## _wp08189 - 1. Unit Root Tests

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### Introduction
- Purpose: examine determinants of inflation in Sudan, focusing on money supply growth and nominal exchange rate developments, to provide elasticities of inflation to money supply growth and nominal exchange rate appreciation to inform monetary programming and the central bank’s policy framework.
- Methods: single-equation model, recursive SVAR, and vector error correction model (VECM).
- Caveats: limits in data quality, relatively low number of observations, and possible structural breaks.

### Background
- Institutional and recent macro context:
  - Financial liberalization reforms began in 1997; since May 2002 BOS uses broad money as the policy target and reserve money as the operational target.
  - Broad money growth rate (12-month) was over 40 percent during 2005 and 2006.
  - Sudanese dinar/pound nominal appreciation by about 20 percent against the U.S. dollar during 2005–2006.
  - BOS net international reserves fell from US$2.3 billion (equivalent to 2.8 months of imports) in August 2006 to about US$0.6 billion (equivalent to 0.6 months of imports) in May 2007 due to liquidity mopping up.
  - Currency conversion in mid-2007: BOS prioritized rebuilding reserves and allowing greater exchange rate flexibility; the nominal value of the pound vis-à-vis the U.S. dollar declined by over 3 percent with wider day-to-day fluctuations.
- Inflation developments:
  - Inflation excluding food, energy, and transportation declined from 16.5 percent (12-month) in December 2006 to 7.8 percent in December 2007.
  - A one-off cut in fuel subsidy in August 2006 caused a spike in the transportation sector after September 2006.

### Model
- Conceptual structure:
  - Overall price index P decomposed into domestic and foreign components with share α: P = P_d^{α} (E P^*_ )^{1-α} (log-linear form used).
  - Domestic prices follow the quantity theory: M V = P_d Y, with velocity featuring a negative time trend (θ < 0).
  - Combined log-linear relation yields regression of overall inflation on money supply, real GDP, nominal exchange rate, foreign inflation, and control variables (including time trend).
- Expected signs:
  - Money supply: positive effect on inflation.
  - Nominal appreciation: negative effect on inflation (pass-through).
  - Foreign deflator: positive effect on inflation (imported inflation).
- Estimation approaches:
  - Single-equation in first differences (with optional lagged inflation and error correction term).
  - Recursive structural VAR (McCarthy (2000) recursive disturbance ordering).
  - VECM assuming cointegration among regressors.
- Elasticities computed from impulse responses as cumulative CPI response divided by cumulative shock in money growth or nominal exchange rate over j months.

### Data issues and estimation strategy
- Data span Q1 1995 to Q2 2007; all series quarterly.
- Structural breaks and regime shifts considered: 1997 monetary framework change dummy; Q3 2006 fuel subsidy cut dummy; large 1994 devaluation excluded.
- Trade-offs: longer samples increase degrees of freedom but risk structural breaks (CPA in 2005, 1997 framework change, oil production from 1998).
- Proxy and adjustments:
  - CPI (seasonally adjusted) from IFS; money supply from IFS with X-12 ARIMA seasonal adjustment; quarterly non-oil GDP estimated by linear projection; foreign inflation proxied by world GDP deflator (imports weighted) from GEE; nominal exchange rate proxy uses import-weighted averages.

### Single-equation model — Main empirical findings
- Estimation framework: first-differenced equation with AR(1) Cochrane-Orcutt correction; variants include lagged inflation and error correction term (lagged levels of price index, money supply, real non-oil GDP, nominal exchange rate, foreign prices).
- Key findings:
  - Δfx (nominal appreciation/depreciation) affects inflation in all specifications (pass-through present).
  - Δp* (foreign inflation) is marginally significant when the error correction component is included (specifications (iii) and (iv)).
  - The error correction component is significant (specifications (iii) and (iv)). Including it renders the effect of contemporary money supply growth on inflation insignificant, implying monetary effects may materialize with lags and the error correction term captures accumulated past money supply changes.
  - Coefficient signs in the error correction term align with theory: money supply increases raise the price level; nominal appreciation reduces the price level; higher foreign prices increase the overall price level.
- Reported adjusted R^2 values across specifications: 0.904, 0.929, 0.930, 0.921.
- Error correction term coefficients reported: -0.307 and -0.313 (t-statistics (-2.85) and (-2.88)).

