## _wp09131

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---

### Financial system changes and implications for monetary policy
- Structural changes cited:
  - Gradual movement toward a more flexible exchange rate regime.
  - Ongoing interest rate liberalization.
  - Rapid development of capital markets.
- Potential consequences for money demand:
  - These changes may raise the opportunity costs of holding money.
  - They may provide alternative assets for holding value, leading to asset substitution between domestic and foreign currencies, and between monetary and nonmonetary assets.

### Stability of money demand and measurement issues
- Stability:
  - Stability of the money demand function is crucial for predictable monetary transmission (see Judd and Scadding (1982)).
  - Recent evidence suggests money demand functions in many industrialized and emerging market economies have become less stable.
- Measurement concerns:
  - Song (2007) argues M2 may understate true money holdings because some deposit-like liabilities of deposit-taking institutions are excluded.
  - Estimates may fail to capture the impact of rapid capital market development (see Liang (2007)).
  - Implication: A broader estimate of money demand could improve monetary targeting and forecasting of aggregate demand.

### China’s historical practice on M2 targeting and outcomes
- The People’s Bank of China (PBC) traditionally set an annual target for M2.
  - Footnote: In 2008, the PBC did not announce an annual target for M2 as it typically does.
- Empirical observation for 1999–2007:
  - Most of the time M2 growth exceeded the annual target.
  - Figure 1 caption: China: Actual and Targeted M2 Growth Rate, 1999–2007 (Year-on-year percent change).

### Recent financial developments (key facts)
- Long-run growth:
  - Since the late 1970s, real GDP growth in China has averaged 9 percent a year.
- Interest rate liberalization (timing and measures):
  - Reform sequencing: liberalize interest rates in money and bond markets first, then loans and deposits; foreign currencies ahead of domestic; loans ahead of deposits; long-term and large-value instruments ahead of short-term and small-value instruments.
  - Since 1996: interbank market rate, bond market rate, and issuing rate on government bonds and policy financial bonds liberalized; interest rates on foreign currency loans and large-value foreign currency deposits deregulated; floating band around the RMB lending rate widened gradually.
  - In 2004: introduced a floating central bank lending rate system and removed the ceiling on lending rates and floor on deposit rates of commercial banks; floor lending and ceiling deposit rates still exist.
  - January 2007: Shanghai Interbank Offered Rate (SHIBOR) was formally launched and has since become the benchmark rate in the money market.
- Exchange rate reform:
  - July 21, 2005: PBC adopted a market-based managed floating exchange rate regime with reference to a basket of currencies.
  - During July 2005–March 2008:
    - the RMB appreciated by nearly 18 percent against the U.S. dollar;
    - the RMB appreciated in real effective terms by around 14 percent.
  - Other measures: market-maker system and over-the-counter transactions in the interbank foreign exchange market; introduction of forward and swap transactions; widening of the daily floating band of the RMB against the U.S. dollar in the interbank spot foreign exchange market.
  - Currency substitution concern: M2 statistics do not include foreign currencies; ongoing currency substitution could affect the size of M2.
- Capital markets development (selected figures):
  - Shanghai Stock Exchange established in 1990; mutual funds accounts allowed from 1991.
  - By end-2007:
    - stock issues of listed companies totaled US$204 billion;
    - bond issues totaled US$124 billion (of which US$7.5 billion were from convertible bond issues).
  - Number of individual investor accounts increased from fewer than 9 million in 1992 to nearly 138 million at end-2007.

### Model approach and specification
- Primary methodology:
  - Single-equation error correction model (ECM) of broad money demand using general-to-specific modeling and Johansen cointegration framework.
- Variables considered: broad money, domestic goods, equity shares, foreign currency; nominal returns denoted Rd (RMB deposit interest rate), pΔ (inflation), sΔ (change of stock prices), Rf and eΔ (foreign currency nominal return and change in exchange rate).
- Log-linear specification (equation (2) in source):
  - pm− = μ0 + μ1 y + μ2 Rd + μ3 Rf + μ4 pΔ + μ5 sΔ + μ6 eΔ
  - Expected signs: μ1 > 0; μ2 < 0; μ3 < 0; μ4 < 0; μ5 < 0; μ6 < 0.

