## Money Growth and Inflation, 1958/59–2005/06

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---

### Introduction
- Iran has a history of relatively high inflation, with CPI inflation averaging more than 17 percent since the 1979 revolution.
- Measured inflation is likely to underestimate “true” inflation owing to price controls and direct and indirect government subsidies.
- Excessive money creation, fueled by government spending out of oil revenues, has been identified in most of the literature as the main cause of high inflation.
- From 2002/03 up until to the first quarter of 2006/07, inflation declined despite continued rapid money growth, raising questions about the stability of the money–inflation relationship.
- This paper:
  - Examines determinants of inflation in Iran in the short run and long run.
  - Uses a parsimonious error correction model estimated for the period 1988/89–2005/06, based on new national accounts series released by the Central Bank of Iran.
  - Focuses directly on the relationship between nominal variables and inflation rather than on traditional real money demand functions.
- The Iranian year starts March 21.

### Main results (summary)
- Long-run relationship:
  - A long-term relationship exists between the price level and money, its rate of return, real output, and the exchange rate.
  - Money has a prominent role in determining the equilibrium price level.
- Short-run dynamics:
  - Money growth drives inflation even in the short-run, with lags of up to four quarters.
  - Adjustment to equilibrium is slow, possibly owing to extensive administrative controls on prices, with a half life of about four quarters.
- Structural stability and recent inflation decline:
  - There is no evidence of a structural change in the relationship between money and inflation.
  - The recent decline in inflation up until the sample end is fully predicted by the model and can be explained almost entirely by the lagged impact of the past deceleration in M1 growth.
- Outlook:
  - The decline in inflation is unlikely to continue.
  - The model predicts that the recent acceleration of money growth is likely to be reflected in higher inflation after a few quarters.

### Stylized facts (historical overview)
- Over the last fifty years, the Iranian economy experienced major shocks, including the 1979 revolution, the 1980–88 war with Iraq, and the 1993 balance of payments crisis; these episodes strongly influenced macroeconomic variables.
- Inflation experienced sudden bursts corresponding to these episodes; on average it has been moderately high (12.6 percent since 1958/59).
- Inflation has generally been associated with rapid persistent money growth (24.2 percent for M2).
- The 1979 revolution represents a breaking point in the money–inflation relationship: inflation increased significantly following the revolution (from 6.6 percent to 17.4 percent on average), while the acceleration in money growth was almost negligible.

### Recent inflation and money-growth developments
- After a peak of 50 percent in the mid-1990s, inflation declined up until the first quarter of 2006/07, though the annual average remained in the double digits.
- M1 and M2 continued to grow quite rapidly even as inflation declined.
- Under the Five-Year Development Plans (FYDPs):
  - Inflation exceeded targets by about 4 percentage points on average under the First FYDP (1989/90–1993/94) and by almost 14 percentage points on average under the Second FYDP (1995/96–1999/2000).
  - The target for M2 growth was missed by almost 16 percentage points on average under the First FYDP, and by 13 percentage points under the Second FYDP.
- Under the Third FYDP (2000/01–2004/05) and first year of the Fourth FYDP (2005/06–2010/11):
  - Performance in reaching the inflation target improved somewhat up until 2005/06.
  - The money growth target was consistently missed by a significant margin.
- Factors that may have contributed to the divergence between inflation and money growth:
  - Trade reforms and gradual opening of the economy.
  - Parallel market appreciation preceding the 2002 exchange rate unification improved inflation performance in the first two years under the Third FYDP.
  - Favorable weather conditions affecting agricultural prices.
  - Stricter annual limits to price increases for goods and services by public sector enterprises.