### Elasticities of inflation to money supply and nominal exchange rate (single-equation results)
- Based on specification (iv) (unconstrained):
  - A permanent increase in money supply growth by one percentage point raises inflation by 0.32 over 12-months and 0.48 over 24-months.
  - A permanent nominal appreciation by one percentage point changes inflation by -0.63 over 12-months and -0.73 over 24-months.
- Under the theoretical long-run neutrality constraint (sum of estimated coefficients of money and nominal exchange rate in lagged levels equals one):
  - A permanent increase in money supply growth by one percentage point raises inflation by 0.46 over 12-months and 0.71 over 24-months.
  - A permanent nominal appreciation by one percentage point changes inflation by -0.26 over 12-months and -0.34 over 24-months.
- Interpretation: imposing the neutrality constraint increases the estimated elasticity of inflation to money supply and reduces the elasticity to nominal exchange rate, indicating part of the money supply effect operates through induced nominal depreciation.

### Structural VAR (recursive) — identifying assumptions and results
- Identifying assumptions (McCarthy (2000) recursive ordering):
  - (i) foreign inflation is exogenous to the system;
  - (ii) demand shocks to GDP affect other disturbances except foreign inflation;
  - (iii) money supply shocks affect nominal appreciation/depreciation and inflation disturbances;
  - (iv) nominal appreciation/depreciation shocks do not affect money supply shocks (central bank sets money supply growth).
- Lag length selection via SIC:
  - # of lags = 1: SIC = -27.90
  - # of lags = 2: SIC = -27.54
  - # of lags = 3: SIC = -27.29
  - # of lags = 4: SIC = -26.31
  - # of lags = 5: SIC = -26.85
- Main SVAR findings (lag = 1 unless noted):
  - Both nominal depreciation and an increase in money supply growth raise inflation; response to nominal appreciation is marginally significant.
  - Most adjustment of inflation occurs within one year.
- Elasticities from structural VAR (lag = 1):
  - 12-months: money supply = 0.57; nominal exchange rate = -0.23
  - 24-months: money supply = 0.57; nominal exchange rate = -0.25
- Alternative SVAR (2 lags) elasticities:
  - 12-months: money supply = 0.26; nominal exchange rate = -0.48
  - 24-months: money supply = 0.21; nominal exchange rate = -0.63
- Interpretation: with longer lag length elasticity to nominal exchange rate becomes larger than to money supply, consistent with monetary policy time-lag effects.

### Vector Error Correction Model (VECM) results
- VECM specification: Δx_t = φ(L) Δx_{t-1} + δ z_{t-1} + γ' u_t; lag length selected as 2 based on SIC.
- Lag selection for VECM:
  - # of lags = 1: SIC = -28.00; AIC = -29.98
  - # of lags = 2: SIC = -28.15; AIC = -31.12
  - # of lags = 3: SIC = -27.50; AIC = -31.44
- Johansen co-integration test results indicate two co-integration vectors (Trace and Max-Eigen reject "None" and "At most 1" at 5%).
- VECM-derived elasticities (impulse responses):
  - 12-months: money supply = 0.15; nominal exchange rate = -0.41
  - 24-months: money supply = 0.34; nominal exchange rate = -0.99
- Variance decomposition (# of lags = 2 VEC system):
  - More than 80 percent of CPI inflation fluctuations can be explained by:
    - money supply: about 25 percent
    - nominal exchange rate: about 55 percent
  - Suggests most adjustment of inflation occurs over 18-24 months—longer than implied by the structural VAR—reflecting the long-run relation captured by the VEC system.

