## 7. Velocity of Business Quasi-Money

## Source details

**Canonical URL:** [7. Velocity of Business Quasi-Money](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0789.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0789.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0789.pdf.json)

---

### Introduction: motivation and main argument
- Broad money holdings became substantially susceptible to financial market fluctuations since the early 1990s.
- Real balances growth:
  - About 1 percent per year in 1987–1996.
  - About 5 percent per year in 1997–2005.
- Hypothesis: broad money holdings are part of investors’ overall portfolio and are sensitive to financial market risk; after controlling for stock and bond market risk measures, money demand recovers stability.
- Structural change: household-to-business broad-money holdings ratio fell from approximately $10 to $1 in 1970 to about $3 to $1 by 2005; business holdings grew rapidly and became more risk-sensitive.

### Data: risk, money aggregates, opportunity cost, and income
- Stock-market illiquidity (Amihud, 2002):
  - ILLIQ for stock j in month t: average of |daily return| / daily turnover.
  - Aggregate illiquidity: cross-sectional average of j_t ILLIQ over eligible NYSE/AMEX stocks (sample: CRSP daily data, November 1962–December 2005).
  - Normalized illiquidity: illiquidity_t = ILLIQ_t × MARKETCAP_{t−24}; Liquidity Risk_t = 8-quarter moving average of illiquidity_t.
  - Liquidity Risk standard deviation: above 42 percent.
  - ADF (trend, 7 lags) for Liquidity Risk: ADF = –1.84 (p-value = 0.68).
- Bond-market default risk:
  - Default Risk_t = 1⋅log(1 + i^{BAA}_t) − 1⋅log(1 + i^{AAA}_t).
  - Default Risk: mean about 130 basis points, standard deviation about 30 basis points.
  - ADF (trend, 0 lags) for Default Risk: ADF = –3.10 (p-value = 0.10).
- Monetary aggregates:
  - M2PF = M2 + Institutional Money Market Mutual Funds (IMMMF).
  - M1RS = M1 + Retail Sweeps.
  - Quasi-money QM = M2PF − M1RS.
- Velocity: ln(M_t / P_t / GDP_t); QM velocity responsible for most post-1990 monetary instability; velocity trough in 2003: more than 20 percent below early 1990s level.
- Opportunity cost: oc_t = log(1 + i^{3 MoTBill}_t) − log(1 + OwnRate_{t}).
- Selected ADF unit-root evidence (tests include constant and trend):
  - M2PF (real balances): ADF = –2.10 (7 lags), p-value = 0.54.
  - Opportunity cost for M2PF: ADF = –2.95 (2 lags), p-value = 0.15.
  - Real GDP (ln GDP_t / P_t): ADF = –0.77 (1 lag), p-value = 0.97.

### Empirical approach: traditional vs. financial risk models
- Traditional long-run money-demand specification (semi-log):
  - ln(M_t / P_t / GDP_t) = β0 + β1 ln(GDP_t / P_t) + β2 oc_t + ω_t.
  - Prior broad money semi-elasticity estimates roughly –2 to –7 (some outliers as large as –12.62).
- Financial risk–augmented specification:
  - ln(M_t / P_t / GDP_t) = β0 + β1 ln(GDP_t / P_t) + β2 oc_t + β3 DefaultRisk_t + β4 LiquidityRisk_t + ω_t.
  - β3 and β4 expected positive.
- Estimation methods:
  - Johansen maximum-likelihood VAR cointegration tests and DOLS with Newey-West SEs.
  - Leads/lags in DOLS chosen by AIC (max 4); VAR lags by Schwartz (max 5).

### Key empirical findings from financial risk models
- Including Default Risk_t and Liquidity Risk_t yields stronger cointegration evidence and income elasticity near unity:
  - Johansen and DOLS cointegration tests reject no cointegrating vector at 5% (and sometimes 1%) for M2PF, M2, M2M, and MZM.
  - Example DOLS (1970:Q1–2005:Q4):
    - M2PF: income elasticity = 0.943** (0.027); oc = –5.217** (0.624); Default Risk = 16.493** (2.253); Liquidity Risk = 0.072** (0.018). Std. dev. of coint vector: 0.068.
    - M2: income elasticity = 0.788** (0.013); oc = –5.558** (0.519); Default Risk = 14.013** (1.625); Liquidity Risk = 0.017 (0.01). Std. dev.: 0.061.
- DOLS with break trend t_{9094} for M2PF (traditional model) indicates a permanent drop in money holdings in early 1990s: income elasticity ≈ 1.013** (0.043); oc = –4.044** (0.888); coefficient on t_{9094} = –0.068* (0.034).
- Financial risk variables reduce EC-term volatility after 1990:
  - For M2PF over 1983–2005, EC-term std. dev.:
    - Financial risk model: less than 4 percent.
    - Traditional model: about 6 percent.
  - For 1970–1982, financial risk model EC std. dev. > 10 percent; traditional model EC std. dev. < 5 percent.
- Model fit:
  - Traditional model overpredicts money demand by 5–10 percent in early–mid 1990s; underpredicts in late 1990s.
  - Financial risk model better predicts the sharp rise in money demand during 1998–2003 but underpredicts 2004–2005.
- Robustness:
  - Excluding one risk variable reduces explanatory power.
  - Stock Premium_t (5⋅ln(1 + DY_t) − ln(1 + GS5_t)) yields positive and significant coefficient at 1%.
  - Corporate Spread and Implied Volatility alternatives examined; Implied Volatility not significant in 1986:Q1–2005:Q4.

### Financial risk measures and cointegrating vectors
- EC term similar whether Liquidity Risk or Stock Premium used: standard deviation slightly smaller with Stock Premium (0.063 versus 0.067).
- Table 4 DOLS examples (1970:Q1–2005:Q4):
  - Liquidity Risk = 0.052* (0.023) in one specification.
  - Stock Premium = 2.562** (0.666) in one specification.
  - Corporate Spread = 6.090** (2.204) in one specification.
  - Implied Volatility = –0.001 (0.001) (not significant).
- Carpenter and Lange VXO (1986:Q1–2005:Q4) not statistically significant for money demand in that sample.