### Model of inflation in Iran
- Framework: IS-LM model for a small open economy, augmented with Purchasing Power Parity (PPP) and Uncovered Interest Parity (UIP) conditions; PPP and UIP are unlikely to hold for Iran over the sample period (1988:Q2–2006:Q1).
- Core approach: invert the money demand function to obtain the price level as a function of nominal money supply.
- Domestic price level specification (log variables):
  - p is the log of the domestic price level (consumer price index)
  - m is the log of the money supply (M1)
  - y is the log of income (GDP at constant market prices)
  - r is the nominal rate of return on time deposits (3-month deposit rate)
  - s is the log of the nominal effective exchange rate
- Stated inverted real money demand relation (equation form in text):
  - p = ... (see source text for full functional expression)

### Data properties and estimation approach
- Sample period: 1988:Q2–2006:Q1.
- Variables visually trended; unit root tests indicate nonstationarity.
- Seasonality present (notably in GDP); HEGY test detects unit roots at seasonal frequencies for y.
- Seasonal components filtered using X-12-Arima; after seasonal adjustment, unit root tests suggest all variables are I(1).
- Cointegration analysis:
  - VAR dynamic specification chosen to eliminate serial correlation in residuals.
  - Four Islamic festive dummies included: Muharram, Ramadan, Shawal, Thul-Hujia.
  - Johansen trace and maximum eigenvalue statistics indicate one cointegrating vector at the 5 percent confidence level.

### Long-run cointegrating relationship (estimated signs and coefficients)
- Estimated cointegrating vector (signs and coefficients as reported; standard errors in parentheses):
  - s - r - y + m ≈ p
  - Reported in text as: s r y m p 13.0 03.0 63.0 83.0 − + − = (0.02) (0.10) (0.01) (0.03)
- Interpretation:
  - Money is by far the most important determinant of the long-run price level.
  - The coefficient of money differs from unity but is reasonably close; deviation likely reflects extensive price controls.
  - A more appreciated nominal effective exchange rate and higher income are associated with a lower equilibrium price level.
  - Higher rates of return on deposits reduce demand for real money balances (M1), raising the equilibrium price.

### Short-run error-correction model and key statistics
- Weak exogeneity tests: money, output, the rate of return, and the nominal effective exchange rate are weakly exogenous to the cointegrating vector; deviations from long-run equilibrium bring adjustments only in the price level.
- Parsimonious error-correction specification (standard errors in parentheses):
  - dp = 0.27 dp_{t-1} - 0.31 dm_{t-1} + 0.16 dm_{t-2} + 0.10 dm_{t-3} - 0.05 dm_{t-4} + 0.01 dy - 0.05 dr - 0.01 ds + 0.16 DM - 0.11 EC_{t-1}
- Model fit and diagnostics:
  - RSS = 0.01
  - R^2 = 0.75
  - Adj. R^2 = 0.72
  - T = 67
  - Specification tests (selected):
    - Chow (1997:4): Value 0.82, Prob. 0.71
    - Chow (2004:3): Value 1.44, Prob. 0.22
    - Normality test: Value 0.06, Prob. 0.97
    - AR 1–4 test: Value 0.80, Prob. 0.53
    - ARCH 1–4 test: Value 0.57, Prob. 0.69
    - Heteroskedasticity test: Value 17.28, Prob. 0.37
- Model diagnostics:
  - Residuals approximately normal, no evidence of autocorrelation or heteroskedasticity (with some exceptions noted for the exchange rate).
  - Stability tests suggest absence of structural breaks; parameter instability rejection clearer for midpoint breakpoint (1997:Q4) than near end (2004:Q3).
  - Recursive estimation suggests coefficient estimates have remained stable since 1995.

### Short-run dynamics and transmission
- Inflation persistence: positive lagged coefficient indicates some persistence.
- Main drivers of short-run inflation:
  - Money growth (M1) is the dominant driver; impact operates with lags up to four quarters.
  - Income and rates of return have contemporaneous effects of expected sign.
  - Exchange rate pass-through to inflation is relatively small but fast.
  - Of Islamic festivities, only Muharram seems to affect inflation.
- Mean half life of adjustment of inflation to a unit shock: about four quarters.

### Model implications for recent inflation decline (up to 2006:Q1)
- The model underpredicts inflation since mid-2004, except for 2005:Q3 when quarterly inflation dropped to zero.
- Fitted-value decomposition indicates the decline in inflation up until recently can be explained almost exclusively by a slowdown in M1 growth in previous quarters.
- Contribution of other factors—rapid GDP growth and exchange rate appreciation—to the decline in inflation has been almost negligible.

