## _wp11291 - References

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---

### I. Introduction — scope and modeling approach
- Objective:
  - Generalize Esfahani et al. (2009) to an oil-importing but labor-exporting small open economy receiving large inflows of external income (remittances, grants, and FDI), and examine the importance of external income shocks (mainly arising from oil price disturbances) in growth dynamics.
- Empirical framework:
  - Cointegrating vector autoregressive model with exogenous variables (VARX* model) estimated jointly for a set of endogenous and foreign variables to account for simultaneity.
- Endogenous variables in the VARX* model:
  - real GDP
  - consumer price index (CPI) inflation
  - real exchange rate
  - the differential between the foreign interest rate and the Central Bank of Jordan rediscount (policy) rate
- Key foreign (exogenous) variables (weighted averages across 33 major trading partners using trade shares):
  - rest of the world’s output
  - foreign inflation
  - foreign interest rate
- Data frequency and sample size:
  - quarterly data
  - model has only 121 observations
  - VARX* estimated using quarterly data over the period 1979Q2 to 2009Q4 (modeling and tests reference 1979Q4 to 2009Q4 for specific estimations)
- Estimation methods and safeguards:
  - Bootstrap non-parametric method used to address small-sample issues (for cointegration tests, LR statistics of over-identifying restrictions, and impulse response confidence intervals)
  - Use of generalized impulse response functions and persistence profiles (with 95 percent bootstrapped confidence bounds) to analyze dynamics and speed of adjustment

### II. Theoretical model and long-run output relation
- Economic intuition:
  - Oil price booms have two effects on a labor-exporting, oil-importing country: direct negative effect via higher import bill; indirect positive effect via larger inflows of external income.
  - If the external income to GDP ratio remains high or stable, the indirect positive effect can dominate, making oil prices a long-run driver of real output.
- Definition of external income:
  - X_t = sum of general government transfers, workers’ remittances, and foreign direct investment (FDI)
- Empirical observation motivating model choice:
  - External income and oil prices share the same long-run trend with short-run deviations; oil prices are an excellent proxy for external income in Jordan.
  - Co-trending restriction (zero coefficient on trend) is not rejected, and the hypothesis that the long-run elasticity of external income to oil prices is unity cannot be rejected, yielding x_t = p_oil_t + ξ_{x,t}, where ξ_{x,t} is I(0).
- Rationale for using oil prices p_oil_t rather than external income x_t in the long-run relation:
  - p_oil_t is likely exogenous to Jordan while x_t may not be.
  - Inclusion of p_oil_t captures both direct negative and indirect positive effects of oil price movements on equilibrium output, whereas x_t would capture primarily the indirect positive impact.
- Concerns addressed:
  - Persistence of external income depends on oil-producing countries’ ability to continue production; reserves-to-extraction ratios indicate many major exporters can produce for many decades.
  - Oil income to GDP ratios for major exporters have remained relatively stable (and in some cases rising), implying continued external income flows to Jordan in the foreseeable future.

### III. Long-run output equation (augmented output gap)
- Augmented output gap equation:
  - y_t − 1 y’_t = 2 (e_t − p_t) + 3 p_oil_t + c_y + y_t + ξ_{y,t} ; (1)
- Variable definitions in equation (1):
  - y_t (y’_t) is the logarithm of real domestic (foreign) output
  - e_t is the log of the nominal exchange rate
  - p_t is the logarithm of the domestic Consumer Price Index (CPI)
  - p_oil_t is the log of nominal oil prices
  - c_y is a fixed constant
  - ξ_{y,t} is a mean zero stationary process representing the error correction term of the long-run output equation