### Comparative elasticities (selected results)
- Single-equation (unconstrained):
  - 12 months: Money Supply = 0.32; Nominal Exchange Rate = -0.63
  - 24 months: Money Supply = 0.48; Nominal Exchange Rate = -0.73
- Single-equation (with long-run constraint):
  - 12 months: Money Supply = 0.46; Nominal Exchange Rate = -0.26
  - 24 months: Money Supply = 0.71; Nominal Exchange Rate = -0.34
- Structural VAR:
  - 12 months: Money Supply = 0.57; Nominal Exchange Rate = -0.23
  - 24 months: Money Supply = 0.57; Nominal Exchange Rate = -0.25
- VECM:
  - 12 months: Money Supply = 0.15; Nominal Exchange Rate = -0.41
  - 24 months: Money Supply = 0.34; Nominal Exchange Rate = -0.99

### Policy implications and conclusions
- Robust empirical conclusions across methods:
  - Both money supply and nominal exchange rate affect inflation in Sudan.
  - Nominal exchange rate appears to have a stronger impact on inflation than money supply when time-lag effects and long-run relations are accounted for.
  - Long-run relations (error correction and co-integration) materially affect inflation dynamics; estimated adjustment horizon is 18 to 24 months.
  - The estimated elasticity of inflation to money supply is substantially lower than one; the sum of elasticities to money supply and nominal exchange rate is not far from one in the long run, broadly consistent with the quantity theory of money in an open economy.
- Policy considerations for Bank of Sudan (BOS):
  - High elasticity of inflation to the nominal exchange rate supports authorities’ emphasis on nominal exchange rate stability; since early 2007 BOS has intervened by selling foreign exchange to stabilize the nominal exchange rate at the cost of a sharp decline in international reserves.
  - Exchange rate flexibility is necessary to rebuild reserves but smoothing short-term volatility is important for macroeconomic stability.
  - Nominal depreciation associated with exchange rate flexibility would cause higher inflation, raising the user cost of capital and potentially reducing investment.
  - Given the relation between oil prices and the real exchange rate, BOS should fine tune policy to focus more on maintaining stable inflation.
- Empirical context:
  - Stable food prices helped keep overall CPI inflation low during H2 2005 and throughout 2006 despite faster monetary growth since early 2005.
  - The dinar/pound nominal appreciation of about 20 percent vis-à-vis the U.S. dollar during 2005–2006 mitigated inflationary pressures by lowering import prices.
  - Decline in money supply growth after sharp appreciation of dinar/pound after H2 2006 appears to have lessened inflationary pressures during 2007 (excluding food, energy, and transportation, and accounting for fuel subsidy elimination level shift).
- Caution: data limitations and possible structural changes warrant cautious use of estimates in policy design.

### Data, tests, and auxiliary results
- Data span: Q1 1995 to Q2 2007; excludes 1994 large devaluation (~45 percent Q2–Q3).
- Unit root test (first difference) selected values:
  - CPI: ADF = -1.450; DF-GLS = -3.456**; PP = -3.737**
  - Broad money: ADF = -6.014***; DF-GLS = -6.004***; PP = -6.081***
  - Non-oil GDP: ADF = -3.088; DF-GLS = -3.154*; PP = -3.221*
  - Trade weighted FX: ADF = -5.733***; DF-GLS = -4.864***; PP = -8.784***
  - Foreign deflator: ADF = -3.032**; DF-GLS = -2.167; PP = -2.926**
- Johansen co-integration test excerpts:
  - Unrestricted Trace test "None" Trace Statistic = 46.477 (5% Critical Value = 38.804, P-value = 0.000) → reject none.
  - Unrestricted Max-Eigen test "None" Max-Eigen Statistic = 22.014 (5% Critical Value = 38.331, P-value = 0.000).
- Selected model diagnostics:
  - Single-equation error correction term coefficients: -0.307 and -0.313 (t-statistics (-2.85) and (-2.88)).
  - Single-equation adjusted R^2 values: 0.904, 0.929, 0.930, 0.921.
  - VECM lag selection: SIC favors # of lags = 2 (SIC = -28.15; AIC = -31.12).

