## _wp0878 - 4.    VAR    Residual    Serial    Correlation LM Tests

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---

### Key objectives and scope
- Assess extent to which external shocks (exchange rate, oil, and import prices) affect inflation in Sri Lanka using a VAR model that incorporates a distribution chain of pricing.
- Determine pass-through coefficients and use variance decompositions to assess how much external shocks explain variation in inflation.
- Sample period: 2003m1 to 2007m7 (monthly data).

### Main findings — high-level
- Inflation rose from about 7 percent to 19 percent between the beginning of 2006 and the end of 2007.
- Pass-through of external shocks to domestic consumer prices is incomplete:
  - Pass-through to consumer prices: about 10 percent during the first month rising to about 40 percent in four months (introductory summary).
  - Pass-through of oil price shocks to consumer prices: about 2 percent during the first month rising to about 6 percent in four months (introductory summary).
  - Pass-through of import prices to consumer prices: about 4 percent in the first month rising to about 28 percent in three months (introductory summary).
- External shocks explain about 25 percent of the variation in consumer prices:
  - Oil: about 6 percent
  - Exchange rate: about 10 percent
  - Import prices: about 11 percent
- External shocks explain about 22 percent of the variation in wholesale prices:
  - Oil: about 5 percent
  - Exchange rate: about 6 percent
  - Import prices: about 11 percent
- Other contributors to variation in consumer price inflation:
  - Wholesale price inflation: about 11 percent
  - Broad money: about 10 percent
  - Output gap: about 6 percent
- Core inflation: external shocks appear to explain about 32 percent of the variation in core inflation (introductory summary).

### Relevant background and motivation
- Recent sharp increase in Sri Lanka inflation prompted analysis of sources: rising international oil prices, demand pressures, adjustments in administered prices, and exchange rate movements.
- Exchange rate is an important monetary transmission channel; the study focuses on exchange rate channel, oil prices (as they feed through the exchange rate), and import prices.
- Administered prices and government subsidies in Sri Lanka help explain low and incomplete pass-through.

### VAR model structure and identification
- Model: recursive VAR with Cholesky orthogonalization; distribution-chain pricing model linking import, wholesale, and consumer price inflation.
- Variables included (7):
  - Oil price inflation (π_oil)
  - Output gap (ygap)
  - Change in nominal exchange rate (Δe) — Sri Lankan rupees per U.S. dollar (an increase = depreciation)
  - Import price inflation (π_MP)
  - Wholesale price inflation (π_WPI)
  - Colombo consumer price inflation (π_CCPIN)
  - Broad money (Δm)
- Ordering rationale: broad money last to capture a monetary policy reaction function under Sri Lanka’s reserve money targeting framework with indicative broad money targets.
- Identification: shocks ε_sit, ε_dit, ε_eit are supply, demand, and exchange rate shocks; shocks assumed serially uncorrelated and uncorrelated with one another within a period. Expectation operator E_{t-1} used in model equations.

### Data transformations and stationarity
- Variables expressed in log terms (except output gap).
- Unit root test results (ADF Statistic and Order of Integration):
  - Oil price: ADF Statistic -7.432904*   Order of Integration I(1)
  - Output gap: ADF Statistic -6.422854*   Order of Integration I(0)
  - Exchange rate: ADF Statistic -6.332869*   Order of Integration I(1)
  - Import prices: ADF Statistic -9.892428*   Order of Integration I(1)
  - Wholesale prices: ADF Statistic -7.808793*   Order of Integration I(1)
  - Colombo consumer price inflation (New): ADF Statistic -5.684348*   Order of Integration I(1)
  - Broad money: ADF Statistic -5.646375*   Order of Integration I(1)
- Cointegration tests (with output gap exogenous): variables found not to be cointegrated.
- VAR uses stationary transformations: all variables enter in first differences except the output gap (enters in levels).

