## _wp0966 — 1. Long-Term Trends and Business Cycle Movements from Trends

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---

### Introduction
- Purpose: extend a small open economy quarterly projections model (QPM) for Armenia into a New Keynesian-type DSGE model with microeconomic foundations to analyze monetary policy transmission and responses to shocks.
- Model features emphasized:
  - imperfect competition and nominal rigidities;
  - deviations of macro variables from long-term trends (“gap” model);
  - explicit LOP gap (wedge between world price in domestic currency and domestic price of same imported goods);
  - imported-goods distributors use domestic labor as an input, so domestic unit labor costs influence imported-goods pricing;
  - remittances modeled as a foreign consumption/preference shock that induces remittances and affects the exchange rate via uncovered interest parity.
- Calibration and evaluation: model calibrated to Armenia; impulse response functions and business-cycle pattern comparisons used to assess behavior.
- Paper organization: Section II (stylized facts), Section III (model environment), Section IV (model responses and data correspondence), Section V (conclusions).

### Stylized Facts about the Armenian Economy (2001–07)
- Macro context:
  - Successful disinflation and double-digit economic growth since 2001.
  - Fiscal and quasi-fiscal consolidation in late 1990s reduced inflation to single digits; largely independent central bank supported tight monetary policy.
  - Since end-2003, large external shocks in the form of sizeable remittance inflows.
  - Shift toward implicit inflation targeting; since 2006 short-term inflation targets using the interest rate as instrument were adopted.
- Key long-term features and averages (2001–07):
  - GDP growth: 11.6 percent.
  - Consumption growth: 8.5 percent.
  - Productivity growth averaged: 12 percent.
  - Consumption share decline: from 92 percent in 2001 to 72 percent in 2007.
  - Remittances growth:
    - grew on average by 20 percent in 2001–03;
    - grew on average by 38 percent from 2004 onwards.
  - Inflation:
    - average inflation: 3.4 percent during 2001–07;
    - domestic inflation: 4.3 percent (average);
    - imported good inflation: 1.7 percent (average).
  - Exchange rate movements:
    - nominal exchange rate appreciated by more than 40 percent during 2004-2007 while imported good prices declined by less than 5 percent;
    - real exchange rate: depreciated during 2002–03, then permanent appreciating trend from second half of 2004.
  - Interest rates: declining trend associated with financial deepening, foreign bank entry, and increased bank capital.
- Structural interpretations relevant for modeling:
  - incomplete pass-through of exchange rate to imported goods due to distribution/retailing frictions and domestic unit labor costs influence;
  - demand for imported goods influences domestic output via labor demand in imported-goods distribution sector (evidence: sustained exchange rate appreciation coincided with increased labor in imported-goods distribution at expense of export sector employment);
  - remittances operate as capital inflows and stimulate domestic demand via foreign-preference shocks.

### Business Cycle Fluctuations (detrended HP-filter deviations)
- Notable cyclical episodes:
  - 2002Q4–2003Q4:
    - positive output gap associated with large increase in government expenditures and a real exchange rate depreciation;
    - home good inflation increased with the positive output gap;
    - co-movement between imported good inflation and the nominal exchange rate depreciation is very small.
  - 2004Q3–2005Q3:
    - surge in private remittance inflows;
    - associated with nominal and real exchange rate appreciation and a negative output gap;
    - overall inflation declined; imported goods prices declined by significantly less than the nominal exchange rate appreciation.
  - Since 2005:
    - increasing dedollarisation further fueled appreciation pressures;
    - real exchange rate appreciation contributed to a negative output gap and deflation.
- Interest rate behavior:
  - cyclical interest rate deviations suggest interest rates responded to output gap and inflation;
  - prior to 2006 (monetary targeting era): monetary policy largely countercyclical;
  - from 2006 (implicit inflation targeting): interest rate became the key policy lever and moved mainly in line with inflation.
- Additional cyclical correlations:
  - negative relationship between consumption and the real interest rate (transmission from interest rates to consumption);
  - real exchange rate impact on output gap evident but weakened from 2005 onward, suggesting a changing role for the LOP gap.

### Modeling implications and emphasis for policy analysis
- Model must capture:
  - incomplete exchange rate pass-through in imported goods sector, amplified by domestic unit labor cost considerations;
  - remittances as demand shocks and capital inflows (foreign preference shocks);
  - interaction between imported-goods demand and domestic labor allocation across sectors;
  - changing transmission properties over time (e.g., weakening real exchange rate effect post-2005, dedollarisation).
- Use of model:
  - provide qualitative impulse response analysis to shocks: imported-good inflation shocks, home-good inflation shocks, productivity shocks, remittance shocks, foreign output shocks, policy interest rate shocks;
  - assess ability to replicate key business cycle patterns observed in Armenian data for 2001–07.