*Italic: Content derived from _wp08189 (PDF chapter/section provided).*

### 1. Unit Root Tests .....................................................................................................

### _wp08189 - 1. Unit Root Tests .....................................................................................................

### Introduction
- Inflation projection is central to IMF–country policy dialogue, especially for low-income and post-conflict countries with weak institutions and capacity.
- Recent pressures on inflation arise from higher commodity prices, strong capital inflows, and rapid credit growth.
- This paper examines determinants of inflation in Sudan, focusing on money supply growth and nominal exchange rate developments, using three estimation methods: single-equation model, recursive SVAR, and vector error correction model (VECM).
- Purpose: provide elasticities of inflation to money supply growth and nominal exchange rate appreciation to inform monetary programming and the central bank’s policy framework.
- Cautions: limits in data quality, relatively low number of observations, and possible structural breaks.

### Background
- Until the mid-1990s, monetary instruments at the Central Bank of Sudan (BOS) were limited; reforms began in 1997 to liberalize the financial system and introduce indirect instruments.
- Since May 2002, BOS has used broad money as the policy target, with reserve money as the operational target; however, the monetary policy framework has been vague and lacked estimated parameter relations among monetary aggregates, nominal exchange rate, and inflation.
- Recent monetary stance and outcomes:
  - Broad money growth rate (12-month) was over 40 percent during 2005 and 2006.
  - Sudanese dinar/pound nominal appreciation by about 20 percent against the U.S. dollar (and trade-weighted NEER appreciation) occurred during this period.
  - BOS intervention to mop up liquidity beginning in the second half of 2006 reduced net international reserves from US$2.3 billion (equivalent to 2.8 months of imports) in August 2006 to about US$0.6 billion (equivalent to 0.6 months of imports) in May 2007.
  - The currency conversion in mid-2007 led BOS to prioritize rebuilding reserves and allowing greater exchange rate flexibility; the nominal value of the pound vis-à-vis the U.S. dollar declined by over 3 percent with wider day-to-day fluctuations.
- Inflation dynamics:
  - Inflation excluding food, energy, and transportation declined from 16.5 percent (12-month) in December 2006 to 7.8 percent in December 2007.
  - A one-off cut in fuel subsidy in August 2006 caused a spike in the transportation sector after September 2006.

### Model
- The paper employs nonstructural time-series approaches (error correction model, VAR, VECM) due to limited guidance from economic theory on dynamic specification and endogeneity concerns.
- Conceptual structure:
  - Overall price index composed of domestic price and foreign price components with share α (assumed constant): P = P_d^{α} (E P^*_ )^{1-α} (log-linear form used).
  - Domestic prices follow the quantity theory of money: M V = P_d Y, with velocity having a negative time trend (θ < 0).
  - Combined log-linear relation yields the regression: overall inflation as a function of money supply, real GDP, nominal exchange rate, foreign inflation, and control variables (including time trend).
- Expectations from model:
  - Positive effect of money supply on inflation.
  - Negative effect of nominal appreciation on inflation (pass-through).
  - Positive effect of foreign deflator on inflation (imported inflation).
- Estimation approaches:
  - Single-equation model in first differences with optional lagged inflation and error correction term.
  - Structural (recursive) VAR following McCarthy (2000) assumptions on recursive disturbance structure.
  - VECM assuming cointegration among regressors.
- Short- and medium-term elasticities are computed from impulse response functions by dividing cumulative CPI response after j months by cumulative response of money growth (or nominal exchange rate changes) shock after j months.

### Data issues and estimation strategy
- Sudan faces trade-offs: longer time series increase degrees of freedom but are likelier to contain structural breaks (CPA in 2005, new monetary framework in 1997, start of oil production in 1998).
- Regressions include dummies for the monetary policy framework change and a fuel subsidy cut dummy during Q3 2006.
- Three estimation methods are applied to equation (4) conditional on unit root test results.