### VAR specification, lag selection, and residual diagnostics
- Lag selection criteria (sequential modified LR, AIC, FPE, HQ, BIC) initially select zero lags.
- Wald lag exclusion tests indicate two lags are jointly significant for all equations; VAR estimated with two lags.
- Residual serial correlation LM tests (multivariate serial correlation Lagrange Multiplier test; Probabilities from chi-square with 36 df; null is no serial correlation at lag order h):
  - Lag 1: LM-Stat 131.4624  Prob 0.9757
  - Lag 2: LM-Stat 41.37715  Prob 0.7721
  - Lag 3: LM-Stat 42.73531  Prob 0.7237
  - Lag 4: LM-Stat 29.27955  Prob 0.9886
  - Lag 5: LM-Stat 58.29207  Prob 0.1707
- Note: Null hypothesis of no serial correlation at lag order 2 cannot be rejected.
- Visual inspection of residuals reveals no major outliers.

### Impulse response and pass-through results (detailed)
- Impulse responses (orthogonalized) for wholesale and consumer prices to one standard deviation innovations in exchange rate, oil prices, and import prices:
  - Exchange rate shock (depreciation):
    - Immediate and positive effect on wholesale and consumer prices.
    - Maximum effect on wholesale prices in the second month; on consumer prices between the second and third month.
    - Impact falls and dies out more quickly on wholesale prices than on consumer prices.
    - Impact on consumer prices turns negative after four months, reflecting consumer adjustment processes.
  - Oil price shocks:
    - Ambiguous; appear to have an immediate negative impact on prices (an effect during the first month).
    - Pass-through of oil price shocks to prices is small and negative in impulse responses; oil subsidies and administered pricing help contain the pass-through.
    - Oil price shock has a positive impact on administered prices (high weights of kerosene and electricity).
  - Import price shocks:
    - Immediate and positive impact on wholesale and consumer prices.
    - Maximum effect: first month for wholesale prices; second month for consumer prices.
    - Shock persists for about seven to eight months in both wholesale and consumer prices.
- Cumulative pass-through coefficients (examples of reported figures):
  - Exchange rate pass-through:
    - Pass-through to consumer prices rises from about 8 percent in the first month to about 40 percent in six months.
    - Exchange rate pass-through to wholesale prices: about 20 percent in first month rising to about 49 percent in six months.
    - Bulk of pass-through to both consumer and wholesale prices occurs in the first four months.
    - About 40 percent of a depreciation is reflected in consumer prices after 10 months.
  - Oil price pass-through:
    - Small and negative overall; limited impact on inflation owing to implicit and explicit oil subsidies and administered pricing.
  - Import price pass-through:
    - Positive and more pronounced on wholesale than consumer prices.
    - About 19 percent of an import price shock is reflected in consumer prices after 10 months.

### Explanations and contextual factors for low/incomplete pass-through
- Government subsidies (especially oil subsidies) and administered prices have long curtailed impact of oil prices and the exchange rate on consumer prices. Recent elimination of subsidies in the budget and gradual administered price increases between 2006 and 2007 contributed to the rise in inflation.
- Food prices carry the largest weight (about 47 percent) on the CCPIN and are subject to erratic weather, affecting inflation.
- Low volatility of the exchange rate: variance of residuals from the exchange rate equation is low, contributing to low pass-through.
- Low persistence of the exchange rate: response of exchange rate to own shock dies out in about six to eight months in Sri Lanka, implying lower pass-through relative to economies where it dies out after at least two years.

### Policy-relevant implications
- The limited pass-through of external shocks suggests that other domestic shocks explain most of the variation in inflation; monetary and fiscal policies and administered price reforms have played important roles.
- Monitoring administered price adjustments, subsidy reforms, and food price volatility is important for understanding and managing inflation dynamics.
- Broad money matters for inflation variation (about 10 percent); monetary policy stance and its interaction with exchange rate movements are relevant for inflation control.
- Fiscal stance: fiscal policy was rather loose with fiscal deficits at 7 percent and above in the recent past, contributing to domestic inflationary pressures.
- Conclusion: Given low pass-through of external shocks and that external shocks explain a small percentage of the variation in inflation, domestic shocks likely play a more significant role; thus domestic policies can be very important in containing inflation.

### Sensitivity analysis and robustness
- Two alternative Cholesky orderings were tested; results are robust to different orderings:
  - Ordering A: oil prices, import prices, exchange rate, output gap, wholesale prices, consumer prices, broad money (import prices before exchange rate and output gap). This ordering did not change the findings.
  - Ordering B: oil prices, exchange rate, output gap, broad money, import prices, wholesale prices, consumer price inflation (broad money placed after output gap). This ordering did not change the findings.
- Impulse response functions and variance decompositions were used throughout; standard error bands are reported in appendices.