### IV. Data, construction, and integration properties
- Sample and coverage:
  - quarterly observations for Jordan and 33 countries from 1979Q1 to 2009Q4.
  - Quarterly GDP available since 1992Q1; annual data back to 1959; quarterly series between 1979Q1 and 1991Q4 interpolated (backwards) linearly from annual series.
  - Seasonal adjustment: U.S. Census Bureau’s X-12 ARIMA.
- Domestic variables definitions:
  - yt = ln(GDPt)
  - rt = 0:25 ln(1 + Rt =100)
  - et = ln(Et)
  - pt = ln(CPIt)
  - xt = ln (Xt)
  - Xt (external income) = sum of general government transfers, workers’ remittances, and foreign direct investment (FDI).
- Foreign variables:
  - xt = (yt, t, poilt)′ with poilt = ln(Poilt), Poilt = nominal price of oil per barrel in US dollars.
  - Foreign variables computed as trade-weighted averages across N = 33 trading partners; trade weights ωj.
  - Most important trading partners by weight: Saudi Arabia (26 percent), eight euro area economies (19 percent total; Germany 7 percent), United States (14 percent), China (11 percent), India (8 percent).
- Integration order:
  - Variables tested: yt, t, et pt, rt rt, yt, t, poilt.
  - Tests used: ADF, ADF-GLS (Elliott et al. (1996)), ADF-WS (Park and Fuller (1995)).
  - First differences of all seven variables: unit root hypothesis rejected by all three tests.
  - Levels: unit root not rejected.
  - Conclusion: variables are I(1).

### V. Cointegration approach, lag selection, and rank
- Model: cointegrating VARX* (VECX*(s;s)) with endogenous xt = (yt, t, et pt, rt rt)′ and exogenous xt = (yt, t, poilt)′.
- Lag selection:
  - AIC and SBC with quarterly data, max lag 4 select ^s = ^s = 2; base analysis on VARX*(2,2).
- Cointegration rank test results (VARX*(2,2)):
  - Maximal eigenvalue statistic suggests r = 1.
  - Trace statistic indicates r = 2 at 5 percent level.
  - Decision: set r = 2 (two cointegrating relations).
- Identification:
  - First cointegrating relation normalized on yt (output gap, equation (1)); second normalized on t (inflation relation, equation (3)).
  - Co-trending restrictions ′0 = (y; )′ = 0: LR statistic = 7.91; bootstrapped critical values (1,000 replications): 9.91 (5 percent), 15.26 (1 percent).
  - Conclusion: co-trending restrictions cannot be rejected based on bootstrapped critical values.

### VI. Long-run estimates and hypothesis tests (oil price included)
- Restrictions on first cointegrating relation:
  - 12 = 0; 16 = 0; 13 = 17 =  (coefficients on real exchange rate and nominal oil prices same and equal to ; coefficient on foreign output 16 free).
- Estimated parameters (reported):
  - ^ 1 = 0:9846 (0:0698)
  - ^ 2 = ^ 3 = ^ = 0:2050 (0:0616)
- LR statistic for these 3 restrictions = 26.50; bootstrapped critical values: 21.45 (5 percent), 29.06 (1 percent).
  - Rejected at 5 percent but not at 1 percent; outcome inconclusive.
- Implicit estimate of  derived from 0:9846 and 0:2050 reported as 1.24 ( > 1).
- Inflation long-run relation (second relation) restrictions:
  - 21 = 0; 23 = 0; 24 = 0; 25 = 0.
- Imposed estimates (reported):
  - ^ 1 = 0:9902 (0:0727)
  - ^ = 0:2519 (0:0717)
  - ^ 1 = 0:7558 (0:2774)
  - Coefficient on foreign inflation close to unity; null that it equals 1 cannot be rejected.
- Imposing 1 = 1 and re-estimating under 8 over-identifying restrictions yields:
  - ^ 1 = 1:0074 (0:0753)
  - ^ = 0:2477 (0::0770)
  - 1 = 1
  - Implicit  = 1:0074/(1 0:2477) = 1:34 (reported) > 1.
- LR test of eight over-identifying restrictions: LR = 31.77; bootstrapped critical values 32.13 (5 percent) and 40.65 (1 percent).
  - Conclusion: restrictions cannot be rejected at conventional levels; once oil price effects accounted for, estimates support output growth convergence between Jordan and rest of world.