### Unit roots, cointegration, and long-run estimates
- Integration results (ADF tests):
  - pm−, Rd, Rf, pΔ, eΔ, and sΔ are I(1);
  - p, e, s are I(2);
  - y likely I(1) based on estimated root for yΔ = 0.19 ( = 1 - 0.81).
- VAR and cointegration:
  - VAR order selection started with VAR(4), data simplifiable to VAR(1) based on Schwarz criterion.
  - Johansen tests: maximal eigenvalue and trace statistics strongly reject no cointegration in favor of at least two cointegrating vectors; degree-of-freedom adjusted statistics suggest at least one cointegrating vector and likely two.
- Standardized cointegrating vector (first row of β) and long-run relation (equation (3) in source):
  - Preserve the source presentation: )3( ,6.882(4)5.312(41.1390.1770.0340.758 epsRRypm fd Δ⋅−Δ⋅−Δ+−++=−^μ
  - Inflation exhibits a high semi-elasticity in the cointegrating vector.
- Adjustment coefficients α:
  - money equation feedback coefficient = -0.011 (implies approximately 1.1 percent adjustment in the first quarter; slow adjustment).
  - Comparison: adjustment coefficients in Netherlands, Germany, France were -0.26, -0.15, -0.20; Argentina and Greece -0.12 and -0.08.
- Weak exogeneity tests:
  - y, Rd, sΔ, and pΔ appear weakly exogenous individually;
  - Rf and eΔ do not appear weakly exogenous.

### ADL, parsimonious ECM, and diagnostic statistics
- ADL long-run solution (equation (4), t = 52 [1995Q2–2008Q1]):
  - Preserve source numeric presentation: (4) pm− = 4.589 + 34.884 y + 0.006 Rd + 0.141 Rf + 0.081 pΔ + 0.615 sΔ + 1.239 eΔ (standard errors in source parentheses).
- Parsimonious ECM (equation (5), t = 52 [1995Q2–2008Q1]) diagnostics:
  - 2 R = 0.74;
  - σ^ = 0.795;
  - Durbin Watson statistic = 2.5;
  - AR: F(4,34) = 1.033;
  - ARCH: F(4,30) = 0.563;
  - Normality: χ^2(2) = 5.872;
  - RESET: F(1,37) = 0.154;
  - Hetero: F(27,10) = 0.308.
- Dummies used in starting ADL:
  - t_crD_ for 1997Q3–1998Q3 (Asian financial crisis);
  - t_exD_ for 2005Q3–2008Q1 (RMB exchange rate reform and appreciation expectations).

### Short-run and long-run empirical findings
- Error-correction:
  - Error-correction terms highly significant; long-run relationship established among real money, real output, RMB and foreign currency deposit interest rates, and inflation.
  - Adjustment to equilibrium via the error correction term is slow.
- Short-run influences:
  - previous quarter’s real GDP growth: positive effect;
  - RMB and foreign currency deposit rates: very small coefficients (money demand less sensitive to interest rates);
  - inflation and its lags: mixed impacts; current inflation has a significantly negative effect;
  - changes in exchange rates do not enter the final model directly, but the exchange rate reform dummy (t_exD_) induces more money demand;
  - changes in stock prices (s−Δ) and Asian financial crisis dummy (t_crD_) are statistically insignificant.
- Long-run static money demand function from ECM (equation (6) in source):
  - Preserve source presentation: )6()4(81.2082.0742.0)(pRypm fs Δ⋅−−=−
  - Interpretation: real money demand depends positively on output and negatively on foreign deposit interest rate and the inflation rate.
  - Notable: U.S. dollar deposit interest rate (Rf) enters the long-run function rather than RMB interest rate; coefficient is very small. Ceilings on RMB deposit rates may reduce their effectiveness in influencing money holdings.
- Dynamic equilibrium when pm−Δ = yΔ ≡ g (equation (7) in source):
  - Preserve source presentation: )7()4(778.1)4(81.2082.0742.0()(gpRypm fd ⋅−Δ⋅−−=−