### Conclusions and policy implications
- Monetary policy failed to meet inflation and monetary targets under the FYDPs, owing mainly to the monetary impact of government spending out of oil revenue.
- The objective of gradual disinflation to single-digit levels has not been achieved.
- The persistent double-digit inflation is mainly due to problems adhering to monetary targets.
- Long-run relationship exists between the price level, money, output, the rate of return on money, and the exchange rate; money’s role is prevalent.
- The estimated error-correction model explains short-run inflation dynamics in terms of:
  - Deviations from the long-run price level,
  - Current and lagged money growth,
  - Current output growth and exchange rate depreciation,
  - Changes in the rate of return on deposits.
- According to the model, the recent decline in inflation is mostly due to earlier slowdown in M1 growth and is likely to be reversed once current acceleration in money growth feeds through to inflation.
- Policy recommendations emphasized:
  - Controlling money growth is key to successful disinflation.
  - Money growth can be a useful intermediate target given stability of the money–inflation relationship.
  - The challenge is achieving the monetary targets; requires improved coordination of fiscal policy with monetary policy and subordinating exchange rate objectives to achieving inflation targets.

*Source: IMF Working Paper — section "Money Growth and Inflation, 1958/59–2005/06" (content unit _wp07119).*

### 1.     Money Growth and Inflation, 1958/59–2005/06................................................................4

### Money Growth and Inflation, 1958/59–2005/06

### Introduction
- Iran has a history of relatively high inflation, with CPI inflation averaging more than 17 percent since the 1979 revolution.
- Measured inflation is likely to underestimate “true” inflation owing to price controls and direct and indirect government subsidies.
- Excessive money creation, fueled by government spending out of oil revenues, has been identified in most of the literature as the main cause of high inflation.
- From 2002/03 up until to the first quarter of 2006/07, inflation declined despite continued rapid money growth, raising questions about the stability of the money–inflation relationship.
- This paper:
  - Examines determinants of inflation in Iran in the short run and long run.
  - Uses a parsimonious error correction model estimated for the period 1988/89–2005/06, based on new national accounts series released by the Central Bank of Iran.
  - Focuses directly on the relationship between nominal variables and inflation rather than on traditional real money demand functions.
- The Iranian year starts March 21.

### Main results (summary)
- Long-run relationship:
  - A long-term relationship exists between the price level and money, its rate of return, real output, and the exchange rate.
  - Money has a prominent role in determining the equilibrium price level.
- Short-run dynamics:
  - Money growth drives inflation even in the short-run, with lags of up to four quarters.
  - Adjustment to equilibrium is slow, possibly owing to extensive administrative controls on prices, with a half life of about four quarters.
- Structural stability and recent inflation decline:
  - There is no evidence of a structural change in the relationship between money and inflation.
  - The recent decline in inflation up until the sample end is fully predicted by the model and can be explained almost entirely by the lagged impact of the past deceleration in M1 growth.
- Outlook:
  - The decline in inflation is unlikely to continue.
  - The model predicts that the recent acceleration of money growth is likely to be reflected in higher inflation after a few quarters.

### Stylized facts (historical overview)
- Over the last fifty years, the Iranian economy experienced major shocks, including the 1979 revolution, the 1980–88 war with Iraq, and the 1993 balance of payments crisis; these episodes strongly influenced macroeconomic variables.
- Inflation experienced sudden bursts corresponding to these episodes; on average it has been moderately high (12.6 percent since 1958/59).
- Inflation has generally been associated with rapid persistent money growth (24.2 percent for M2).
- The 1979 revolution represents a breaking point in the money–inflation relationship: inflation increased significantly following the revolution (from 6.6 percent to 17.4 percent on average), while the acceleration in money growth was almost negligible.