### VII. Robustness: external income included instead of price of oil
- Re-specify model with external income xt included and poilt excluded; endogenous xt dimension becomes 5 and exogenous xt = (yt, t)′.
- Cointegration rank tests for this VARX*(2,2):
  - Trace statistic suggests r = 2 at 5 percent; maximal eigenvalue indicates two cointegrating relationships at 10 percent; set r = 2.
- Imposed co-trending and seven over-identifying restrictions: estimated parameters (reported):
  - ^ 1 = 0:7122 (0:0692)
  - ^ = 0:3744 (0:0640)
  - ^ 1 = 0:9325 (0:2494)
- LR statistic for these restrictions = 22.65; bootstrapped critical values: 23.89 (10 percent), 26.16 (5 percent).
  - Restrictions cannot be rejected even at 10 percent.
- Implicit  = 0:7122/(1 0:3744) = 1:14 (reported).
- Imposing 1 = 1 and 15 + 14 = 1 =>  = 1 yields:
  - ^ = 0:3756 (0:0735)
  -  = 1
  - 1 = 1
- Nine over-identifying restrictions tested: LR = 25.94; bootstrapped critical values 27.17 (10 percent) and 30.12 (5 percent). Restrictions not rejected at 10 percent.
- Comparison of estimates:
  - Impact of external income on GDP (b = 0:3756) larger than estimate with poilt (b = 0:2477).
  - Interpretation: poilt measures net effect of oil price increase on income (positive via larger external inflows increasing GDP; negative via higher cost of importing oil). Positive effect dominates.

### VIII. Short-run dynamics, persistence profiles, and impulse responses
- Persistence profiles (PPs) for cointegrating relations:
  - Inflation equation:
    - Half life < a quarter.
    - Life of shock ≈ 14 quarters.
    - Fast convergence attributed to openness and high pass-through.
  - Output equation:
    - Half life = 7 quarters.
    - Life of shock ≈ 20 quarters.
    - Persistence profile overshoots unity initially but tends to zero, verifying cointegration.
- Generalized Impulse Response Functions (GIRFs) for shocks to exogenous variables:
  - Footnote calibration: one standard error = 15, 0.6, and 0.4 percent for price of oil, foreign output, and foreign inflation respectively.
  - Unit shock to price of oil:
    - Increases domestic output yt by 4 percent (reported).
    - Increases domestic inflation t by 0.5 percent per annum (reported).
    - Appreciates real exchange rate et pt by around 4 percent (reported).
    - No statistically significant effect on interest rate spread rt rt.
    - Effects tend to be permanent due to unit roots.
    - Channel for Jordan: higher inflows of external income (remittances/grants/FDI) rather than export revenues; evidence consistent with Dutch disease-like appreciation but accompanied by higher output.
  - Unit shock to foreign output:
    - Domestic output increases by around 1.6 percent in the long run.
    - Effects on remaining variables statistically insignificant.
  - Unit shock to foreign inflation:
    - Domestic inflation increases by 1.4 percent per annum.
    - Interest rate spread decreases by 0.4 percent per annum.
  - Conclusion: oil price shock has largest and most persistent effects; foreign output and inflation shocks have smaller but non-negligible effects.

### IX. Error-correction equations and short-run fit
- Reduced-form error correction equations for endogenous variables [yt, t, (et pt), (rt rt)]:
  - Estimated significance of error correction terms ^y;t 1 and ^;t 1:
    - ^y;t 1 statistically significant in output, inflation, and real exchange rate equations; not significant in interest rate spread equation.
    - ^;t 1 significant in inflation and interest rate spread equations; not significant in output and real exchange rate equations.
  - Two error correction terms defined:
    - y;t = yt 0:2477 (0:0770) (et pt) 1:0074 (0:0753) yt 0:2477 (0:0770) poilt
    - ;t = t t
- Explanatory power and diagnostics:
  - Adjusted R2 for four equations lie in [0:260; 0:523].
  - Some large outliers in residuals noted (interest rate spread late 1980s/early 1990s; real exchange rate and inflation early sample and mid-1990s).
  - Normality of errors massively rejected for interest rate spread equation.
- Fit:
  - Actual vs fitted values track main movements reasonably well despite outliers.