### Single-Equation Model — Main empirical findings
- Estimation performed on first-differenced equation with AR(1) error process using Cochrane-Orcutt; specifications considered:
  - Variants with/without lagged inflation.
  - Variants with/without error correction component (lagged levels of price index, money supply, real non-oil GDP, nominal exchange rate, foreign prices).
- Key results summarized:
  - Nominal appreciation/depreciation (Δfx) affects inflation in all specifications, indicating pass-through effects.
  - Foreign inflation (Δp*) is marginally significant in specifications with the error correction component (specifications (iii) and (iv)), indicating some imported inflation.
  - The error correction component is significant (specifications (iii) and (iv)). Including it renders the effect of contemporary money supply growth on inflation insignificant, suggesting monetary effects may materialize with lags and that the error correction term captures accumulated past money supply changes.
  - Signs of coefficients in the error correction component align with model predictions: money supply increases raise price level; nominal appreciation reduces price level; higher foreign prices increase overall price level.

### Elasticities of inflation to money supply and nominal exchange rate (single-equation results)
- Based on specification (iv) (unconstrained):
  - A permanent increase in money supply growth by one percentage point raises inflation by 0.32 over 12-months and 0.48 over 24-months.
  - A permanent nominal appreciation by one percentage point changes inflation by -0.63 over 12-months and -0.73 over 24-months.
- Under the theoretical constraint that money is neutral in the long run (sum of the estimated coefficients of money and nominal exchange rate in the lagged levels equals one):
  - A permanent increase in money supply growth by one percentage point raises inflation by 0.46 over 12-months and 0.71 over 24-months.
  - A permanent nominal appreciation by one percentage point changes inflation by -0.26 over 12-months and -0.34 over 24-months.
- Interpretation:
  - Imposing the neutrality constraint increases the estimated elasticity of inflation to money supply and reduces the elasticity to nominal exchange rate, implying part of the money supply effect operates through induced nominal depreciation.

### Limitations noted by the paper
- Data quality issues, limited observations, and structural breaks in Sudan’s economic history may bias estimates.
- Single-equation specifications do not account for interrelations among variables; SVAR and VECM approaches are applied subsequently to mitigate such biases.

*Italic: IMF Working Paper content unit _wp08189 - 1. Unit Root Tests (source PDF provided).*

### 25.      This model follows McCarthy (2000) by assuming the recursive structure of the

### _wp08189 - 25.      This model follows McCarthy (2000) by assuming the recursive structure of the

### Model structure and identifying assumptions
- The model follows McCarthy (2000) and assumes a recursive structure of the economy (Appendix II) with the following ordering and restrictions:
  - (i) foreign inflation is exogenous to the system and thus affects all disturbances to real GDP growth, nominal appreciation/depreciation, money supply growth, and inflation;
  - (ii) demand shocks to GDP (y^u) affect disturbances of the variables other than foreign inflation;
  - (iii) money supply shocks affect the disturbances of nominal appreciation/depreciation and inflation;
  - (iv) nominal appreciation/depreciation shock does not affect money supply shocks, reflecting the assumption that the central bank can set money supply growth as a policy variable.
- The recursive structural VAR implied by these assumptions is presented in Appendix II as a linear system of five equations and summarized in matrix form as a recursive (structural) VAR: B y_t = A(L) y_{t-1}.

### Structural VAR estimation and impulse responses
- Lag length selection:
  - The length of lag is selected based on the Schwarz Information Criterion (SIC) (Table 4). For the structural VAR the SIC values reported are:
    - # of lags = 1: SIC = -27.90
    - # of lags = 2: SIC = -27.54
    - # of lags = 3: SIC = -27.29
    - # of lags = 4: SIC = -26.31
    - # of lags = 5: SIC = -26.85
- Main structural VAR findings (lag = 1 unless noted):
  - Both nominal depreciation and an increase in money supply growth result in higher inflation; the response of inflation to nominal appreciation is marginally significant.
  - Most of the adjustment of inflation occurs within one year (impulse response charts).
- Elasticities from the structural VAR (lag = 1):
  - Estimated elasticities of inflation to money supply and nominal exchange rate are:
    - 12-months: 0.57 and -0.23
    - 24-months: 0.57 and -0.25
  - Alternative structural VAR with 2 lags (the second smallest SIC value) yields elasticities:
    - 12-months: 0.26 and -0.48
    - 24-months: 0.21 and -0.63
  - Interpretation: with longer lag length the elasticity to nominal exchange rate becomes larger than that to money supply, consistent with time-lag effects of monetary policy.

