman Foundation Program in Asian Political Economy at the Claremont Colleges. Funding from Central University of Finance and Economics 121 Youth Scholar Fund are also greatly acknowledged. The usual disclaimer applies. Appendix 1: The modified BGT model (2002) Similar to Brissimis-Gibson-Tsakalotos (BGT) (2002) model, we derive the theoretical model by explicitly minimizing a simple loss function of the monetary authority, subject to a number of constraints that reflect the workings of the economy. But we modify the BGT model in different ways (see Ouyang et al., 2008 for more details).The loss function of the monetary authority is: 38 In related work, Burdekin and Siklos (2005) regress the change of base money on the change of foreign reserves for the period of 1990:q1-2002:q4 and find that 1 unit increases in the change of foreign reserves will lead to decreases of 0.1-0.2 units in the change of base money (based on OLS and GMM). However, they also find that 1 unit increases in the change of foreign reserves has significantly increased M2 growth by 0.11 units. Using VAR analysis, He et al. (2005) find that sterilization intensity increased somewhat in 2003:m1-2004:m12 compared to 1998:m1-2002:m12 . They also find that 1 unit increases in NFAs will lead to a decline of around 1 unit in NDAs.