### X. Policy implications and concluding remarks
- Main empirical conclusions:
  - Two cointegrating relations identified: (i) domestic-foreign inflation relation; (ii) augmented output equation linking domestic output, external income (or oil price), and foreign GDP.
  - Likelihood ratio tests do not reject over-identifying restrictions implied by economic theory.
  - Price of oil, through its impact on external income and capital accumulation, is a main long-run driver of real output in Jordan.
  - Persistence profiles and GIRFs support validity and economic relevance of identified long-run relations.
- Policy recommendations:
  - Jordan faces frequent and large external income shocks and has a relatively small tradables sector; sudden stops or reversals of capital/current inflows pose significant risks.
  - Macroeconomic and structural policies should aim to reduce vulnerability to external income shocks.
  - Suggested strategy: outward-oriented growth with a more balanced contribution of tradables and nontradables sectors to:
    - Diversify exports and provide external stimuli via exports rather than net transfers.
    - Facilitate transfer of technology and knowledge to raise productivity.
  - Acknowledged constraints: regional political/economic uncertainties, intra-regional trade barriers — hence increased tradables growth likely requires searching for new markets outside the region.
- Suggested extensions:
  - Link Jordanian VARX* to the global VAR (GVAR) framework to investigate regional shocks and differential supply/demand shock effects.
  - Apply framework to other labour-exporting, remittance-dependent countries (e.g., Bangladesh, Dominican Republic) to evaluate long-run effects of oil prices and external income on real output.

*Source: _wp11291 (PDF chapter content provided).*

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

### _wp11291 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

### I. Introduction — scope and modeling approach
- Objective: Generalize Esfahani et al. (2009) to an oil-importing but labor-exporting small open economy receiving large inflows of external income (remittances, grants, and FDI), and examine the importance of external income shocks (mainly arising from oil price disturbances) in growth dynamics.
- Empirical framework: Cointegrating vector autoregressive model with exogenous variables (VARX* model) estimated jointly for a set of endogenous and foreign variables to account for simultaneity.
- Endogenous variables in the VARX* model:
  - real GDP
  - consumer price index (CPI) inflation
  - real exchange rate
  - the differential between the foreign interest rate and the Central Bank of Jordan rediscount (policy) rate
- Key foreign (exogenous) variables (weighted averages across 33 major trading partners using trade shares):
  - rest of the world’s output
  - foreign inflation
  - foreign interest rate
- Data frequency and sample size:
  - quarterly data
  - model has only 121 observations
  - VARX* estimated using quarterly data over the period 1979Q2 to 2009Q4 (modeling and tests reference 1979Q4 to 2009Q4 for specific estimations)
- Estimation methods and safeguards:
  - Bootstrap non-parametric method used to address small-sample issues (for cointegration tests, LR statistics of over-identifying restrictions, and impulse response confidence intervals)
  - Use of generalized impulse response functions and persistence profiles (with 95 percent bootstrapped confidence bounds) to analyze dynamics and speed of adjustment

### II. Theoretical model and long-run output relation
- Economic intuition:
  - Oil price booms have two effects on a labor-exporting, oil-importing country: direct negative effect via higher import bill; indirect positive effect via larger inflows of external income.
  - If the external income to GDP ratio remains high or stable, the indirect positive effect can dominate, making oil prices a long-run driver of real output.
- Definition of external income:
  - X_t = sum of general government transfers, workers’ remittances, and foreign direct investment (FDI)
- Empirical observation motivating model choice:
  - External income and oil prices share the same long-run trend with short-run deviations; oil prices are an excellent proxy for external income in Jordan.
  - Co-trending restriction (zero coefficient on trend) is not rejected, and the hypothesis that the long-run elasticity of external income to oil prices is unity cannot be rejected, yielding x_t = p_oil_t + ξ_{x,t}, where ξ_{x,t} is I(0).
- Rationale for using oil prices p_oil_t rather than external income x_t in the long-run relation:
  - p_oil_t is likely exogenous to Jordan while x_t may not be.
  - Inclusion of p_oil_t captures both direct negative and indirect positive effects of oil price movements on equilibrium output, whereas x_t would capture primarily the indirect positive impact.
- Concerns addressed:
  - Persistence of external income depends on oil-producing countries’ ability to continue production; reserves-to-extraction ratios indicate many major exporters can produce for many decades.
  - Oil income to GDP ratios for major exporters have remained relatively stable (and in some cases rising), implying continued external income flows to Jordan in the foreseeable future.