*Source: IMF Working Paper — section "Money Growth and Inflation, 1958/59–2005/06" (content unit _wp07119).*

### 24.6 percent on average).

### _wp07119 - 24.6 percent on average)

### Recent inflation and money-growth developments
- After a peak of 50 percent in the mid-1990s, inflation declined up until the first quarter of 2006/07, though the annual average remained in the double digits.
- M1 and M2 continued to grow quite rapidly even as inflation declined.
- Under the Five-Year Development Plans (FYDPs):
  - Inflation exceeded targets by about 4 percentage points on average under the First FYDP (1989/90–1993/94) and by almost 14 percentage points on average under the Second FYDP (1995/96–1999/2000).
  - The target for M2 growth was missed by almost 16 percentage points on average under the First FYDP, and by 13 percentage points under the Second FYDP.
- Under the Third FYDP (2000/01–2004/05) and first year of the Fourth FYDP (2005/06–2010/11):
  - Performance in reaching the inflation target improved somewhat up until 2005/06.
  - The money growth target was consistently missed by a significant margin.
- Factors that may have contributed to the divergence between inflation and money growth:
  - Trade reforms and gradual opening of the economy.
  - Parallel market appreciation preceding the 2002 exchange rate unification improved inflation performance in the first two years under the Third FYDP.
  - Favorable weather conditions affecting agricultural prices.
  - Stricter annual limits to price increases for goods and services by public sector enterprises.

### Model of inflation in Iran
- Framework: IS-LM model for a small open economy, augmented with Purchasing Power Parity (PPP) and Uncovered Interest Parity (UIP) conditions; PPP and UIP are unlikely to hold for Iran over the sample period (1988:Q2–2006:Q1).
- Core approach: invert the money demand function to obtain the price level as a function of nominal money supply.
- Domestic price level specification (log variables):
  - p is the log of the domestic price level (consumer price index)
  - m is the log of the money supply (M1)
  - y is the log of income (GDP at constant market prices)
  - r is the nominal rate of return on time deposits (3-month deposit rate)
  - s is the log of the nominal effective exchange rate
- Stated inverted real money demand relation (equation form in text):
  - p = ... (see source text for full functional expression)

### Data properties and estimation approach
- Sample period: 1988:Q2–2006:Q1.
- Variables visually trended; unit root tests indicate nonstationarity.
- Seasonality present (notably in GDP); HEGY test detects unit roots at seasonal frequencies for y.
- Seasonal components filtered using X-12-Arima; after seasonal adjustment, unit root tests suggest all variables are I(1).
- Cointegration analysis:
  - VAR dynamic specification chosen to eliminate serial correlation in residuals.
  - Four Islamic festive dummies included: Muharram, Ramadan, Shawal, Thul-Hujia.
  - Johansen trace and maximum eigenvalue statistics indicate one cointegrating vector at the 5 percent confidence level.

### Long-run cointegrating relationship (estimated signs and coefficients)
- Estimated cointegrating vector (signs and coefficients as reported; standard errors in parentheses):
  - s - r - y + m ≈ p
  - Reported in text as: s r y m p 13.0 03.0 63.0 83.0 − + − = (0.02) (0.10) (0.01) (0.03)
  - Interpretation:
    - Money is by far the most important determinant of the long-run price level.
    - The coefficient of money differs from unity but is reasonably close; deviation likely reflects extensive price controls.
    - A more appreciated nominal effective exchange rate and higher income are associated with a lower equilibrium price level.
    - Higher rates of return on deposits reduce demand for real money balances (M1), raising the equilibrium price.