### Statistical robustness, residuals, and constancy analyses
- Robustness:
  - Single-equation ECM estimates (equation (6)) are numerically close to system cointegrating vector estimates (equation (3)) and single-equation ADL long-run estimates (equation (4)).
- Residual diagnostics (unrestricted ECM, sample T = 52 [1995Q2–2008Q1]):
  - 2 R = 0.882
  - ∧σ = 0.947
  - DW = 2.45
  - AR: F(2,10) = 1.301
  - ARCH: F(2,8) = 0.093
  - Normality: χ2(2) = 2.317
  - RESET: F(1,11) = 0.263
- Actual and fitted values (Figure 7):
  - Residuals scaled by ∧σ with ±2 band used to identify outliers; squared residuals indicate major outliers.
  - Possible explanation for outliers around 2001: PBC began incorporating clients’ deposits in security companies into M2 (starting 2001) and made other revisions since 2002 in line with IMF’s Monetary and Financial Statistics Manual (2000).
- Residual analysis (Figure 8):
  - Correlelogram: most autocorrelations close to zero; residuals consistent with white-noise.
  - Spectral density: flat spectrum consistent with white-noise.
  - Histogram and QQ plot: upper-tail departures from normal consistent with outliers.
- Recursive analysis and parameter constancy (Figures 9–11):
  - Recursive least squares: most coefficients appear constant, becoming significantly so only after 2002.
  - RSS and standard error bands: standard error increases around 2000, then bands relatively constant.
  - Break-point Chow tests and p-values plotted to assess structural breaks.
- Ex post forecasts (Figure 12):
  - Equation (5) re-estimated through 2006Q2 and used to forecast 2006(3)–2010(2); model tracks recent performance relatively well with ±2*SE bands.

### Major findings and policy-relevant conclusions
- Model stability and constancy:
  - The estimated model of money demand has sensible statistical properties over 1994Q1–2008Q1, suggesting empirical constancy holds despite interest rate liberalization, exchange rate reforms, and capital market development.
  - A stable broad money demand function exists when taking account of asset substitution and using appropriate econometric techniques.
- Elasticities and sensitivities:
  - Strong evidence for a stable long-run relationship between real money and real GDP, with an estimated income elasticity of less than unity.
  - Current inflation has a significantly negative impact on money demand.
  - Impact of RMB and foreign deposit interest rates on money demand are relatively small, possibly reflecting remaining caps on deposit rates.
- Exchange rate expectations and capital markets:
  - Expectations of RMB appreciation since 2005 appear to induce slightly more money demand in the model.
  - Stock prices do not enter the short- and long-run models, reflecting underdevelopment of capital markets and incentives to hold money for cautionary purposes during transition.
- Policy implications:
  - Fundamental changes (further interest rate liberalization, more flexible exchange rate regime, capital market development, greater availability of alternative assets, liberalization of capital flows, efficiency gains in the financial system) are likely to alter the money demand structure over time and complicate monetary policy conduct.