### Key statistics and data sample
- Data period used for calibration/estimation: 2002Q4 to 2007Q4.
- Selected calibrated steady-state values:
  - Ratio of government expenditure to GDP = 0.15.
  - Ratio of exports to GDP = 0.2.
  - Imported good distribution sectors’ share in total demand = 0.1.
  - Ratio of imports to GDP = 0.38.
  - Ratio of private expenditures to GDP = 0.55.
  - Share of imported goods in consumption = 0.25.

---

### Section III — Exchange rate pass-through, model environment, and pricing implications

### Exchange rate pass-through and pricing implications
- Limited role of the exchange rate in affecting imported good inflation in Armenia implies muted exchange rate pass-through.
- Key mechanism: distributive trade accounts for an important share of retail imported goods because of local labor-intensive distribution services; domestic unit labor costs therefore influence importer pricing behavior.
- Even with flexible imported goods prices, incomplete pass-through holds due to movements in nominal marginal costs.
- Modeling implication: account for domestic nominal marginal costs in the import distribution sector to capture short-term monetary transmission.

### Model environment — overview and extensions
- Structural equations derived from Galí and Monacelli (2005) and Monacelli (2005); dynamics enriched with adjustment costs, habit formation, and indexation of prices (as in Fuhrer (2000), Justiniano and Preston (2004), Svensson (2000)).
- Representative household maximizes expected discounted utility (equation label (1) in source).
- Composite consumption index of foreign and domestically produced goods defined in (2) with γ ∈ [0,1] as the degree of openness (import share in consumption) and as the elasticity of substitution between home and imported goods.
- CES aggregation across varieties with elasticity w.

### Households and remittances
- Budget constraint in period form given in (3); prices m_jt and P_t denote domestic and foreign good prices (expressed in domestic currency).
- Demand allocation between domestic and imported goods given by (4) and (5); CPI defined in (6).
- First-order conditions: Euler equation (8) and labor condition (9).
- Foreign household utility modified in (10) to introduce ξ_t as exogenous consumption/investment preference capturing remittances; ξ_t follows AR(1): ξ_t = ρ ξ_{t−1} + ε_t^ξ with 0 ≤ ρ_ξ ≤ 1 and ε_t^ξ i.i.d.
- Foreign Euler equation and foreign demand for imported goods given in (11).

### Linearized system and notation
- Log-linear approximations of (2), (5)-(6), FOCs (8)-(9), and (11) yield equations (12)–(18).
- Lower case variables denote percentage deviations from steady state; π_t = ln p_t − ln p_{t−1} is CPI inflation.

### Inflation, real exchange rate, and terms of trade
- Terms of trade (TOT) defined as price of foreign good per unit of home good.
- Log-linearized relationships linking domestic goods inflation, CPI inflation, and changes in TOT shown in (19) and (20).
- Equation (19): difference between overall CPI and domestic goods inflation is proportional to change in TOT; strength increases with openness γ.
- LOP assumptions:
  - LOP holds for export sector; incomplete pass-through in import sector (LOP gap).
  - Import-side rationale: monopolistic retail distribution and local labor-intensive distribution services allow domestic retail import prices to deviate from world prices.
  - LOP gap and real exchange rate definitions in (21) and (22); log-linearized forms in (23) and (24).
  - Equation (23): LOP gap positively related to the real exchange rate and negatively related to international competitiveness.

### International risk sharing and uncovered interest parity
- With complete international financial markets and perfect capital mobility, expected nominal returns on risk-free bonds equate (equation in source).
- Remittance preference ξ_t enters international risk sharing; ξ_t follows AR(1).
- Rearranged risk sharing condition given in (26); equilibrium linking consumption and asset positions in (27); log-linearized form in (28).
- Domestic consumption linked to world consumption, real exchange rate, and remittances per (28).
- Uncovered interest parity (real) condition (29) relates domestic CPI-based real interest rate to foreign real interest rate and includes a remittance-inflows term akin to an exogenous stochastic risk premium.

### Firms, production, and real marginal costs
- Continuum of identical monopolistically-competitive firms with production function in (30); productivity follows AR(1).
- Aggregate production log-linearized in (31).
- Real marginal cost from cost minimization log-linearized in (32).
  - Equation (32) shows the LOP gap reduces influence of real exchange rate on firms’ real marginal costs.
  - Real marginal costs increase with domestic output and decrease with labor productivity.