### Short-run error-correction model and key statistics
- Weak exogeneity tests: money, output, the rate of return, and the nominal effective exchange rate are weakly exogenous to the cointegrating vector; deviations from long-run equilibrium bring adjustments only in the price level.
- Parsimonious error-correction specification (standard errors in parentheses):
  - dp = 0.27 dp_{t-1} - 0.31 dm_{t-1} + 0.16 dm_{t-2} + 0.10 dm_{t-3} - 0.05 dm_{t-4} + 0.01 dy - 0.05 dr - 0.01 ds + 0.16 DM - 0.11 EC_{t-1}
  - (Parenthetical standard errors reported in source; see source text for exact formatting.)
- Model fit and diagnostics:
  - RSS = 0.01
  - R^2 = 0.75
  - Adj. R^2 = 0.72
  - T = 67
  - Specification tests (selected):
    - Chow (1997:4): Value 0.82, Prob. 0.71
    - Chow (2004:3): Value 1.44, Prob. 0.22
    - Normality test: Value 0.06, Prob. 0.97
    - AR 1–4 test: Value 0.80, Prob. 0.53
    - ARCH 1–4 test: Value 0.57, Prob. 0.69
    - Heteroskedasticity test: Value 17.28, Prob. 0.37
- Model diagnostics:
  - Residuals approximately normal, no evidence of autocorrelation or heteroskedasticity (with some exceptions noted for the exchange rate).
  - Stability tests suggest absence of structural breaks; parameter instability rejection clearer for midpoint breakpoint (1997:Q4) than near end (2004:Q3).
  - Recursive estimation suggests coefficient estimates have remained stable since 1995.

### Short-run dynamics and transmission
- Inflation persistence: positive lagged coefficient indicates some persistence.
- Main drivers of short-run inflation:
  - Money growth (M1) is the dominant driver; impact operates with lags up to four quarters.
  - Income and rates of return have contemporaneous effects of expected sign.
  - Exchange rate pass-through to inflation is relatively small but fast.
  - Of Islamic festivities, only Muharram seems to affect inflation.
- Mean half life of adjustment of inflation to a unit shock: about four quarters (estimated).

### Model implications for recent inflation decline (up to 2006:Q1)
- The model underpredicts inflation since mid-2004, except for 2005:Q3 when quarterly inflation dropped to zero.
- Fitted-value decomposition indicates the decline in inflation up until recently can be explained almost exclusively by a slowdown in M1 growth in previous quarters.
- Contribution of other factors—rapid GDP growth and exchange rate appreciation—to the decline in inflation has been almost negligible.

### Conclusions and policy implications
- Monetary policy failed to meet inflation and monetary targets under the FYDPs, owing mainly to the monetary impact of government spending out of oil revenue.
- The objective of gradual disinflation to single-digit levels has not been achieved.
- The persistent double-digit inflation is mainly due to problems adhering to monetary targets.
- Long-run relationship exists between the price level, money, output, the rate of return on money, and the exchange rate; money’s role is prevalent.
- The estimated error-correction model explains short-run inflation dynamics in terms of:
  - Deviations from the long-run price level,
  - Current and lagged money growth,
  - Current output growth and exchange rate depreciation,
  - Changes in the rate of return on deposits.
- According to the model, the recent decline in inflation is mostly due to earlier slowdown in M1 growth and is likely to be reversed once current acceleration in money growth feeds through to inflation.
- Policy recommendations emphasized:
  - Controlling money growth is key to successful disinflation.
  - Money growth can be a useful intermediate target given stability of the money–inflation relationship.
  - The challenge is achieving the monetary targets; requires improved coordination of fiscal policy with monetary policy and subordinating exchange rate objectives to achieving inflation targets.

*Italic: Source: IMF staff estimates and analysis, based on data and results presented in the supplied document.*