### Vector Error Correction Model (VECM) results
- System specification:
  - The VECM is expressed as Δx_t = φ(L) Δx_{t-1} + δ z_{t-1} + γ' u_t where Δ denotes first difference and δ is the co-integration vector(s). The lag length for the VECM is selected to be 2 based on SIC (Table 4).
- Co-integration test results:
  - Johansen tests (Table 5) suggest two co-integration vectors. Trace and Max-Eigen statistics indicate rejection of "None" and "At most 1" at 5% significance.
- VECM-derived elasticities (from impulse responses):
  - 12-months: money supply = 0.15; nominal exchange rate = -0.41
  - 24-months: money supply = 0.34; nominal exchange rate = -0.99
- Variance decomposition (based on the estimated VEC system, # of lags = 2):
  - More than 80 percent of CPI inflation fluctuations in Sudan in recent years could be explained by:
    - money supply: about 25 percent
    - nominal exchange rate: about 55 percent
  - This VECM decomposition explains inflation substantially better than the structural VAR (lag = 1) and suggests most adjustment of inflation occurs over 18-24 months—longer than the structural VAR—reflecting the long-run relation captured by the VEC system.

### Single-equation model and comparisons (selected results)
- Single-equation elasticities of inflation to money supply and nominal exchange rate (Table 3 excerpts):
  - (Based on the single-equation model)
    - 12 months: Money Supply = 0.32; Nominal Exchange Rate = -0.63
    - 24 months: Money Supply = 0.48; Nominal Exchange Rate = -0.73
  - (Based on the single-equation model with the long-run constraint)
    - 12 months: Money Supply = 0.46; Nominal Exchange Rate = -0.26
    - 24 months: Money Supply = 0.71; Nominal Exchange Rate = -0.34
  - (Based on the structural VAR)
    - 12 months: Money Supply = 0.57; Nominal Exchange Rate = -0.23
    - 24 months: Money Supply = 0.57; Nominal Exchange Rate = -0.25
  - (Based on the VECM)
    - 12 months: Money Supply = 0.15; Nominal Exchange Rate = -0.41
    - 24 months: Money Supply = 0.34; Nominal Exchange Rate = -0.99