### Data, sample, and computational details
- Sample: Quarterly data for 1994Q1–2008Q1. Series not seasonally adjusted; seasonal dummies used.
- Series definitions:
  - Money aggregate (M): Money supply M2, nominal — RMB, billions — CEIC
  - Price (P): Consumer price index, end-of-period — Index — WEO (IMF)
  - Real output (Y): GDP at constant prices — RMB, billions — WEO (IMF)
  - RMB deposit interest rate (dR): One-year household saving rate for RMB, net of withholding interest tax — Percent — IFS
  - USD deposit interest rate (fR): One-year time deposit rate for USD, net of withholding interest tax — Percent — IFS (IMF); PBC; Bank of China
  - Stock prices (S): Shanghai Stock Exchange Composite Index — Index — CEIC
  - Exchange rate (E): Nominal exchange rate RMB per USD — IFS (IMF)
- Tax note: Interest earned on savings deposits taxed at 20 percent effective November 1, 1999; decreased to 5 percent effective August 15, 2007.
- Software: GiveWin 2.20, PcGive 10.3, and PcGets 1.02 used for empirical results.

*Source: _wp09131 - IMF Working Paper (excerpt provided).*

### 1. Actual and Targeted M2 Growth Rate, 1999–2007.......................................................5

### 1. Actual and Targeted M2 Growth Rate, 1999–2007.......................................................5

### Financial system changes and implications for monetary policy
- Recent changes in China’s financial system and greater use of market-based signals for macroeconomic management pose challenges for the conduct of monetary policy.
- Specific structural changes cited:
  - Gradual movement toward a more flexible exchange rate regime.
  - Ongoing interest rate liberalization.
  - Rapid development of capital markets.
- Potential consequences for money demand:
  - These changes may raise the opportunity costs of holding money.
  - They may provide alternative assets for holding value, leading to asset substitution between domestic and foreign currencies, and between monetary and nonmonetary assets.

### Stability of the money demand function
- The stability of the money demand function is crucial to ensure that money exerts a predictable influence on the economy and that central bank control of the money supply is an effective policy instrument (see Judd and Scadding (1982)).
- Recent evidence (general, as reported) suggests money demand functions in a number of highly industrialized and emerging market economies have become less stable.

### China’s historical practice on M2 targeting and observed outcomes
- Traditionally, the People’s Bank of China (PBC) has set an annual target for broad money (M2) growth.
  - Footnote: However, in 2008, the PBC did not announce an annual target for M2, as it typically does at its annual working conference.
- Empirical observation: Most of the time during 1999–2007, M2 growth in China exceeded the annual target (Figure 1).
  - Figure 1 caption: China: Actual and Targeted M2 Growth Rate, 1999–2007 (Year-on-year percent change).
  - Figure 1 sources: People's Bank of China; CEIC Data Company, Ltd.; and author’s estimates.

### Measurement and modeling issues motivating the analysis
- Measurement concerns:
  - Song (2007) argues the current measure of M2 in China may understate true money holdings because some deposit-like liabilities of deposit-taking institutions are excluded.
  - Estimates may fail to capture the impact of rapid development of China’s capital markets (see Liang (2007)).
- Implication: A broader estimate of money demand could improve the establishment of monetary targets and forecasting of aggregate demand.

### Methodology and focus of the paper
- The paper uses an error correction model (ECM) to examine the empirical relationship between broad money and a range of macroeconomic and financial determinants in China.
- Primary focus: The constancy of the money demand relationship in light of recent financial system changes.
- Organization of the paper:
  - Section II: Brief description of recent financial developments.
  - Section III: Estimation results for a single-equation ECM of money demand using general-to-specific modeling.
  - Section IV: Summary of the main findings.

*Source: _wp09131 - 1. Actual and Targeted M2 Growth Rate, 1999–2007 (excerpt).*

### conclusions.

### conclusions.

### Recent developments
- Since the late 1970s, real GDP growth in China has averaged 9 percent a year.
- Recent important changes to the financial system that may influence money demand include:
  - interest rate liberalization;
  - exchange rate reform; and
  - capital markets development.