### III. Long-run output equation (augmented output gap)
- Augmented output gap equation presented:
  y_t − 1 y’_t = 2 (e_t − p_t) + 3 p_oil_t + c_y + y_t + ξ_{y,t} ; (1)
- Variable definitions in equation (1):
  - y_t (y’_t) is the logarithm of real domestic (foreign) output
  - e_t is the log of the nominal exchange rate
  - p_t is the logarithm of the domestic Consumer Price Index (CPI)
  - p_oil_t is the log of nominal oil prices
  - c_y is a fixed constant
  - ξ_{y,t} is a mean zero stationary process representing the error correction term of the long-run output equation

### IV. Empirical findings and tests (selected results)
- Cointegration evidence between external income and oil prices:
  - Estimation: cointegrating VAR(2) for external income and oil prices
  - Table 1. Cointegration Rank Test Statistics for the VAR(2) Model with External Income and Price of Oil
    - (a) Maximal eigenvalue statistic
      - H0: r = 0 vs H1: r = 1 — Test statistic: 120.271 ; 95% Critical Value: 9.22 ; 90% Critical Value: 17.18
      - H0: r ≤ 1 vs H1: r = 2 — Test statistic: 25.89 ; 95% Critical Value: 12.39 ; 90% Critical Value: 10.55
    - (b) Trace statistic
      - H0: r = 0 vs H1: r = 2 — Test statistic: 126.16 ; 95% Critical Value: 25.77 ; 90% Critical Value: 23.08
      - H0: r ≤ 1 vs H1: r = 2 — Test statistic: 25.89 ; 95% Critical Value: 12.39 ; 90% Critical Value: 10.55
    - Notes: Test statistics are Johansen’s max-eigenvalue and trace statistics computed using 121 observations from 1979Q4 to 2009Q4.
- Long-run relations tested and retained:
  - The augmented output equation is not rejected within the VARX* model.
  - The relation involving co-movements of domestic and foreign inflations (supporting purchasing power parity, PPP) is not rejected.
  - After accounting for external income effects, estimates support output convergence between Jordan and the rest of the world.
  - Hypothesis that there are no linear trends in the cointegrating relations cannot be rejected.
- Dynamics and shock responses:
  - Persistence profiles for system-wide shocks to cointegrating relations are well-behaved: effects are transitory and die out eventually.
  - Impulse response analysis provides evidence for the importance of oil price shocks for the Jordanian economy.
- Methodological notes:
  - All estimations and test results obtained using Microfit 5.0; for technical details see Pesaran and Pesaran (2009), Section 22.10.

### V. Organization of the paper (content roadmap)
- Section II: Theory-based long-run restrictions testable within VARX*.
- Section III: Data and main macroeconomic trends in Jordan during 1979–2009.
- Section IV: Vector error correction (VECX*) model that nests long-run restrictions.
- Section V: Testing and imposing theory-driven long-run relationships within the model.
- Section VI: Short-run dynamics — speed of convergence to equilibrium, impulse responses, and error correction estimates.
- Section VII: Conclusions and policy recommendations.

*Source: _wp11291 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (PDF chapter content provided).*

### 2.1 inEsfahani et al. (2009), the coefficient of the variables in equation (1) have further

### _wp11291 - 2.1 inEsfahani et al. (2009), the coefficient of the variables in equation (1) have further

### Long-run theory and identifying restrictions
- Long-run output equation restrictions (from Section 2.1 in Esfahani et al. (2009)):
  - 1 = (1 )
  - 2 = 3 = 
  - y = (1 )(n n)
  - Definitions:  is the share of capital in output; n(n) is domestic (foreign) population growth rate;  measures diffusion/adaptation of foreign technology.
  - Interpretation of :
    -  = 1: diffusion at par with rest of world.
    -  < 1: inefficiency / prevents adoption of best practice.
    -  > 1: steady state per capita output growth in Jordan can exceed trading partners only if external income per capita rises faster than rest of world.
- Additional long-run relation for inflation (equation (3)):
  - t 1t = c + t + ;t
  - ;t is the stationary error correcting term; relation derived also from PPP (equation (4)) under fixed exchange rate.