### Methodological notes
- Results are derived from a recursive VAR model using impulse response functions and variance decompositions.
- Variable transformations: “D” denotes the first difference operator; “L” denotes the log (e.g., D(LOIL) is the first difference of the log of oil; YGAP is the output gap; D(LE) is the first difference of the log of the exchange rate; D(LMP) is the first difference of the log of import prices; D(LWPI) is the first difference of the log of wholesale prices; D(LCCPIN) is the first difference of the log of consumer prices; D(LM) is the first difference of the log of broad money).
- The administered price variable was found stationary in first differences and not in levels; administered-price model estimated with data up to 2007m3 due to data limitations.

*Source: _wp0878 - 4.    VAR    Residual    Serial    Correlation LM Tests.*

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

### _wp0878 - References..............................................................................................................

### Figures
- 1.    Headline Inflation in Selected Asian Countries..................................................................5
- 2.    Exchange Rates and Prices .................................................................................................5

### Tables
- 1.    Unit Root Tests ...................................................................................................................8
- 2.    VAR Lag Length Selection Criteria ...................................................................................9
- 3.    VAR Lag Exclusion Wald Tests.........................................................................................9

*Source: _wp0878 - References.*

### 4.    VAR    Residual    Serial    Correlation LM Tests ................................................................

### _wp0878 - 4.    VAR    Residual    Serial    Correlation LM Tests ................................................................ 

### Key objectives and scope
- Assess extent to which external shocks (exchange rate, oil, and import prices) affect inflation in Sri Lanka using a VAR model that incorporates a distribution chain of pricing.
- Determine pass-through coefficients and use variance decompositions to assess how much external shocks explain variation in inflation.
- Sample period: 2003m1 to 2007m7 (monthly data).

### Main findings — high-level
- Inflation rose from about 7 percent to 19 percent between the beginning of 2006 and the end of 2007.
- Pass-through of external shocks to domestic consumer prices is incomplete.
  - Pass-through to consumer prices: about 10 percent during the first month rising to about 40 percent in four months (introductory summary).
  - Pass-through of oil price shocks to consumer prices: about 2 percent during the first month rising to about 6 percent in four months (introductory summary).
  - Pass-through of import prices to consumer prices: about 4 percent in the first month rising to about 28 percent in three months (introductory summary).
- External shocks explain about 25 percent of the variation in consumer prices (breakdown: 6 percent from oil, 10 percent from the exchange rate, and 11 percent from import prices).
- External shocks explain about 22 percent of the variation in wholesale prices (breakdown: 5 percent from oil, 6 percent from the exchange rate, and 11 percent from import prices).
- Other contributors to variation in consumer price inflation:
  - Wholesale price inflation: about 11 percent.
  - Broad money: about 10 percent.
  - Output gap: about 6 percent.
- Core inflation: external shocks appear to explain about 32 percent of the variation in core inflation (introductory summary).

### Relevant background and motivation
- Recent sharp increase in Sri Lanka inflation prompted analysis of sources: rising international oil prices, demand pressures, adjustments in administered prices, and exchange rate movements.
- Exchange rate is an important monetary transmission channel; the study focuses on exchange rate channel, oil prices (as they feed through the exchange rate), and import prices.
- Administered prices and government subsidies in Sri Lanka help explain low and incomplete pass-through.

### VAR model structure and identification
- Model: recursive VAR with Cholesky orthogonalization; distribution-chain pricing model linking import, wholesale, and consumer price inflation.
- Variables included (7):
  - Oil price inflation (π_oil)
  - Output gap (ygap)
  - Change in nominal exchange rate (Δe) — Sri Lankan rupees per U.S. dollar (an increase = depreciation)
  - Import price inflation (π_MP)
  - Wholesale price inflation (π_WPI)
  - Colombo consumer price inflation (π_CCPIN)
  - Broad money (Δm)
- Ordering rationale: broad money last to capture a monetary policy reaction function under Sri Lanka’s reserve money targeting framework with indicative broad money targets.
- Identification: shocks ε_sit, ε_dit, ε_eit are supply, demand, and exchange rate shocks; shocks assumed serially uncorrelated and uncorrelated with one another within a period. Expectation operator E_{t-1} used in model equations (see equations (1)–(7) in source).