### Policy implications and conclusions
- Robust results across methods:
  - (i) Both money supply and the nominal exchange rate affect inflation in Sudan; the nominal exchange rate appears to have a stronger impact on inflation than money supply when time-lag effects and long-run relations are accounted for.
  - (ii) The long-run relationship implied by the error correction term and the co-integration vectors significantly affects inflation dynamics in Sudan; estimated time lag is from 18 to 24 months.
  - (iii) The estimated elasticity of inflation to money supply is substantially lower than one. The single-equation model with a long-run constraint suggests money supply growth may affect inflation through nominal exchange rate fluctuations.
  - (iv) The sum of the elasticities of inflation to money supply and nominal exchange rate is not far from one in the long run, broadly confirming the simple quantity theory of money in an open economy and implying usefulness for monetary programming over the short to medium term.
- Empirical context and recent developments:
  - Stable food prices contributed to low overall CPI inflation during H2 2005 and throughout 2006 despite faster monetary growth since early 2005.
  - The nominal appreciation of the dinar/pound by about 20 percent vis-à-vis the U.S. dollar during 2005 and 2006 helped mitigate inflationary pressures through lower import prices.
  - Decline in money supply growth after sharp appreciation of dinar/pound after H2 2006 appears to have lessened inflationary pressures during 2007 (excluding food, energy, and transportation, accounting for fuel subsidy elimination level shift).
- Policy recommendations and considerations for the Bank of Sudan (BOS):
  - The large elasticity of inflation to the nominal exchange rate aligns with authorities’ emphasis on nominal exchange rate stability; since early 2007 the BOS has intervened by selling foreign exchange to stabilize the nominal exchange rate—even at the cost of a sharp decline in international reserves.
  - Authorities recognize that exchange rate flexibility is necessary to rebuild reserves but emphasize smoothing short-term volatility for macroeconomic stability.
  - High elasticity of inflation to the nominal exchange rate implies nominal depreciation from allowing exchange rate flexibility would cause higher inflation, raising the user cost of capital and potentially causing a sharp decline in investment.
  - Given the relation between oil prices and the real exchange rate, BOS should fine tune policy to focus more on maintaining stable inflation.
  - Caution is warranted due to data limitations and possible structural changes; nevertheless, the estimated relations between inflation, money supply, and nominal exchange rate should help BOS construct and implement its monetary policy framework based on economic theory and empirical results.

### Data, tests, and auxiliary results
- Data span and features:
  - The data in this paper spans Q1 1995 to Q2 2007 and excludes the large devaluation of the domestic currency in 1994 (by about 45 percent from Q2 to Q3).
  - A dummy variable captures the 1997 change in the monetary policy regime; a Q3 2006 dummy captures level change in price level caused by the reduction in the domestic fuel subsidy.
  - All data are quarterly. CPI (seasonally adjusted) from IFS; money supply (money plus quasi-money) from IFS with X-12 ARIMA seasonal adjustment; quarterly non-oil GDP estimated by linear projection of annual non-oil GDP from WEO and IMF staff estimates; foreign inflation proxied by the world GDP deflator (imports weighted average) from GEE.
  - Nominal exchange rate proxy: import weighted average of the nominal exchange rate (calculated from Direction of Trade Statistics) and the nominal exchange rate (from INS) used as proxy for imported price index.
- Unit root and cointegration diagnostics:
  - Unit root tests (first difference) reported in Table 1 (ADF, DF-GLS, PP tests) broadly consistent with I(1) for CPI, broad money, non-oil GDP, trade-weighted FX, foreign deflator. Selected values (first difference) include:
    - CPI: ADF = -1.450; DF-GLS = -3.456**; PP = -3.737**
    - Broad money: ADF = -6.014***; DF-GLS = -6.004***; PP = -6.081***
    - Non-oil GDP: ADF = -3.088; DF-GLS = -3.154*; PP = -3.221*
    - Trade weighted FX: ADF = -5.733***; DF-GLS = -4.864***; PP = -8.784***
    - Foreign deflator: ADF = -3.032**; DF-GLS = -2.167; PP = -2.926**
  - Johansen co-integration tests (Table 5) show:
    - Unrestricted Trace test: "None" Trace Statistic = 46.477 (5% Critical Value = 38.804, P-value = 0.000) → reject none.
    - Unrestricted Max-Eigen test: "None" Max-Eigen Statistic = 22.014 (5% Critical Value = 38.331, P-value = 0.000) and subsequent rows lead to conclusion of two co-integration vectors overall.
- Estimated single-equation regressions (Table 2) include:
  - Error correction term coefficients: -0.307 and -0.313 (t-statistics (-2.85) and (-2.88)).
  - Adjusted R^2 values: 0.904, 0.929, 0.930, 0.921 across reported specifications.
- SIC/AIC reporting for VECM (Table 4) shows:
  - VECM # of lags = 1: SIC = -28.00; AIC = -29.98
  - VECM # of lags = 2: SIC = -28.15; AIC = -31.12
  - VECM # of lags = 3: SIC = -27.50; AIC = -31.44

*Italic: Content derived from _wp08189 (PDF chapter/section provided).*

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