### Data, variables construction, and sample
- Sample: quarterly observations for Jordan and 33 countries from 1979Q1 to 2009Q4 (dataset used in analysis).
- Domestic variables (log or rates) defined in equation (5):
  - yt = ln(GDPt)
  - rt = 0:25 ln(1 + Rt =100)
  - et = ln(Et)
  - pt = ln(CPIt)
  - xt = ln (Xt)
  - Xt (external income) = sum of general government transfers, workers’ remittances, and foreign direct investment (FDI).
- Seasonality and interpolation:
  - Quarterly GDP available since 1992Q1; annual data back to 1959.
  - Seasonal adjustment: U.S. Census Bureau’s X-12 ARIMA.
  - Quarterly series between 1979Q1 and 1991Q4 interpolated (backwards) linearly from annual series.
- Exogenous foreign variables:
  - xt = (yt, t, poilt)′ with poilt = ln(Poilt), Poilt = nominal price of oil per barrel in US dollars.
  - Foreign variables computed as trade-weighted averages across N = 33 trading partners; trade weights ωj given in equation (6).
  - Most important trading partners by weight: Saudi Arabia (26 percent), eight euro area economies (19 percent total; Germany 7 percent), United States (14 percent), China (11 percent), India (8 percent).

### Cointegration approach and model specification
- Model: cointegrating VARX* (VECX*(s;s)) with endogenous xt = (yt, t, et pt, rt rt)′ and exogenous xt = (yt, t, poilt)′.
- Compact long-run deviations: t = ′zt c t (equation (7)), with zt = (x′t, x′t)′ as specified.
- Restrictions for embedding theory in VECX*:
  -x = x′0 implying rank(x) = 2.
  - Co-trending restrictions:x =x′0 =, allowing possible absence of trend in long-run relations.
  - Total over-identifying restrictions: 14 4 = 10; structural parameters to estimate: , , and 1; leaving 7 over-identifying restrictions to test.

### Unit root tests and integration order
- Variables tested: yt, t, et pt, rt rt, yt, t, poilt.
- Tests used: ADF, ADF-GLS (Elliott et al. (1996)), ADF-WS (Park and Fuller (1995)).
- Result summary (Table 2):
  - First differences of all seven variables: unit root hypothesis rejected by all three tests.
  - Levels: unit root not rejected.
  - Conclusion: variables are I(1).

### Lag selection and cointegration rank
- Lag order selection (AIC and SBC) with quarterly data, max lag 4:
  - Both AIC and SBC select ^s = ^s = 2; base analysis on VARX*(2,2).
- Cointegration rank tests for VARX*(2,2) (Table 4):
  - Maximal eigenvalue statistic suggests r = 1.
  - Trace statistic indicates r = 2 at 5 percent level.
  - Decision: set r = 2 (two cointegrating relations).

### Exact identification of cointegrating vectors and imposed restrictions
- First cointegrating relation normalized on yt (output gap, equation (1)); second normalized on t (inflation relation, equation (3)).
- Exactly identified specification for cointegrating vectors given in equation (12) with rows corresponding to zt = (yt, t, et pt, rt rt, yt, t, poilt)′.
- Co-trending restrictions tested: ′0 = (y; )′ = 0.
  - LR statistic = 7.91; bootstrapped critical values (1,000 replications): 9.91 (5 percent), 15.26 (1 percent).
  - Conclusion: co-trending restrictions cannot be rejected based on bootstrapped critical values.