### Out-of-sample forecasts using the long-run relationship
- Imposed unitary income elasticity (β1 = 1) for financial risk velocity model; sample results (selected):
  - Sample 1970:Q1–2005:Q4, Johansen (A): oc = –6.526** (1.415); Default Risk = 22.899** (3.856); Liquidity Risk = 0.116** (0.033); Std. Dev. = 0.095.
  - DOLS (B): oc = –4.004** (0.724); Default Risk = 17.190** (2.502); Liquidity Risk = 0.066** (0.015); Std. Dev. = 0.065.
  - Subsample 1970:Q1–1998:Q3, Johansen (E financial risk): oc = –6.755** (1.536); Default Risk = 23.051** (4.349); Liquidity Risk = 0.136** (0.042); Std. Dev. = 0.106.
  - Subsample 1970:Q1–1989:Q4, Johansen (G): oc = –2.993** (0.321); Default Risk = 1.660 (1.086); Liquidity Risk = 0.035 (0.008); Std. Dev. = 0.030.
- Forecast performance:
  - Traditional model with t9094 underpredicts money demand by about 15 percent after 2001 (out-of-sample).
  - Financial risk model underpredicts only after 2003 and by much less.

### Time variation in financial risk sensitivity
- Cointegrating vectors with interaction dummies since 1990 show:
  - Interaction coefficients positive and strongly significant for Johansen and DOLS.
  - Standard deviation of cointegrating vector much smaller than time-invariant specifications.
- Pre-1990 financial risk model (1970:Q1–1989:Q4):
  - Liquidity Risk coefficient smaller but sometimes significant; Default Risk essentially zero and insignificant.

### Error Correction Models (ECM) and forecasts
- ECM general form uses lagged EC term from DOLS; includes dummy D03Q4 = 1 at 2003:Q4.
- Estimation and forecast samples: 1993:Q1–2005:Q4 (in-sample) and 1993:Q1–2002:Q4 for out-of-sample (2003:Q1–2005:Q4).
- Key ECM results (Table 6):
  - Panel A. Financial Risk Model (1993:Q1–2005:Q4)
    - Lagged Δ ln(M2PF/P) persistence ≈ 0.363.
    - EC term coefficient = –0.149 (significant at 1%): about 15 percent of deviations corrected per quarter.
    - 2 R = 0.831; SE = 0.436%; DW = 2.03.
    - Within-sample dynamic simulation: ME = –0.0002, RMSE = 0.008.
  - Panel B. Traditional Model (1993:Q1–2005:Q4)
    - EC term = –0.068 (significant at 5%).
    - 2 R = 0.802; SE = 0.472%; DW = 2.06.
    - Within-sample dynamic simulation: ME = –0.003, RMSE = 0.014.
  - Out-of-sample (2003:Q1–2005:Q4) based on 1993:Q1–2002:Q4:
    - Financial risk model: ME = –0.008 (–0.8 percent), RMSE = 0.022 (2.2 percent).
    - Traditional model: ME = 0.020 (2.0 percent), RMSE = 0.023 (2.3 percent).
- Diagnostics:
  - Financial risk ECM passes serial correlation, ARCH, and normality tests; traditional ECM fails normality at 5%.
  - Both marginally pass Ramsey RESET at 5%.
  - CUSUM and CUSUM squares tests do not reject structural stability at 5%.
  - Hansen (1997) structural-change tests: “Sup,” “Exp,” “Ave” statistics do not reject no structural change at 10%.

### Sectoral money demand: households vs businesses
- Construction:
  - Household money MHt and business money MBt from Flow of Funds categories: (i) currency and checkable deposits; (ii) savings and time deposits; (iii) money market mutual funds.
  - Own rates for categories derived from user cost benchmark.
- Stylized facts:
  - Business money grew faster in the 1990s than household money.
  - Business money velocity sharply decreases in last ten years; household velocity increases secularly beginning in 1990.
  - MB/(MB+MH) increased to about 23 percent in 2004 from 10–12 percent in 1970s–1980s.
  - QMB/MB increased from 10 percent in 1970 to more than 70 percent in recent years.
- Household money demand:
  - Traditional model with t9094 yields stable demand after accounting for decline in trading costs; DOLS Std. Dev. of cointegrating vector < 0.03.
  - Financial risk model for household shows inconsistent signs (Default Risk negative; Liquidity Risk large positive), and larger deviations than traditional model.
- Business money demand:
  - Traditional model performs poorly for business holdings.
  - Financial risk model provides better fit:
    - Example DOLS H: income elasticity = 1.531** (0.061); Liquidity Risk = 20.090** (6.271); oc = 0.223** (0.052); Std. Dev. = 0.138.
  - Conclusion: financial risk variables help explain long-term fluctuations in business money holdings; traditional model does not fit well.

### Business holdings of quasi-money (QMB)
- Trends:
  - QMB velocity fell relatively linearly over 1962–1997 with large increases late 1960s–early 1970s.
  - 1998–2002: business money holdings increased by about 100% before leveling off.
- Financial risk model estimates for ln(QMB/P) (selected):
  - Sample 1970–2005, DOLS B: income elasticity = 2.863** (0.148); Liquidity Risk = 64.696** (10.929); oc = 0.231** (0.07); Std. Dev. = 0.210.
  - Sample 1970–1995, DOLS D: income elasticity = 2.522** (0.284); Liquidity Risk = 56.370** (12.265); Std. Dev. = 0.216.
  - Sample 1970–1989, DOLS F: income elasticity = 2.820** (0.314); Liquidity Risk = 40.938** (11.065); Std. Dev. = 0.214.
- Findings:
  - Income elasticity often significantly greater than unity.
  - Interest semi-elasticity unstable and often insignificant.
  - Liquidity Risk coefficient positive and significant for whole period; surge in business quasi-money during 1998–2002 coincides with substantial increases in liquidity risk.

### Conclusions and policy implications
- Long-term fluctuations in financial market risk (stock and bond markets) explain persistent fluctuations in broad money demand over the last 15 years: money holdings increase with financial-market risk.
- Sensitivity of broad money demand to financial market risk became relevant over the last 20 years (post-financial deregulation).
- Two factors likely increased sensitivity:
  - Decline in cost of investing in stocks and bonds for ordinary savers and increased mutual-fund holdings.
  - Sectoral shift: household holdings declined while business quasi-money holdings increased and became risk-sensitive.
- Implications for policy:
  - Accounting for evolution of financial markets helps regain stability of broad money demand.
  - Policymakers should monitor persistent shifts in financial risk for implications on future inflation if money demand retains informational value for inflation forecasting.
- Suggestions for future research:
  - Analyze interactions of money holdings with financial markets and innovations, and their effects on economic activity.
  - Develop analytical links between money demand and financial risk, accounting for transaction costs and portfolio substitution.
  - Seek better surrogates than broken time trends or dummies for the evolving financial-development environment.