### Interest rate liberalization
- Reform strategy: liberalize interest rates in money and bond markets first, then loans and deposits; foreign currencies ahead of domestic; loans ahead of deposits; long-term and large-value instruments ahead of short-term and small-value instruments.
- Since 1996:
  - interbank market rate, bond market rate, and issuing rate on government bonds and policy financial bonds have been liberalized;
  - interest rates on foreign currency loans and large-value foreign currency deposits have been deregulated;
  - the floating band around the renminbi (RMB) lending rate has been widened gradually.
- In 2004:
  - China introduced a floating central bank lending rate system and removed the ceiling on lending rates and floor on deposit rates of commercial banks; floor lending and ceiling deposit rates still exist.
- January 2007: Shanghai Interbank Offered Rate (SHIBOR) was formally launched and has since become the benchmark rate in the money market.

### Reform of the exchange rate regime
- July 21, 2005: PBC adopted a market-based managed floating exchange rate regime with reference to a basket of currencies, increasing RMB flexibility.
- During July 2005–March 2008:
  - the RMB appreciated by nearly 18 percent against the U.S. dollar;
  - the RMB appreciated in real effective terms by around 14 percent.
- Other market-enhancing measures: market-maker system and over-the-counter transactions in the interbank foreign exchange market; introduction of forward and swap transactions; widening of the daily floating band of the RMB against the U.S. dollar in the interbank spot foreign exchange market.
- Currency substitution and expectations:
  - Increased expectations of further RMB appreciation may affect the currency composition of deposits and willingness to hold RMB balances.
  - M2 statistics in China do not include foreign currencies; ongoing currency substitution could affect the size of M2.
- The exchange rate can enter money demand functions because changes alter domestic value of foreign assets (wealth effect) and expected exchange rate changes indicate expected return on foreign monetary assets, influencing the opportunity cost of holding domestic monetary assets.

### Development of capital markets
- Shanghai Stock Exchange established in 1990; households allowed to open mutual funds accounts in 1991.
- From 1993 to 1998: consolidation of capital markets and regulations; establishment of China Securities Regulatory Commission (CSRC).
- From 1998 onward: Securities Law promulgation and reforms including nontradable share reform, restructuring of securities companies, improvement in share issuance procedures, and promotion of institutional investors.
- By end-2007:
  - stock issues of listed companies totaled US$204 billion;
  - bond issues totaled US$124 billion (of which US$7.5 billion were from convertible bond issues).
- Investor accounts:
  - number of individual investor accounts increased from fewer than 9 million in 1992 to nearly 138 million at end-2007.
- Household financial holdings (2001–07):
  - expansion of investment products and wealth management services likely altered factors influencing money holdings.

### A model of money demand in China — overview
- Approach: estimate a single-equation error-correction model (ECM) of broad money demand using general-to-specific modeling and Johansen cointegration framework.
- Variables considered (consistent with Chinese financial structure): broad money, domestic goods, equity shares, and foreign currency.
- Nominal returns denoted: Rd (RMB deposit interest rate), pΔ (inflation), sΔ (change of stock prices), Rf and eΔ (foreign currency nominal return and change in exchange rate).
- Log-linear specification (equation (2) in source):
  - pm− = μ0 + μ1 y + μ2 Rd + μ3 Rf + μ4 pΔ + μ5 sΔ + μ6 eΔ
  - Expected signs: μ1 > 0; μ2 < 0; μ3 < 0; μ4 < 0; μ5 < 0; μ6 < 0.

### Earlier studies
- Two modeling approaches in prior work:
  - conventional money demand models used for advanced economies (e.g., Chow (1987), Chen (1997), Deng and Liu (1999), Hafer and Kutan (1993 and 1994), Huang (1994), Yu and Tsui (2000));
  - adaptations to Chinese-specific conditions adding variables for transition features (e.g., Feltenstein and Farhadian (1987), Feltenstein and Ha (1992), Girardin (1996), Ma (1993), Qin (1994), Yi (1993)).
- Key lessons: choice of opportunity cost variables and use of ECMs are important for meaningful money demand estimation.