### Data transformations and stationarity
- Variables expressed in log terms (except output gap); unit root tests show:
  - Oil price: ADF Statistic -7.432904*   Order of Integration I(1)
  - Output gap: ADF Statistic -6.422854*   Order of Integration I(0)
  - Exchange rate: ADF Statistic -6.332869*   Order of Integration I(1)
  - Import prices: ADF Statistic -9.892428*   Order of Integration I(1)
  - Wholesale prices: ADF Statistic -7.808793*   Order of Integration I(1)
  - Colombo consumer price inflation (New): ADF Statistic -5.684348*   Order of Integration I(1)
  - Broad money: ADF Statistic -5.646375*   Order of Integration I(1)
- Cointegration tests (with output gap exogenous): variables found not to be cointegrated.
- VAR uses stationary transformations: all variables enter in first differences except the output gap (enters in levels).

### VAR specification, lag selection, and residual diagnostics
- Lag selection criteria (sequential modified LR, AIC, FPE, HQ, BIC) initially select zero lags (Table 2).
- Wald lag exclusion tests indicate two lags are jointly significant for all equations; VAR estimated with two lags.
- Residual serial correlation LM tests (Table 4) — multivariate serial correlation Lagrange Multiplier (LM) test shows the null hypothesis of no serial correlation at lag order 2 cannot be rejected:
  - Lag 1: LM-Stat 131.4624  Prob 0.9757
  - Lag 2: LM-Stat 41.37715  Prob 0.7721
  - Lag 3: LM-Stat 42.73531  Prob 0.7237
  - Lag 4: LM-Stat 29.27955  Prob 0.9886
  - Lag 5: LM-Stat 58.29207  Prob 0.1707
  - Note: Probabilities are from chi-square with 36 df; null is no serial correlation at lag order h.
- Visual inspection of residuals reveals no major outliers.

### Impulse response and pass-through results (detailed)
- Impulse responses (orthogonalized) for wholesale and consumer prices to one standard deviation innovations in exchange rate, oil prices, and import prices (Appendix II):
  - Exchange rate shock (depreciation):
    - Immediate and positive effect on wholesale and consumer prices.
    - Maximum effect on wholesale prices in the second month; on consumer prices between the second and third month.
    - Impact falls and dies out more quickly on wholesale prices than on consumer prices.
    - Impact on consumer prices turns negative after four months, reflecting consumer adjustment processes.
  - Oil price shocks:
    - Ambiguous; appear to have an immediate negative impact on prices (an effect during the first month).
    - Pass-through of oil price shocks to prices is small and negative in impulse responses; oil subsidies and administered pricing help contain the pass-through.
    - Oil price shock has a positive impact on administered prices (high weights of kerosene and electricity).
  - Import price shocks:
    - Immediate and positive impact on wholesale and consumer prices.
    - Maximum effect: first month for wholesale prices; second month for consumer prices.
    - Shock persists for about seven to eight months in both wholesale and consumer prices.
- Cumulative pass-through coefficients (Appendix III) — examples of reported figures:
  - Exchange rate pass-through:
    - Pass-through to consumer prices rises from about 8 percent in the first month to about 40 percent in six months (model results section).
    - Exchange rate pass-through to wholesale prices: about 20 percent in first month rising to about 49 percent in six months.
    - Bulk of pass-through to both consumer and wholesale prices occurs in the first four months.
    - About 40 percent of a depreciation is reflected in consumer prices after 10 months (model results section).
  - Oil price pass-through:
    - Small and negative overall; limited impact on inflation owing to implicit and explicit oil subsidies and administered pricing.
  - Import price pass-through:
    - Positive and more pronounced on wholesale than consumer prices.
    - About 19 percent of an import price shock is reflected in consumer prices after 10 months (model results section).

### Explanations and contextual factors for low/incomplete pass-through
- Government subsidies (especially oil subsidies) and administered prices have long curtailed impact of oil prices and the exchange rate on consumer prices. Recent elimination of subsidies in the budget and gradual administered price increases between 2006 and 2007 contributed to the rise in inflation.
- Food prices: carry the largest weight (about 47 percent) on the CCPIN and are subject to erratic weather, affecting inflation.
- Low volatility of the exchange rate: variance of residuals from the exchange rate equation is low, contributing to low pass-through.
- Low persistence of the exchange rate: response of exchange rate to own shock dies out in about six to eight months in Sri Lanka (compared to economies where it can die out after at least two years), implying lower pass-through.