*Source: IMF Working Paper chapter “7. Velocity of Business Quasi-Money” (excerpted content).*

### References..............................................................................................................

### _wp0789 - References

### Tables
- 1. Augmented Dickey-Fuller Tests ............................................................................................9
- 2. Cointegrating Vectors: Traditional Money Demand Model ................................................11
- 3. Cointegrating Vectors: Financial Risk Models of Money Demand.....................................13
- 4. Cointegrating Vectors: Variations of Financial Risk Models of Money Demand...............16
- 5. Sub-Period Cointegrating Vectors: Variations of Financial Risk Models of  
    Money Demand....................................................................................................................18
- 6. Error Correction Models of Money Demand with Financial Risk ......................................21
- 7. Cointegrating Vectors for Sectoral Money Holdings ..........................................................26
- 8. Cointegrating Vectors for Business Quai-Money Holdings ................................................28

### Figures
- 1. Measures of Illiquidity, Liquidity Risk, and Default Risk.....................................................6
- 2. Movements in the Velocity of Money ...................................................................................8
- 3. Deviations from the Whole-Period Contegrating Vectors...................................................14
- 4. Deviations from the Sub-Period Contegrating Vectors .......................................................19
- 5. Dynamic Forecast of Money Demand using ECM..............................................................22
- 6. Money and Velocity in Household and Business Sectors............................................24

*Source: _wp0789 - References*

### 7. Velocity of Business Quasi-Money ....................................................................................

### 7. Velocity of Business Quasi-Money

### Introduction: motivation and main argument
- Broad money holdings became substantially susceptible to financial market fluctuations since the early 1990s.
- Real balances growth:
  - About 1 percent per year in 1987–1996.
  - About 5 percent per year in 1997–2005.
- Paper hypothesis: broad money holdings are part of investors’ overall portfolio and are therefore sensitive to financial market risk. After controlling for stock and bond market risk measures, money demand recovers stability.
- Policy relevance: stability of money demand is important for monetary-policy frameworks that target monetary aggregates; instability undermines ability to predict effects of money-supply changes on interest rates, income, and prices.
- Observed structural change: from 1970 to 2005 the household-to-business broad-money holdings ratio fell from approximately $10 to $1 to about $3 to $1. Conditional on a permanent level drop in money demand in the early 1990s, household holdings remained stable while business holdings grew rapidly and became more sensitive to financial market risk.

### Data: risk, money aggregates, opportunity cost, and income
- Stock market illiquidity measure (Amihud, 2002):
  - ILLIQ for stock j in month t: average of |daily return| / daily turnover.
  - Aggregate illiquidity: cross-sectional average of j_t ILLIQ over eligible NYSE/AMEX common stocks with at least 10 observations and prices between 5 and 1000 dollars.
  - Sample: CRSP daily data, November 1962–December 2005.
- Normalized illiquidity series:
  - illiquidity_t = ILLIQ_t × MARKETCAP_{t−24} (natural log specified as ln(ILLIQ × MARKETCAP_{t−24})).
  - Liquidity Risk_t = 8-quarter moving average of illiquidity_t.
  - Liquidity Risk standard deviation: above 42 percent.
  - Augmented Dickey-Fuller (ADF) test for Liquidity Risk (trend, 7 lags): ADF = –1.84 (p-value = 0.68) — fails to reject unit root.
- Bond-market default risk:
  - Default Risk_t = 1⋅log(1 + i^{BAA}_t) − 1⋅log(1 + i^{AAA}_t) (spread between BAA and AAA yields in logs).
  - Default Risk: mean about 130 basis points, standard deviation about 30 basis points.
  - ADF test with trend (0 lags): ADF = –3.10 (p-value = 0.10) — fails to reject unit root at 10% level.
- Monetary aggregates and definitions:
  - M2PF = M2 + Institutional Money Market Mutual Funds (IMMMF). Includes small time deposits; differs from MZM which treats large money market funds as checkable.
  - Narrow money M1RS = M1 + Retail Sweeps.
  - Quasi-money QM = M2PF − M1RS.
- Velocity and recent movements:
  - Income velocity defined as ln(M_t / P_t / GDP_t).
  - Velocity of broad money (M2PF and M2) rose persistently in first half of 1990s and fell sharply for 2000–2003.
  - Quasi-money velocity (QM) responsible for most post-1990 monetary instability; M1RS velocity remained relatively stable over last 15 years.
  - Velocity trough in 2003: more than 20 percent below early 1990s level.
- Opportunity cost of holding money:
  - oc_t = log(1 + i^{3 MoTBill}_t) − log(1 + OwnRate_{t}).
  - Own Rate on aggregates constructed as weighted averages of component user costs; FRED reports own rates for M2, M2M, and MZM.
- Unit-root evidence (selected ADF results, tests include constant and trend; lag choice by Modified Schwarz criterion):
  - M2PF (real balances): ADF = –2.10 (7 lags), p-value = 0.54 — unit root not rejected.
  - Opportunity cost for M2PF: ADF = –2.95 (2 lags), p-value = 0.15.
  - Real GDP (ln GDP_t / P_t): ADF = –0.77 (1 lag), p-value = 0.97.