### Model specification, integration, and cointegration testing
- Unit root tests (ADF) indicate:
  - pm−, Rd, Rf, pΔ, eΔ, and sΔ are I(1);
  - p, e, s are I(2);
  - y likely I(1) based on estimated root for yΔ = 0.19 ( = 1 - 0.81).
- Johansen cointegration tests conducted among I(1) variables: pm−, y, Rd, Rf, sΔ, pΔ, eΔ.
- VAR order selection: starting with VAR(4), data simplifiable to VAR(1) based on Schwarz criterion (Table 2).
- Cointegration results (Table 3):
  - maximal eigenvalue and trace statistics strongly reject null of no cointegration in favor of at least two cointegrating vectors; degree-of-freedom adjusted statistics suggest at least one cointegrating vector and likely two.
  - Standardized cointegrating vector (first row of β) yields estimated long-run relation (equation (3) in source):
    - pm− = 0.177 eΔ − 0.034 sΔ − 0.758 y + 0.177 Rf − 0.034 Rd + 21.247 pΔ + 27.527 (coefficients presented; source denotes equation (3) as:)
    - (Source presents estimated: )3( ,6.882(4)5.312(41.1390.1770.0340.758 epsRRypm fd Δ⋅−Δ⋅−Δ+−++=−^μ — preserve that formulation in source.)
  - Inflation exhibits a high semi-elasticity in the cointegrating vector.
- Adjustment coefficients α:
  - money equation feedback coefficient = -0.011 (implies approximately 1.1 percent adjustment in the first quarter; slow adjustment).
  - Comparison: adjustment coefficients in Netherlands, Germany, France were -0.26, -0.15, -0.20; Argentina and Greece -0.12 and -0.08.
- Weak exogeneity tests:
  - y, Rd, sΔ, and pΔ appear weakly exogenous individually;
  - Rf and eΔ do not appear weakly exogenous, permitting single-equation conditional ECM analysis under confirmation of weak exogeneity for some variables.
- Significance tests on cointegrating vector: Rf, sΔ, pΔ, and eΔ appear very significant.

### A dynamic model of money demand — ADL to parsimonious ECM
- Fourth-order ADL used as starting point, modified with dummies:
  - t_crD_ for 1997Q3–1998Q3 (Asian financial crisis);
  - t_exD_ for 2005Q3–2008Q1 (RMB exchange rate regime reform, capturing appreciation expectations).
- Long-run solution of the ADL (equation (4) in source), t = 52 [1995Q2–2008Q1], standard errors in parentheses:
  - (4) pm− = 4.589 + 34.884 y + 0.006 Rd + 0.141 Rf + 0.081 pΔ + 0.615 sΔ + 1.239 eΔ (with standard errors shown in parentheses in source as: )21.45()114.9()0.93()0.39()33.0()2.64()20.83( ).
  - (Preserve the exact numeric presentation from source.)
- General-to-specific (PcGets) used to simplify ADL to parsimonious ECM (equation (5) in source). Equation (5) (t = 52 [1995Q2–2008Q1]) includes:
  - 2 R = 0.74;
  - σ^ = 0.795;
  - Durbin Watson statistic = 2.5;
  - AR: F(4,34) = 1.033;
  - ARCH: F(4,30) = 0.563;
  - Normality: χ^2(2) = 5.872;
  - RESET: F(1,37) = 0.154;
  - Hetero: F(27,10) = 0.308.
- Equation (5) in source (preserve coefficients and structure exactly as given):
  - (5) [full ECM representation with coefficients and lags as presented in source; ordinary equation standard errors in parentheses].