### Long-run estimates and hypothesis tests (price of oil included)
- Restrictions imposed on first cointegrating relation: 12 = 0; 16 = 0; 13 = 17 =  (i.e., coefficients on real exchange rate and nominal oil prices same and equal to ; allow coefficient on foreign output 16 free).
- Estimated parameters (as reported):
  - ^ 1 = 0:9846 (0:0698)  — implicit estimate of 1/(1 )? (context: coefficient on foreign output normalization).
  - ^ 2 = ^ 3 = ^ = 0:2050 (0:0616)
  - LR statistic for these 3 restrictions = 26.50; bootstrapped critical values: 21.45 (5 percent), 29.06 (1 percent).
    - Rejected at 5 percent but not at 1 percent; outcome inconclusive.
- Implicit estimate of  (from 0:9846 = (1 0:2050) -> computed in text as 1.24) — reported as significantly larger than unity suggesting  > 1.
- Second long-run inflation relation restrictions: 21 = 0; 23 = 0; 24 = 0; 25 = 0.
  - Imposed estimates reported:
    - ^ 1 = 0:9902 (0:0727)
    - ^ = 0:2519 (0:0717)
    - ^ 1 = 0:7558 (0:2774)
  - Coefficient on foreign inflation close to unity; null that it equals 1 cannot be rejected.
  - Imposing 1 = 1 and re-estimating under 8 over-identifying restrictions yields:
    - ^ 1 = 1:0074 (0:0753)
    - ^ = 0:2477 (0::0770)
    - 1 = 1
  - Implicit  = 1:0074/(1 0:2477) = 1:34 (reported) > 1 — supports hypothesis that Jordanian technological growth faster than rest of world; deviation of domestic real output from foreign output attributable to price of oil.
- LR test of eight over-identifying restrictions: LR = 31.77; bootstrapped critical values 32.13 (5 percent) and 40.65 (1 percent).
  - Conclusion: restrictions cannot be rejected at conventional levels; once oil price effects accounted for, estimates support output growth convergence between Jordan and rest of world.

### Robustness: external income included instead of price of oil
- Re-specify model with external income xt included and poilt excluded; endogenous xt dimension becomes 5 and exogenous xt = (yt, t)′.
- Cointegration rank tests for this VARX*(2,2) (Table 5):
  - Trace statistic suggests r = 2 at 5 percent; maximal eigenvalue indicates two cointegrating relationships at 10 percent; set r = 2.
- Exactly identified cointegrating vectors given in equation (13) for zt = (yt, t, et pt, rt rt, xt, yt, t)′.
- Imposed co-trending and seven over-identifying restrictions:
  - Estimated parameters:
    - ^ 1 = 0:7122 (0:0692)
    - ^ = 0:3744 (0:0640)
    - ^ 1 = 0:9325 (0:2494)
  - LR statistic for these restrictions = 22.65; bootstrapped critical values: 23.89 (10 percent), 26.16 (5 percent).
    - Restrictions cannot be rejected even at 10 percent.
  - Implicit  = 0:7122/(1 0:3744) = 1:14 (reported).
  - Imposing 1 = 1 and 15 + 14 = 1 =>  = 1 and estimates become:
    - ^ = 0:3756 (0:0735)
    -  = 1
    - 1 = 1
  - Now nine over-identifying restrictions tested: LR = 25.94; bootstrapped critical values 27.17 (10 percent) and 30.12 (5 percent). Restrictions not rejected at 10 percent.
- Comparison:
  - Impact of external income on GDP (b = 0:3756) larger than estimate with poilt (b = 0:2477).
  - Interpretation: poilt measures net effect of oil price increase on income (positive via larger external inflows increasing GDP; negative via higher cost of importing oil). Positive effect dominates.