### Empirical approach: traditional vs. financial risk models
- Traditional long-run money-demand specification (semi-log):
  - ln(M_t / P_t / GDP_t) = β0 + β1 ln(GDP_t / P_t) + β2 oc_t + ω_t.
  - β1: income elasticity (transaction/precautionary motives imply < 1.0; theory sometimes suggests ≈ 1.0).
  - β2: interest semi-elasticity (negative); prior estimates for broad money semi-elasticity in range roughly –2 to –7 (some outliers as large as –12.62).
- Estimation methods:
  - Johansen maximum-likelihood (VAR) cointegration tests and DOLS (Dynamic OLS) with Newey-West standard errors.
  - Leads and lags in DOLS chosen by AIC (max 4); VAR lags by Schwartz criterion (max 5).
- Traditional model cointegration results (sample 1970:Q1–2005:Q4):
  - Johansen trace tests: unable to reject no cointegrating vector at 10% level for monetary aggregates.
  - DOLS results (selected):
    - For M2PF (DOLS): income elasticity = 0.907** (std. dev. 0.032); oc coefficient = –4.972** (1.136). Std. dev. of coint vector: 0.056.
    - For M2 (DOLS): income elasticity = 0.747** (0.023); oc = –4.583** (0.836). Std. dev. of coint vector: 0.045.
  - Including a break linear trend t_{9094} (zero before 1990, linear to 1 in 1995:Q1) in DOLS for M2PF: income elasticity ≈ 1.013** (0.043); oc = –4.044** (0.888); coefficient on t_{9094} = –0.068* (0.034) — consistent with a permanent drop in money holdings early 1990s.
- Financial risk–augmented model:
  - ln(M_t / P_t / GDP_t) = β0 + β1 ln(GDP_t / P_t) + β2 oc_t + β3 DefaultRisk_t + β4 LiquidityRisk_t + ω_t.
  - β3 and β4 expected positive (money substitutes for riskier/less-liquid assets).

### Key empirical findings from financial risk models
- Inclusion of Default Risk_t and Liquidity Risk_t yields stronger cointegration evidence and income elasticity near unity:
  - Johansen and DOLS cointegration tests reject no cointegrating vector at 5% (and in some cases 1%) for M2PF, M2, M2M, and MZM.
  - Typical estimated long-run coefficients (example DOLS estimates, sample 1970:Q1–2005:Q4):
    - M2PF (DOLS): income elasticity = 0.943** (0.027); oc = –5.217** (0.624); Default Risk = 16.493** (2.253); Liquidity Risk = 0.072** (0.018). Std. dev. of coint vector: 0.068.
    - M2 (DOLS): income elasticity = 0.788** (0.013); oc = –5.558** (0.519); Default Risk = 14.013** (1.625); Liquidity Risk = 0.017 (0.01). Std. dev.: 0.061.
    - M2M and MZM show similar patterns with larger Johansen point estimates for Default Risk.
  - When adding a trend term in DOLS for M2PF with risk variables: income elasticity becomes 1.749** (0.342); oc = –4.914** (0.718); Default Risk = 16.661** (2.171); Liquidity Risk = 0.071** (0.019); trend = –0.006* (0.003). Given sensitivity, authors concentrate on specifications without deterministic trend.
- Role of financial risk variables in explaining residual stationarity:
  - Inclusion of financial risk variables substantially reduces the standard deviation of the error-correction (EC) term after 1990.
  - For M2PF (DOLS-based EC term comparisons depicted in text):
    - Over 1983–2005, standard deviation of EC term:
      - Financial risk model: less than 4 percent.
      - Traditional model: about 6 percent.
    - For 1970–1982:
      - Financial risk model EC std. dev.: more than 10 percent.
      - Traditional model EC std. dev.: less than 5 percent.
- Time-series behavior and model fit:
  - Traditional model overpredicts money demand by 5–10 percent in early–mid 1990s; underpredicts in late 1990s.
  - Financial risk model reduces error magnitudes and persistence especially for 1998–2003, where it accurately predicts the sharp rise in money demand.
  - Both models underpredict money demand in 2004–2005 as financial market risk fell but money demand remained elevated.
  - Financial risk model fits less well during era of Regulation Q (1970s); large swings in risk measures then did not translate into comparable money-demand fluctuations.
- Alternative specifications and robustness:
  - Excluding one of the two financial risk variables reduces predictive power:
    - With β3 = 0 (no Default Risk), Default Risk coefficient in alternative models remains positive and significant when included.
    - With β4 = 0 (no Liquidity Risk), Liquidity Risk coefficient is significant when included alone.
  - Substitute stock-premium for Liquidity Risk:
    - Stock Premium_t = 5⋅ln(1 + DY_t) − ln(1 + GS5_t) (500 DY on S&P 500 dividend yield and 5GS is 5-year Treasury yield in the paper’s formulation).
    - Estimated coefficient on Stock Premium is positive and significant at 1% — suggesting relative risk effect (higher expected risk of stock returns raising money demand) dominates relative return effect.
  - Alternative bond-market measures:
    - Corporate Spread_t = ln(1 + yield_{AAA,t}) − ln(1 + GS5_t) used as proxy more related to liquidity than default risk; results summarized as part of robustness checks (detailed coefficients given in regression tables).

### Interpretation and sectoral dynamics
- Rising sensitivity of aggregate money demand to financial market risk is associated with growing business-sector money holdings:
  - Business sector broad-money holdings increased over time; business holdings grew faster and became more sensitive to financial market risk than household holdings.
- Mechanism:
  - Stock market illiquidity (and related liquidity risk measures) makes investors pay higher prices for more liquid assets—raising demand for monetary assets.
  - Default risk in bond markets shifts portfolio demand toward safer monetary assets.
- Empirical implication: controlling for financial market risk reconciles apparent instability of money demand in the 1990s and late 1990s reversal.

*Source: IMF Working Paper chapter “7. Velocity of Business Quasi-Money” (excerpted content)._*

### 0.042 when both variables are included.

### _wp0789 - 0.042 when both variables are included.

### Financial risk measures and cointegrating vectors
- Over the course of the sample period, the EC term for the financial risk model is very similar regardless of whether Liquidity Risk or Stock Premium is used: it has a slightly smaller standard deviation with the use of Stock Premium (0.063 versus 0.067), which leads to less overprediction of money demand for recent years.
- Table 4 (cointegrating vectors, DOLS estimator; regressions A–D: 1970:Q1–2005:Q4, regression E: 1986:Q1–2005:Q4):
  - Liquidity Risk coefficient in one specification: 0.052* (0.023).
  - Stock Premium coefficient in one specification: 2.562** (0.666).
  - Corporate Spread coefficient in one specification: 6.090** (2.204).
  - Implied Volatility coefficient reported as –0.001 (0.001) (not significant).
  - Johansen trace statistics and leg lengths reported for each regression; significance indicated by **, *, † at 1%, 5%, 10% respectively.
- Carpenter and Lange (2003) VXO volatility measure (S&P 100 Black-Scholes implied volatility) for 1986:Q1–2005:Q4 (column E): not statistically significantly associated with money demand in this sample.