### References

### _wp07119 - References

### References
- Bahmani-Oskooee, M. (1995) “Sources of Inflation in Post-Revolutionary Iran,” International Economic Journal, Vol. 9, No. 2, pp. 61–72.
- Alavirad, A. and S. Athawale (2005) “The Impact of the Budget Deficit on Inflation in the Islamic Republic of Iran,” OPEC Review, (March), pp. 37–49.
- Becker, T. (1999) “Common Trends and Structural Change: A Dynamic Macro Model for the Pre- and Post-Revolution Islamic Republic of Iran,” IMF Working Paper 99/82 (Washington: International Monetary Fund).
- Celasun, O. and M. Goswami (2002), “An Analysis of Money Demand and Inflation in the Islamic Republic of Iran,” IMF Working Paper 02/205 (Washington: International Monetary Fund).
- Hendry, D. and H.-M. Kolzig (2001), “Automatic Econometric Model Selection Using PCGets,” Timberlake Consultants, London.
- Hylleberg, S., Engle, R.F., Granger, C.W.J. and B.S. Yoo (1990), “Seasonal Integration and Cointegration,” Journal of Econometrics, Vol. 44, pp. 215–238.
- Jbili, A., Kramarenko, V., and J. Bailén (2007), “Islamic Republic of Iran: Managing the Transition to a Market Economy,” (Washington: International Monetary Fund).
- Kramarenko, V. (2004) “Islamic Republic of Iran—Inflation Determinants Revisited,” (unpublished manuscript; Washington: International Monetary Fund).
- Kramarenko, V. (2007a) “Moving toward a Market-Based Monetary Policy,” in Jbili, A., Kramarenko, V., and J. Bailén (2007), pp. 32–45.
- Kramarenko, V. (2007b) “The Financial Sector: Issues and Reforms,” in Jbili, A., Kramarenko, V., and J. Bailén (2007), pp.16–31.
- Liu, O. and O.S. Adedeji (2000) “Determinants of Inflation in the Islamic Republic of Iran—A Macroeconomic Analysis,” IMF Working Paper 00/127 (Washington: International Monetary Fund).
- McKinnon, J., Haug, A.A., and L. Michelis (1999) “Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration,” Journal of Applied Econometrics, Vol. 14, No. 5, pp. 563–77.
- Pesaran, H.M. (2000) “Economic Trends and Macroeconomic Policies in Post-Revolutionary Iran” in Alizadeh, P. “The Economy of Iran: Dilemmas of an Islamic State,” (London: I.B. Tauris), Chapter 2, pp.63–100.
- Riazuddin, R. and M. H. Khan (2005) “Detection and Forecasting of Islamic Calendar Effects in Time Series Data,” State Bank of Pakistan Research Bulletin, Vol. 1, No. 1, pp. 25–34.

### Appendix I. Data Sources and Definitions
- Prices: Consumer Price Index (CPI) for urban areas from the IMF IFS database.
- Money supply: M1 from the IMF IFS database.
- Output series: obtained by splicing two series of GDP at constant market prices:
  - 1988:Q2–2005:Q1: database on the Central Bank of Iran website (www.cbi.ir).
  - 2005:Q1–2006:Q1: reported by the Central Bank of Iran in its quarterly publication Economic Trends (available on www.cbi.ir).
- Interest rate: rate of return on 3-month deposits in state-owned banks reported by the Central Bank of Iran in Economic Trends (available on www.cbi.ir).
- Nominal effective exchange rate: trade-weighted index from the IMF’s INS database.
- Dummy variables for Islamic festivities: calculated by Riazuddin and Khan (2005).