### Model’s properties — short- and long-run findings
- Error-correction terms are highly statistically significant, establishing a long-run relationship among real money, real output, RMB and foreign currency deposit interest rates, and inflation.
- Adjustment to equilibrium via the error correction term is slow.
- Short-run influences on growth in real money demand:
  - previous quarter’s real GDP growth: positive effect;
  - RMB and foreign currency deposit rates: very small coefficients (money demand less sensitive to interest rates);
  - inflation and its lags: mixed impacts; current inflation has a significantly negative effect;
  - changes in exchange rates do not enter the final model directly, but greater exchange rate flexibility since 2005 (t_exD_) induces more money demand;
  - changes in stock prices (it s−Δ) and Asian financial crisis dummy (t_crD_) are statistically insignificant.
- Long-run static money demand function from ECM (equation (6) in source):
  - (6) pm− = 0.742 y − 0.082 Rf − 0.481 pΔ (source presents as )6()4(81.2082.0742.0)(pRypm fs Δ⋅−−=− — preserve numeric values and ordering as in source).
  - Interpretation: real money demand depends positively on output and negatively on foreign deposit interest rate and the inflation rate.
  - Notable: U.S. dollar deposit interest rate (Rf) enters the long-run function rather than RMB interest rate; coefficient is very small. Ceilings on RMB deposit rates may reduce their effectiveness in influencing money holdings.
- Dynamic equilibrium solution when money and output grow at same rate (pm−Δ = yΔ ≡ g) (equation (7) in source):
  - (7) pm− = 1.778 g − 0.742 Rf − 0.082 y (source presents as )7()4(778.1)4(81.2082.0742.0()(gpRypm fd ⋅−Δ⋅−−=− — preserve numeric presentation).

### Statistical assessment and implications
- Single-equation ECM estimates (equation (6)) are numerically close to system cointegrating vector estimates (equation (3)) and single-equation ADL long-run estimates (equation (4)), supporting robustness of the long-run money demand relation across specifications.
- Slow adjustment coefficient for money suggests limited availability of alternative assets to M2 and a generally repressed financial system may underlie slower response of money holdings to disequilibria.

*IMF Working Paper — conclusions (conclusions. II–III from provided content).*

### Appendix III, including actual and fitted values and residual and recursive analyses. In

### Appendix III, including actual and fitted values and residual and recursive analyses. In

### Major findings and conclusion
- The estimated model of money demand appears to have sensible statistical properties over the period 1994Q1–2008Q1, suggesting its empirical constancy holds in the face of interest rate liberalization, exchange rate reforms, and capital market development.
- A stable broad money demand function exists when taking proper account of asset substitution and using appropriate econometric techniques.
- Strong evidence supports a stable long-run relationship between real money and real GDP, with an estimated income elasticity of less than unity.
- Current inflation has a significantly negative impact on the money demand.
- The impact of RMB and foreign deposit interest rates on money demand are relatively small, possibly reflecting that some caps on deposit rates still exist.
- Expectations of an RMB appreciation since 2005 appear to induce slightly more money demand in the model.
- Stock prices do not enter the short- and long-run models, reflecting the underdevelopment of capital markets and strong incentives to hold money for cautionary purposes during China’s transition.
- Fundamental changes in China’s financial system (further interest rate liberalization, movement to a more flexible exchange rate regime, development of capital markets, greater availability of alternative assets, liberalization of capital flows, and efficiency gains in the financial system) are likely to alter the structure of the money demand function over time and complicate monetary policy conduct.

### Data definitions and sample
- Quarterly data for the period 1994Q1–2008Q1. Series are not seasonally adjusted; seasonality is captured by seasonal dummies in regressions.
- Series used (name, description, unit, source):
  - Money aggregate (M): Money supply M2, nominal — RMB, billions — CEIC
  - Price (P): Consumer price index, end-of-period — Index — WEO (IMF)
  - Real output (Y): GDP at constant prices — RMB, billions — WEO (IMF)
  - RMB deposit interest rate (dR): One-year household saving rate for RMB, net of withholding interest tax — Percent — IFS
  - USD deposit interest rate (fR): One-year time deposit rate for USD, net of withholding interest tax — Percent — IFS (IMF); PBC; Bank of China
  - Stock prices (S): Shanghai Stock Exchange Composite Index — Index — CEIC
  - Exchange rate (E): Nominal exchange rate RMB per USD — IFS (IMF)
- Notes: Interest earned on savings deposits taxed at 20 percent effective November 1, 1999; decreased to 5 percent effective August 15, 2007.
- All empirical results obtained using GiveWin 2.20, PcGive 10.3, and PcGets 1.02.