### Out-of-sample forecasts using the long-run relationship
- Imposed unitary income elasticity (β1 = 1) for the financial risk velocity model specification:
  - ln(M2PF/P) = ω + β0 oc + β2 Default Risk + β3 Liquidity Risk + β4 ... (equation (4) with unitary income elasticity).
- Cointegration results (Table 5) for various samples:
  - Sample: 1970:Q1–2005:Q4
    - A. Johansen: oc = –6.526** (1.415); Default Risk = 22.899** (3.856); Liquidity Risk = 0.116** (0.033); Trace Statistic = 63.97** (49.09); Std. Dev. of Coint. Vector = 0.095.
    - B. DOLS: oc = –4.004** (0.724); Default Risk = 17.190** (2.502); Liquidity Risk = 0.066** (0.015); Std. Dev. = 0.065.
  - Sample: 1970:Q1–1998:Q3 (traditional and financial risk variants)
    - C. Johansen (traditional): oc = –1.881** (0.404); GDP elasticity ~ near unity; Trace = 24.07** (15.55); Std. Dev. = 0.055.
    - E. Johansen (financial risk): oc = –6.755** (1.536); Default Risk = 23.051** (4.349); Liquidity Risk = 0.136** (0.042); Trace = 57.27** (49.57); Std. Dev. = 0.106.
  - Sample: 1970:Q1–1989:Q4 (financial risk)
    - G. Johansen: oc = –2.993** (0.321); Default Risk = 1.660 (1.086); Liquidity Risk = 0.035 (0.008); Trace = 69.87** (50.37); Std. Dev. = 0.030.
- Forecast performance (discussion and Figure 4):
  - Traditional velocity model without dummy t9094 misses early–mid-1990s drop in money demand.
  - Traditional model with t9094 and financial risk model both predict the 1990s drop reasonably in-sample.
  - Out-of-sample after Q3 1998: traditional model with t9094 underpredicts money demand by about 15 percent after 2001; financial risk model underpredicts money demand only after 2003 and by much less.

### Time variation in financial risk sensitivity
- Estimating cointegrating vectors with interactions of financial risk terms with dummy equal to 1 since 1990 (rows I and J, Table 5) yields:
  - Coefficients on financial risk factors interacting with dummies are positive and strongly significant for both Johansen and DOLS estimators.
  - With this specification, the standard deviation of the cointegrating vector is substantially smaller than traditional models or financial risk models that assume time-invariant effects.
- Pre-1990 financial risk model (sample 1970:Q1–1989:Q4, rows G and H):
  - Liquidity Risk coefficient smaller than full sample but still significant at 1% level in some estimates; Default Risk coefficient essentially zero and insignificant.
  - Rejection of no cointegration is not surprising because traditional model also rejects that hypothesis for pre-1990.

### Error Correction Models (ECM) and forecasts (Table 6 & Figure 5)
- General ECM form (equation (5)), with lagged EC term from DOLS; a dummy D03Q4 equals 1 at 2003:Q4 to control for an unprecedented contraction (~7 percent) during 2003:Q4.
- Estimation period choices: regressions for 1993:Q1–2005:Q4 and out-of-sample forecasts based on 1993:Q1–2002:Q4.
- ECM goodness-of-fit and key coefficients (Table 6):
  - Panel A. Financial Risk Model (sample 1993:Q1–2005:Q4)
    - Coefficient on lagged Δ ln(M2PF/P): 0.363 (showing persistence).
    - Coefficient on Δoc (opportunity cost): –1.9110.021? (exact formatting from source); coefficient on ΔDefault Risk and ΔLiquidity Risk positive and significant at 5% level.
    - EC term coefficient = –0.149 (significant at 1%), implying about 15 percent of deviations corrected in subsequent period.
    - 2 R = 0.831; SE = 0.436%; DW = 2.03.
    - Within-sample dynamic simulation (1993:Q1–2005:Q4): ME = –0.0002, RMSE = 0.008.
  - Panel B. Traditional Model (1993:Q1–2005:Q4)
    - Lagged persistence coefficient up to 0.530 in specification; EC term = –0.068 (significant at 5%).
    - 2 R = 0.802; SE = 0.472%; DW = 2.06.
    - Within-sample dynamic simulation: ME = –0.003, RMSE = 0.014.
  - Panels C and D: analogous ECMs estimated for 1993:Q1–2002:Q4 with out-of-sample forecasts for 2003:Q1–2005:Q4.
    - C. Financial Risk Model out-of-sample (2003:Q1–2005:Q4): ME = –0.008, RMSE = 0.022.
    - D. Traditional Model out-of-sample: ME = 0.020, RMSE = 0.023.
- Diagnostic tests:
  - Financial risk ECM passes serial correlation, ARCH, and normality tests; traditional ECM fails normality at 5% level.
  - Both models marginally pass Ramsey RESET at 5% level.
  - CUSUM and CUSUM squares tests do not reject structural stability at 5% for both models.
  - Hansen (1997) structural-change tests: none of “Sup,” “Exp,” “Ave” statistics reject hypothesis of no structural change at 10%.
- Forecast summary (Figure 5):
  - Within-sample dynamic forecasts (1993:Q1–2005:Q4): financial risk model ME = –0.0002, RMSE = 0.008; traditional model ME = –0.003, RMSE = 0.014. Financial risk model outstrips conventional model.
  - Out-of-sample forecasts (2003:Q1–2005:Q4) based on models estimated 1993:Q1–2002:Q4:
    - Financial risk model: ME = –0.8 percent, RMSE = 2.2 percent.
    - Traditional model: ME = 2.0 percent, RMSE = 2.3 percent.
  - Financial risk model somewhat captures the Q4 2003 deceleration (linked to decreases in financial risk), while traditional model does not; since 2004 financial risk model underpredicts money holdings, possibly indicating a buildup of liquidity due to unidentified factors.