### Appendix II. Unit Root Tests
- Table AII.1. Unit Root Tests, Iran, 1998Q2-2006Q1 — Phillips-Perron t statistics and Augmented Dickey-Fuller t statistics reported for multiple variables and specifications (unadjusted and seasonally adjusted data). Selected reported values (preserve exact entries as presented):
  - For variable p (unadjusted data), No intercept, no trend: Level 1.18; 1st diff. -0.98; 2nd diff. -4.77***; additional columns include 5.89, -3.59***, -18.72***.
  - For variable m (unadjusted data), No intercept, no trend: Level 2.40; 1st diff. -0.46; 2nd diff. -19.85***; additional columns include 9.44, -9.24***, -58.16***.
  - For variable y (unadjusted data), No intercept, no trend: Level 2.75; 1st diff. -2.84***; 2nd diff. -55.33***; additional columns include 1.69, -15.19***, -24.42***.
  - For variable r (unadjusted data), No intercept, no trend: Level 1.10; 1st diff. -8.52***; 2nd diff. -7.29***; additional columns include 1.15, -8.52***, -56.65***.
  - For variable s (unadjusted data), No intercept, no trend: Level (not explicitly listed in excerpt) with 1st diff. -2.87***; 2nd diff. -7.55***; additional columns include -8.87***, -2.96***, -7.56***, -41.61***.
  - Seasonally adjusted data section repeats similar test statistics for p, m, y, r, s with reported values such as for p: No intercept, no trend Level 1.53; 1st diff. -1.31; 2nd diff. -12.18***; additional columns 5.67, -1.56, -12.25***.
- Table AII.2. HEGY Seasonal Unit Root Tests, Iran, 1998Q2-2006Q1 — F statistics and t statistics for zero, biannual, and annual seasonal frequencies. Selected reported values:
  - For p (no intercept, no trend, no seasonal dummies): F-statistic 1.83; zero frequency t -9.17**; biannual -2.84**; annual -4.10**; π4 15.05**.
  - For m (no intercept, no trend, no seasonal dummies): F-statistic 7.54; zero frequency t -1.73*; biannual -4.46**; annual -4.16**; π4 26.14**.
  - For y (no intercept, no trend, no seasonal dummies): F-statistic 6.83; zero frequency t -1.50; biannual -0.92; annual -0.95; π4 0.88.
  - For r (no intercept, no trend, no seasonal dummies): F-statistic 1.14; zero frequency t -4.55**; biannual -4.64**; annual -4.51**; π4 30.81**.
  - For s (no intercept, no trend, no seasonal dummies): test entries include t-statistics such as -2.94**, -4.52**, -4.07**, -5.37**, and π4 33.84**.
- Significance notation:
  - * indicates a p-value of 0.90 or more.
  - ** indicates a p-value of 0.95 or more.
  - *** indicates a p-value of 0.99 or more.

### Appendix III. Cointegration Tests
- Sample (adjusted): 1988:Q4 2006:Q1
- Included observations: 70 after adjustments
- Trend assumption: Linear deterministic trend
- Series: p m y r s
- Exogenous series: DH DM DR DS
- Lags interval (in first differences): 1 to 1
- Unrestricted Cointegration Rank Test (Trace):
  - None: Eigenvalue 0.407090; Trace Statistic 80.32418; 0.05 Critical Value 69.81889; Prob. 0.0057
  - At most 1: Eigenvalue 0.288632; Trace Statistic 43.73432; 0.05 Critical Value 47.85613; Prob. 0.1157
  - At most 2: Eigenvalue 0.136823; Trace Statistic 19.89471; 0.05 Critical Value 29.79707; Prob. 0.4300
  - At most 3: Eigenvalue 0.118694; Trace Statistic 9.595243; 0.05 Critical Value 15.49471; Prob. 0.3132
  - At most 4: Eigenvalue 0.010667; Trace Statistic 0.750692; 0.05 Critical Value 3.841466; Prob. 0.3863
  - Conclusion: Trace test indicates 1 cointegrating eqn(s) at the 0.05 level. (* denotes rejection of the hypothesis at the 0.05 level)
- Unrestricted Cointegration Rank Test (Maximum Eigenvalue):
  - None: Eigenvalue 0.407090; Max-Eigen Statistic 36.58987; 0.05 Critical Value 33.87687; Prob. 0.0231
  - At most 1: Eigenvalue 0.288632; Max-Eigen Statistic 23.83961; 0.05 Critical Value 27.58434; Prob. 0.1404
  - At most 2: Eigenvalue 0.136823; Max-Eigen Statistic 10.29946; 0.05 Critical Value 21.13162; Prob. 0.7161
  - At most 3: Eigenvalue 0.118694; Max-Eigen Statistic 8.844551; 0.05 Critical Value 14.26460; Prob. 0.2993
  - At most 4: Eigenvalue 0.010667; Max-Eigen Statistic 0.750692; 0.05 Critical Value 3.841466; Prob. 0.3863
  - Conclusion: Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level. (* denotes rejection of the hypothesis at the 0.05 level)
- Note: p-values are MacKinnon-Haug-Michelis (1999) p-values where reported.

*Source: _wp07119 - References*

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