### Actual and fitted values (Figure 7)
- Graphical analysis of estimated equation (5):
  - Panels (a) and (b) show time-series and cross-sectional plots of actual and fitted values for the whole sample.
  - Panel (c) shows residuals scaled by ∧σ, with values outside the ±2 band suggesting outliers.
  - Panel (d) shows squared residuals, also indicating major outliers.
- Possible explanation for outliers around 2001:
  - Starting in 2001, the PBC began incorporating clients’ deposits in security companies into M2.
  - Since 2002, the PBC made other revisions to monetary and financial data in line with the IMF’s Monetary and Financial Statistics Manual (2000).

### Residual analysis (Figure 8)
- Correlelogram (Panel (a)): autocorrelations (ACF) and partial autocorrelations (PACF) plotted with approximate 95 percent confidence intervals; most autocorrelations are close to zero, consistent with white-noise residuals.
- Spectral density (Panel (b)): plotted over [0, 1] (PcGets scales [0, π] reported as [0, 1]); a white-noise series has a ‘flat’ spectrum; residual autocorrelation not apparent.
- Histogram with non-parametric interpolated density and matching normal distribution (Panel (c)).
- QQ plot (Panel (d)): transformed cumulative distribution of sample residuals; departure from the normal (straight) line in the upper tail consistent with presence of outliers.

### Unrestricted error-correction representation (Appendix II) — selected diagnostics
- Dependent variable: t pm)(−Δ.
- Sample for reported regression: T = 52 [1995Q2–2008Q1].
- Model statistics:
  - 2 R = 0.882
  - ∧σ = 0.947
  - DW = 2.45
  - AR: F(2,10) = 1.301
  - ARCH: F(2,8) = 0.093
  - Normality: χ2(2) = 2.317
  - RESET: F(1,11) = 0.263
- Reported coefficient examples (lags 0–3) and standard errors are shown in the appendix table (values preserved in source). Example entries:
  - it pm −−Δ)( lag 0 coefficient = -1.000 (-)
  - it p −Δ2 lag 0 coefficient = -1.081 (0.333)
  - ti S seasonal dummy reported with coefficients and standard errors
- The dependent variable and variable labeling conventions are as in the appendix note.

### Recursive analysis and parameter constancy (Figures 9–11)
- Recursive least squares and sequences of test statistics used to investigate parameter constancy.
- Figure 9 (recursive estimates): most coefficients appear constant, but become significantly so only after 2002. The “flat bands” up to 1998Q3 show the initialization period.
- Figure 10 (t-values): t-values for coefficients almost all gradually diverge, as expected with relevant regressors.
- Figure 11 (other RLS constancy statistics):
  - Panel (a): residual sum of squares (RSS) of each observation — standard error increases around 2000, after which bands are relatively constant.
  - Panel (b): one-step residuals plotted with ±2 standard error bands — residuals outside bands indicate outliers or changes in standard error.
  - Panel (c): break-point Chow test (forecast horizon decreasing left to right).
  - Panel (d): Chow test p-value plotted with 5 percent critical value as a straight line.

### Ex post forecasts and constancy assessment (Figure 12)
- Equation (5) re-estimated through 2006Q2 and used to forecast over the last two years.
- Figure 12 plots actual and forecast values of )(pm−Δ from 2006(3) to 2010(2).
- The model tracks recent performance relatively well; forecasts plotted with ±2*SE bands.

*Source: Appendix III, statistical properties, residual and recursive analyses, and related appendices in the supplied IMF PDF content.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09131.pdf_