### Sectoral money demand: households vs businesses
- Definitions:
  - Household money MHt and business money MBt constructed from Flow of Funds categories: (i) currency and checkable deposits; (ii) savings and time deposits; (iii) money market mutual funds.
  - Own rates for categories CCDt,i, STDt,i, MMMFt,i derived via user cost benchmark approach from Anderson and others (1997).
- Stylized facts (Figure 6):
  - Business money exhibited faster growth in the 1990s than household money (Panel A).
  - Business money velocity sharply decreases in last ten years; household velocity increases secularly beginning in 1990 (Panel B).
  - Fraction of monetary assets held by business, MB/(MB+MH), increases since early 1990s to about 23 percent in 2004; previously between 10 and 12 percent in 1970s–1980s (Panel C).
  - Share of quasi-money in business broad money, QMB/MB, increases from 10 percent in 1970 to more than 70 percent in recent years (Panel D).
- Household money demand (Table 7):
  - Traditional model with t9094 (rows A, B; sample 1970:Q1–2005:Q4):
    - Johansen A: income elasticity 1.080** (0.032); oc = –0.056** (0.011); Trace = 40.18** (32.51); Std. Dev. = 0.162.
    - DOLS B: income elasticity 1.118** (0.025); oc = –1.655** (0.471) ; Liquidity Risk coefficient –0.372** (0.019); Std. Dev. = 0.024.
    - Finding: household money demand becomes stable after accounting for decline in financial trading costs (t9094); small Std. Dev. of cointegrating vector in DOLS (< 0.03).
  - Financial risk model for household (rows C, D):
    - Johansen C: income elasticity 0.850** (0.048); Default Risk = –15.648** (2.031); Liquidity Risk = 30.410** (4.49); oc = –0.185** (0.041); Trace = 89.42** (72.33); Std. Dev. = 0.131.
    - DOLS D: income elasticity 0.813** (0.022); Default Risk = –11.568** (1.155); Liquidity Risk = 25.092** (2.741); oc = –0.171** (0.022); Std. Dev. = 0.104.
    - However, financial risk model appears less valid for household money demand: Liquidity Risk coefficient negative and significant in some specifications and deviations larger than traditional model.
- Business money demand (Table 7 rows E–H):
  - Traditional model (E Johansen, F DOLS) shows no evidence of a sensible cointegrating relation under Johansen; DOLS suggests interest semi-elasticity negative and significant only at 10% (–3.901† (2.050)).
  - Financial risk model (G Johansen, H DOLS) provides:
    - G. Johansen: income elasticity 1.454** (0.158); Default Risk = –14.085** (5.156); Liquidity Risk = 61.242** (14.711); oc coefficient positive 0.387** (0.129); Trace = 77.38** (72.33); Std. Dev. = 0.169.
    - H. DOLS: income elasticity 1.531** (0.061); Default Risk = –2.051 (2.169); Liquidity Risk = 20.090** (6.271); oc = 0.223** (0.052); Std. Dev. = 0.138.
  - Conclusion: financial risk terms help explain long-term fluctuations in business money holdings; traditional model does not fit well.

### Business holdings of quasi-money (Table 8, Figure 7)
- Business quasi-money QMB trends:
  - Velocity of business quasi-money fell relatively linearly over 1962–1997 with large increases in late 1960s–early 1970s; average growth rate of QMB relative to BSO before 1998 > 4% per year.
  - 1998–2002 period: money holdings increased by about 100% before leveling off.
- Estimated financial risk model for ln(QMB/P) (Table 8):
  - Sample 1970–2005:
    - A. Johansen: income elasticity 2.961** (0.184); Default Risk = –12.213* (5.517); Liquidity Risk = 103.897** (14.777); oc = 0.473** (0.107); Trace = 91.82** (72.33); Std. Dev. = 0.286.
    - B. DOLS: income elasticity 2.863** (0.148); Default Risk = –5.430 (4.664); Liquidity Risk = 64.696** (10.929); oc = 0.231** (0.07); Std. Dev. = 0.210.
  - Sample 1970–1995:
    - C. Johansen: income elasticity 1.711** (0.181); Default Risk = 1.933 (3.995); Liquidity Risk = 27.798** (9.805); oc = –0.181* (0.086); Trace = 116.12** (73.35); Std. Dev. = 0.273.
    - D. DOLS: income elasticity 2.522** (0.284); Default Risk = –3.705 (5.068); Liquidity Risk = 56.370** (12.265); Std. Dev. = 0.216.
  - Sample 1970–1989:
    - E. Johansen: income elasticity 0.671† (0.406); Default Risk = –17.338† (11.210); Liquidity Risk = 60.334** (23.337); oc = –0.599** (0.170); Trace = 105.62** (79.97); Std. Dev. = 0.504.
    - F. DOLS: income elasticity 2.820** (0.314); Default Risk = 0.531 (5.874); Liquidity Risk = 40.938** (11.065); oc = 0.217** (0.125); Std. Dev. = 0.214.
- Findings:
  - Income elasticity often significantly greater than unity.
  - Interest semi-elasticity unstable and often insignificant.
  - Default Risk coefficient positive and strongly significant for whole period in many specifications.
  - Liquidity Risk coefficient positive and significant for whole period but mixed (negative signs in some sub-samples), suggesting liquidity risk became an important factor in the recent decade; the surge in business quasi-money demand during 1998–2002 coincides with substantial increases in liquidity risk.

### Conclusions and policy implications
- Long-term fluctuations in financial market risk can explain persistent fluctuations in broad money demand over the last 15 years: money holdings increase with stock and bond market risks.
- The sensitivity of broad money demand to financial market risk became relevant over the last 20 years (post-financial deregulation).
- Two possible factors increasing sensitivity of money demand to financial risk:
  - Decline in cost of investing in stocks and bonds for ordinary savers and increased holdings of bond and stock mutual funds—broader holdings of monetary assets make money holdings more sensitive to market risk.
  - Sectoral shift: household holdings secularly declined due to lower investment costs, while business holdings of quasi-money increased rapidly and are sensitive to financial market risk; the business sector share in broad money rose substantially in last 15 years.
- Implications:
  - Accounting for evolution of financial markets can help regain stability of broad money demand.
  - Policymakers should pay attention to implications of persistent shifts in financial risk for future inflation if money demand retains information value for inflation prediction.
- Suggestions for future research:
  - Examine how money holdings, interacting with financial markets and financial innovations, respond to shocks and affect economic activity.
  - Develop analytical relationships between money demand and financial risk in a shifting financial development environment, accounting for transaction costs and portfolio substitutions (for example, substitutions between money and equity when investors face liquidity risk).
  - Seek better surrogates than broken time trends or time dummies for the shifting environment of financial development.