### Policy-relevant implications (as presented)
- The limited pass-through of external shocks suggests that other domestic shocks explain most of the variation in inflation; monetary and fiscal policies and administered price reforms have played important roles.
- Monitoring administered price adjustments, subsidy reforms, and food price volatility is important for understanding and managing inflation dynamics.
- Broad money matters for inflation variation (about 10 percent); monetary policy stance and its interaction with exchange rate movements are relevant for inflation control.

*Source: _wp0878 - 4.    VAR    Residual    Serial    Correlation LM Tests ................................................................*

### 0.05 percent increase in inflation after about two-quarters in Tanzania, partly due to the

### _wp0878 - 0.05 percent increase in inflation after about two-quarters in Tanzania, partly due to the

### Main findings on pass-through to inflation
- Pass-through of external shocks to consumer prices is incomplete: pass-through to consumer prices rises from about 10 percent in the first month of the shock to about 40 percent in six months. The bulk of pass-through occurs in the first four months of the shock.
- Pass-through to wholesale prices is more pronounced than to consumer prices, implying the impact of external shocks declines as one moves down the distribution chain.
- The impact of oil price shocks on consumer prices is rather small and negative, partly reflecting implicit and explicit oil subsidies.
- In a model replacing consumer inflation with administered price inflation:
  - Oil pass-through to administered prices rises from about 2 percent during the second month to about 7 percent in seven months.
  - Oil pass-through to administered prices is slightly larger than to consumer prices.
  - Exchange rate pass-through to administered prices is negative.
  - Import prices explain more variation in administered prices than in consumer prices, suggesting administered prices are adjusted more in line with import price changes.
- Using Sri Lanka core inflation (DCS definition) instead of general consumer inflation:
  - Exchange rate pass-through to core inflation is 18 percent in the month of the shock and rises to 62 percent in four months.
  - This compares with exchange rate pass-through to general consumer prices of 8 percent in the first months to 41 percent in four months.
  - Oil price pass-through to core inflation is also negative but slightly higher compared to that on general consumer prices.
  - External shocks (exchange rate, oil price, and import price shocks) explain about 28 percent of the variation in core inflation.
  - About 50 percent of the variation in core inflation is still not explained by the variables in the model.

### Sensitivity analysis and robustness
- Two alternative Cholesky orderings were tested; results are robust to different orderings:
  - Ordering A: oil prices, import prices, exchange rate, output gap, wholesale prices, consumer prices, broad money (import prices before exchange rate and output gap). This ordering did not change the findings.
  - Ordering B: oil prices, exchange rate, output gap, broad money, import prices, wholesale prices, consumer price inflation (broad money placed after output gap). This ordering did not change the findings.
- Impulse response functions and variance decompositions were used throughout; standard error bands are reported in appendices.

### Domestic policy context and implications
- Low and incomplete exchange rate pass-through implies domestic policies are important for influencing inflation.
- High Sri Lanka inflation partly reflects the policy environment:
  - The output gap was positive in the recent past, indicating the economy operated above potential and resulted in inflationary pressures.
  - Monetary policy tightened somewhat between 2006 and 2007 but was largely insufficient to contain inflation.
  - Fiscal policy was rather loose with fiscal deficits at 7 percent and above in the recent past.
- Conclusion: Given low pass-through of external shocks and that external shocks explain a small percentage of the variation in inflation, domestic shocks likely play a more significant role; thus domestic policies can be very important in containing inflation.

### Methodological notes
- Results are derived from a recursive VAR model using impulse response functions and variance decompositions.
- Variable transformations: “D” denotes the first difference operator; “L” denotes the log (e.g., D(LOIL) is the first difference of the log of oil; YGAP is the output gap; D(LE) is the first difference of the log of the exchange rate; D(LMP) is the first difference of the log of import prices; D(LWPI) is the first difference of the log of wholesale prices; D(LCCPIN) is the first difference of the log of consumer prices; D(LM) is the first difference of the log of broad money).
- The administered price variable was found stationary in first differences and not in levels; administered-price model estimated with data up to 2007m3 due to data limitations.

*Source: IMF working paper content provided in the supplied PDF excerpt.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0878.pdf_