### Short-run dynamics, persistence profiles, and impulse responses
- Persistence profiles (PPs) for cointegrating relations (Figure 6):
  - Inflation equation:
    - Half life < a quarter.
    - Life of shock ≈ 14 quarters.
    - Fast convergence attributed to openness and high pass-through.
  - Output equation:
    - Half life = 7 quarters.
    - Life of shock ≈ 20 quarters.
    - Persistence profile overshoots unity initially but tends to zero, verifying cointegration.
- Generalized Impulse Response Functions (GIRFs) for shocks to exogenous variables (Figures 7–9). A "unit shock" equals one standard error; footnote: one standard error = 15, 0.6, and 0.4 percent for price of oil, foreign output, and foreign inflation respectively.
- GIRFs: unit shock to price of oil (Figure 7):
  - Positive oil price shock effects:
    - Increases domestic output yt: quantitatively increases domestic output by 4 percent (reported).
    - Increases domestic inflation t: 0.5 percent per annum (reported).
    - Appreciates real exchange rate et pt: around 4 percent (reported).
    - No statistically significant effect on interest rate spread rt rt.
  - Effects tend to be permanent due to unit roots.
  - Similarity noted between Jordan and major oil exporters (Iran, Saudi Arabia) in response patterns (Esfahani et al. (2009)). Channel for Jordan: higher inflows of external income (remittances/grants/FDI) rather than export revenues.
  - Evidence consistent with potential Dutch disease-like appreciation but accompanied by higher output (not a clear "curse").
- GIRFs: unit shock to foreign output (Figure 8):
  - Domestic output increases by around 1.6 percent in the long run.
  - Effects on remaining variables statistically insignificant.
- GIRFs: unit shock to foreign inflation (Figure 9):
  - Domestic inflation increases by 1.4 percent per annum.
  - Interest rate spread decreases by 0.4 percent per annum.
- Conclusion: oil price shock has largest and most persistent effects; foreign output and inflation shocks have smaller but non-negligible effects.

### Error-correction equations and short-run fit
- Reduced-form error correction equations (Table 6) for endogenous variables [yt, t, (et pt), (rt rt)]:
  - Estimated significance of error correction terms ^y;t 1 and ^;t 1:
    - ^y;t 1 statistically significant in output, inflation, and real exchange rate equations; not significant in interest rate spread equation.
    - ^;t 1 significant in inflation and interest rate spread equations; not significant in output and real exchange rate equations.
  - Two error correction terms defined:
    - y;t = yt 0:2477 (0:0770) (et pt) 1:0074 (0:0753) yt 0:2477 (0:0770) poilt
    - ;t = t t
  - Explanatory power and diagnostics:
    - Adjusted R2 for four equations lie in [0:260; 0:523].
    - Some large outliers in residuals noted (interest rate spread late 1980s/early 1990s; real exchange rate and inflation early sample and mid-1990s).
    - Normality of errors massively rejected for interest rate spread equation.
- Actual vs fitted (Figure 10): fitted values track main movements reasonably well despite outliers.

### Policy implications and concluding remarks
- Main findings:
  - Two cointegrating relations identified: (i) domestic-foreign inflation relation; (ii) augmented output equation linking domestic output, external income (or oil price), and foreign GDP.
  - Likelihood ratio tests do not reject over-identifying restrictions implied by economic theory.
  - Price of oil, through its impact on external income and capital accumulation, is a main long-run driver of real output in Jordan.
  - Persistence profiles and GIRFs support validity and economic relevance of identified long-run relations.
- Policy recommendations and implications (conclusions):
  - Jordan faces frequent and large external income shocks and has a relatively small tradables sector; sudden stops or reversals of capital/current inflows pose significant risks.
  - Macroeconomic and structural policies should aim to reduce vulnerability to external income shocks.
  - Suggested strategy: outward-oriented growth with a more balanced contribution of tradables and nontradables sectors to:
    - Diversify exports and provide external stimuli via exports rather than net transfers.
    - Facilitate transfer of technology and knowledge to raise productivity.
  - Acknowledged constraints: regional political/economic uncertainties, intra-regional trade barriers — hence increased tradables growth likely requires searching for new markets outside the region.
- Extensions suggested:
  - Link Jordanian VARX* to the global VAR (GVAR) framework (Dees et al. (2007)) to investigate regional shocks and differential supply/demand shock effects.
  - Apply framework to other labour-exporting, remittance-dependent countries (e.g., Bangladesh, Dominican Republic) to evaluate long-run effects of oil prices and external income on real output.

*Italic source: Excerpts from the IMF working paper content unit provided.*

### REFERENCES

### _wp11291 - REFERENCES

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