*Italic: Source — _wp0789 - 0.042 when both variables are included.*

### References

### _wp0789 - References

### Liquidity, Asset Pricing, and Market Microstructure
- Acharya, Viral V., and Lasse Heje Pedersen, 2005, “Asset Pricing with Liquidity Risk,” Journal of Financial Economics, Vol. 77 (August), pp. 375–410.  
- Amihud, Yakov, 2002, “Illiquidity and Stock Returns: Cross-Section and Time-Series Effects,” Journal of Financial Markets, Vol. 5 (January), pp. 31–56.  
- Amihud, Yakov, and Haim Mendelson, 1986, “Asset Pricing and the Bid-Ask Spread,” Journal of Financial Economics, Vol. 17 (December), pp. 223−249.  
- Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2000, “Commonality in Liquidity,” Journal of Financial Economics, Vol. 56 (April), pp. 3–28.  
- Hasbrouck, Joel, 2006, “Trading Costs and Returns for US Equities: Estimating Effective Costs from Daily Data,” Mimeo. New York University.  
- Pastor, Lubos, and Robert F. Stambaugh, 2003, “Liquidity Risk and Expected Stock Returns,” Journal of Political Economy, Vol. 111 (June), pp. 642–685.  
- Sadka, R., 2004, “Liquidity Risk and Asset Pricing,” Mimeo. Northwestern University.  
- Lerner, Josh, and Antoinette Schoar, 2004, “The Illiquidity Puzzle: Theory and Evidence from Private Equity,” Journal of Financial Economics, Vol. 72 (April), pp. 3–40.  
- Choi, Woon Gyu, and David Cook, 2006, “Stock Market Liquidity and the Macroeconomy: Evidence from Japan,” Monetary Policy with Very Low Inflation in the Pacific Rim, NBER East Asia Seminar on Economics, Vol. 15, (edited by) Takatoshi Ito and Andrew Rose, pp. 309–336.  
- Choi, Woon Gyu, and Seonghwan Oh, 2003, “A Money Demand Function with Output Uncertainty, Monetary Uncertainty, and Financial Innovations,” Journal of Money, Credit, and Banking, Vol. 35 (October), pp. 685–709.  

### Money Demand, Monetary Aggregates, and Financial Innovation
- Besci, Zsolt, and Duca, John V., 1994, “Adding Bond Funds to M2 in the P-Star Model of Inflation,” Economics Letters, Vol. 46 (October), pp. 143–147.  
- Carlson, John B., and Benjamin D. Keen, 1996, “MZM: A Monetary Aggregate for the 1990s?” Federal Reserve Bank of Cleveland Economic Review, Vol. 32 (Second Quarter), pp. 15–23.  
- Carlson, John B., Dennis L. Hoffman, Benjamin D. Keen, and Robert H. Rasche, 2000, “Results of a Study of the Stability of Cointegrating Relations Comprised of Broad Monetary Aggregates,” Journal of Monetary Economics, Vol. 46 (October), pp. 345–383.  
- Carlson, John B., and Jeffrey C. Schwarz, 1999, “Effects of Movements in Equities Prices on M2 Demand,” Federal Reserve Bank of Cleveland Economic Review, Vol. 35 (Fourth Quarter), pp. 2–9.  
- Collins, Sean S., and Cheryl L. Edwards, 1994, “An Alternative Monetary Aggregate: M2 Plus Household Holdings of Bond and Equity Mutual Funds,” Federal Reserve Bank of St. Louis Review, Vol.76 (November/December), pp. 7–30.  
- Duca, John V., 2003, “Stock Market Shocks and Broad Money Growth,” Manuscript, Federal Reserve Bank of Dallas.  
- Duca, John V., 2000, “Financial Technology Shocks and the Case of the Missing M2,” Journal of Money, Credit, and Banking, Vol. 32 (November), pp. 820–839.  
- Duca, John V., 1995, “Should Bond Funds Be Included in M2?” Journal of Banking and Finance, Vol. 19 (April), pp. 131–152.  
- Duca, John V., 1994, “Would the Addition of Bond or Equity Funds Make M2 a Better Predictor of Nominal GDP?” Federal Reserve Bank of Dallas Economic Review (Fourth Quarter), pp. 1–13.  
- Duca, John V., 1993, “RTC Activity and the ‘Missing M2’.” Economics Letters, Vol. 41 (n1), pp. 67–71.  
- Duca, John V., 1992, “The Case of the Missing M2,” Federal Reserve Bank of Dallas Economic Review (Second Quarter), pp. 1–19.  
- Orphanides, Athanasios, and Richard D. Porter, 2000, “P* Revisited: Money-Based Inflation Forecasts with a Changing Equilibrium Velocity,” Journal of Economics and Business, Vol. 52 (January-April), pp. 87–100.  
- Orphanides, Athanasios, Brian Reid, and David H. Small, 1994, “The Empirical Properties of a Monetary Aggregate That Adds Bond and Stock Funds to M2,” Federal Reserve Bank of St. Louis Review, pp. 31–52.  
- Leeper, Eric M., and Jennifer E. Roush, 2003, “Putting "M" Back in Monetary Policy,” Journal of Money, Credit, and Banking, Vol. 35 (Part 2, December), pp. 1217–56.  
- Dotsey, Michael, and Andreas Hornstein, 2003, “Should a Monetary Policymaker Look at Money?” Journal of Monetary Economics, Vol. 50 (April) pp. 547–79.  
- Duca, John V., and David D. VanHoose, 2004, “Recent Developments in Understanding the Demand for Money,” Journal of Economics and Business, Vol. 56 (July-August), pp. 247–272.  
- Collins, Sean S., and Cheryl L. Edwards, 1994, “An Alternative Monetary Aggregate: M2 Plus Household Holdings of Bond and Equity Mutual Funds,” Federal Reserve Bank of St. Louis Review, Vol.76 (November/December), pp. 7–30.  
- Dutkowsky, Donald H., and Cynamon, Barry Z., 2003, “Sweep Programs: The Fall of M1 and Rebirth of the Medium of Exchange,” Journal of Money, Credit, and Banking, Vol. 35 (April), pp. 263–279.  
- Anderson, Richard G., Barry Jones, and Travis Nesmith, 1997, “Introduction to the St. Louis Monetary Services Index Project” Federal Reserve Bank of St. Louis Review, Vol. 79 (January-February), pp. 25–30.  
- Anderson, Richard G., 2003, “Retail Deposit Sweep Programs: Issue for Measurement, Modeling, and Analysis,” Federal Reserve Bank of St. Louis, Working Paper 2003-026.  
- Anderson, Richard G., and Robert H. Rasche, 2001, “Retail Sweep Programs and Bank Reserves, 1994–1999,” Federal Reserve Bank of St. Louis Review, (January/February), pp. 51–72.  
- Carpenter, Seth B., and Joe Lange, 2003, “Money Demand and Equity Markets,” Finance and Economics Discussion Series 2003-3 (Washington: Board of Governors of the Federal Reserve System).  
- Dow Jr., James P., and Douglas W. Elmendorf, 1998, “The Effect of Stock Prices on the Demand for Money Market Mutual Funds,” Finance and Economics Discussion Series 98-24 (Washington: Board of Governors of the Federal Reserve System).  
- Feinman, Joshua, and Richard D. Porter, 1992. “The Continued Weakness in M2,” Finance and Economics Discussion Series no. 209 (Washington: Board of Governors of the Federal Reserve System).  

### Empirical Methods, Cointegration, and Time-Series Econometrics
- Johansen, Soren, 1988, “Statistical Analysis of Cointegration Vectors,” Journal of Economic Dynamics and Control, Vol. 12 (June/September), pp 231–254.  
- Cheung, Yin-Wong, and Kon S. Lai, 1993, “Finite-Sample Sizes of Johansen’s Likelihood Ratio Test for Cointegration,” Oxford Bulletin of Economics and Statistics, Vol. 55 (August), pp. 313–328.  
- Saikkonnen, Pentti, 1992, “Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation,” Econometric Theory, Vol. 8 (March), pp. 1–27.  
- Stock James H., and Mark W. Watson, 1993, “A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems,” Econometrica, Vol. 61 (July), pp. 783–820.  
- Ng, Serena, and Pierre Perron, 2001, “Lag Length Selection and the Construction of Unit Root Tests of Good Size and Power,” Econometrica, Vol. 69 (November), pp. 1519–1554.  
- Cheung, Yin-Wong, and Kon S. Lai, 1993, “Finite-Sample Sizes of Johansen’s Likelihood Ratio Test for Cointegration,” Oxford Bulletin of Economics and Statistics, Vol. 55 (August), pp. 313–328.  
- Hansen, Bruce E. 1997, “Approximate Asymptotic P Values for Structural-Change Tests.” Journal of Business and Economic Statistics, Vol. 15 (1997), pp. 60−57.  
- Carlson, John B., Dennis L. Hoffman, Benjamin D. Keen, and Robert H. Rasche, 2000, “Results of a Study of the Stability of Cointegrating Relations Comprised of Broad Monetary Aggregates,” Journal of Monetary Economics, Vol. 46 (October), pp. 345–383.  
- Hallman, Jeffrey J., Richard D. Porter, and David H. Small, 1991, “Is the Price Level Tied to the M2 Monetary Aggregate in the Long Run?” American Economic Review, Vol. 81 (September), pp. 841–858.  
- Hafer, R.W., and Dennis W. Jansen, 1991, “The Demand for Money in the United States: Evidence from Cointegration Tests,” Journal of Money, Credit, and Banking, Vol. 23 (May), pp. 155–168.  

### Monetary Policy, Transmission, and Macroeconomic Implications
- Board of Governors of the Federal Reserve System, 2002, Monetary Policy Report to the Congress, pp. 1–32 (Washington: Board of Governors of the Federal Reserve System).  
- Federal Reserve Board, 2004, “Monetary Policy Report to the Congress,” Federal Reserve Bulletin (spring), pp.125–152.  
- Meltzer, Allan H., 2001, “The Transmission Process,” In: Deutsche Bundesbank (ed.), The Monetary Transmission Process: Recent Developments and Lessons for Europe. Palgrave, London, pp. 112–130.  
- Nelson, Edward, 2002, “Direct Effects of Base Money on Aggregate Demand: Theory and Evidence,” Journal of Monetary Economics, Vol. 49 (May), pp. 687–708.  
- Leeper, Eric M., and Jennifer E. Roush, 2003, “Putting "M" Back in Monetary Policy,” Journal of Money, Credit, and Banking, Vol. 35 (Part 2, December), pp. 1217–56.  
- Cole, Harold L., and Lee E. Ohanian, 2002, “Shrinking Money: The Demand for Money and the Nonneutrality of Money,” Journal of Monetary Economics, Vol. 49 (May), pp. 653–686.  
- Dynan, Karen E., Douglas W. Elmendorf, and Daniel E. Sichel, 2006, “Can Financial Innovation Help to Explain the Reduced Volatility of Economic Activity?” Journal of Monetary Economics, Vol. 53 (January), pp. 123–150.  

### Equity Markets, Risk, and Expected Returns
- Fama, Eugene F., and Kenneth R. French, 1988, “Dividend Yields and Expected Stock Returns,” Journal of Financial Economics, Vol. 22 (October), pp. 3–26.  
- Jagannathan, Ravi, and Zhenyu Wang, 1996, “The Conditional CAPM and the Cross-Section of Expected Returns” Journal of Finance, Vol. 51 (March), pp. 3–53.  
- Harvey, Campbell R., 1989, “Time-Varying Conditional Covariances in Tests of Asset Pricing Models,” Journal of Financial Economics, Vol. 24 (October), pp. 289–317.  
- Duffee, Gregory R., 1998, “The Relation between Treasury Yields and Corporate Bond Yield Spreads,” Journal of Finance, Vol. 53 (December), pp. 2225–2241.  
- Fujimoto, Akiko, 2003, “Macroeconomic Sources of Systematic Liquidity,” Manuscript, Yale University.  
- Guerron, Pablo, 2006, “Time-Dependent Portfolio Adjustment: Yet Another Look at the Dynamics,” Working Paper Series 006, Department of Economics, North Carolina State University.  

*Source: _wp0789 - References*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0789.pdf_