### Price-setting behavior and incomplete pass-through
- Domestic firms: Calvo-staggered pricing; optimal price-setting rule for domestic producers in (33) includes real marginal cost deviations and β; adjustment costs and habit introduce backward-looking inflation components.
- Importers: Calvo mechanism; imported goods distribution requires domestic labor input, so importer costs depend on domestic nominal marginal costs.
- Importer cost function and nominal marginal cost result in equation (35), introducing wedge between world and domestic import prices due to:
  - (i) inefficiencies in distribution and monopolistic retailers (LOP gap),
  - (ii) importer costs depending on domestic nominal marginal costs.
- First-order condition for import-setting and log-linearized imported inflation equations given in (36) and (37).
  - Share (1−γ) ψ is employee compensation share in total cost of imported good distribution sector.
  - Imported price-setting implies retailers care about future imported inflation, LOP gap, and domestic nominal marginal costs — producing short-run incomplete pass-through.
- Model extension relative to Monacelli (2005) and Liu (2006): domestic nominal marginal costs introduced into importers’ cost function, leading to more gradual impact of world import prices on domestic economy.

### Aggregation, goods market clearing, and monetary policy rule
- Goods market clearing: domestic output equals sum of domestic and foreign consumption of home goods (exports) and consumption of distribution services (equation (38)).
  - Distribution service specification: imported goods consumption includes domestically-produced distribution service purchased together with the imported good.
- Linearized goods market condition expressed in (39) and simplified into form (40) in terms of real exchange rate q_t.
- Monetary policy: central bank sets interest rate via a reaction function distinguishing responses to home and imported good inflation, following Benes et al. (2007); reaction function stated in (41) with parameters for interest rate smoothing and relative weights on home and imported goods inflation.

---

### Appendix A — Calibration, impulse responses, and empirical correspondence

### Model calibration and estimation (data treatment and methods)
- Data sample: 2002Q4 to 2007Q4 for Armenia.
- Data treatment: variables re-scaled to mean zero and interpreted as approximate percentage deviations from the mean; all variables are detrended seasonally adjusted deviations from dynamic trends.
- Parameter groups and methods:
  - steady-state values parameterized using Armenian data;
  - autoregressive coefficients and stochastic-process parameters estimated using OLS;
  - behavioral parameters estimated using Bayesian approach; priors guided by Armenian structural characteristics and similar research; standard deviations of priors and shocks adjusted to match Armenian business cycle properties and historical forecast fit.
- Specified steady-state/calibrated values (reiterated):
  - Government expenditure to GDP = 0.15.
  - Exports to GDP = 0.2.
  - Imported good distribution sectors’ share in total demand = 0.1.
  - Imports to GDP = 0.38.
  - Ratio of private expenditures to GDP = 0.55.
  - Share of imported goods in consumption = 0.25.
- Table 1 in source summarizes parameter values (table not reproduced here).

### Impulse response findings (simulation design and key responses)
- Method: dynamic simulation with a temporary shock (unit increase in first period); simulations conducted with the Iris-toolbox.
- Domestic inflation shock:
  - worsens domestic competitiveness via real exchange rate appreciation;
  - central bank raises interest rates, generating further appreciation;
  - reduced output via decline in export demand and consumption and substitution toward imported goods;
  - LOP gap: imported good prices less responsive to exchange rate movements;
  - central bank increases interest rate by more than with complete pass-through; domestic output and consumption decline;
  - inflation returned to equilibrium 20 quarters later.
- Imported inflation shock:
  - improves domestic competitiveness (expenditure switching to domestic goods) but raises overall inflation via higher import prices and production costs;
  - central bank raises interest rates → consumption falls and real exchange rate appreciates;
  - net effect: output reduction.
- Productivity shock:
  - temporary productivity increase reduces real marginal cost → lower domestic goods prices and improved competitiveness;
  - consumption higher on impact; output increases less than productivity increase due to substitution between work and leisure;
  - inflation falls initially; monetary authority lowers interest rates modestly;
  - lower interest rates generate exchange rate depreciation; imported inflation only limitedly affected.
- Remittance shock:
  - nominal and real exchange rate appreciate on impact → worsened competitiveness and initial output decline;
  - rigidities in imported goods sector weaken import-price response to appreciation; domestic prices fall slightly;
  - monetary authority lowers interest rates in response to deflation → nominal depreciation follows;
  - remittances increase consumption via income effect; appreciation partially damps consumption increase.
- Foreign output shock:
  - increases foreign and domestic consumption via risk sharing → higher real marginal costs and domestic inflation;
  - nominal and real exchange rate appreciate; import-price response initially weakened by rigidities;
  - central bank raises interest rates; nominal exchange rate appreciates on impact but eventually depreciates due to permanent positive interest rate differential;
  - contrast with remittances shock: foreign output shock yields higher domestic output and consumption in first period because it affects exports; remittances act as direct income with smoother intertemporal effects and stronger initial exchange-rate appreciation via UIP.
- Policy interest rate shock:
  - one percent increase in the interest rate reduces consumption and sharply appreciates nominal and real exchange rates;
  - substitution out of domestically-produced goods lowers demand; firms reduce nominal wages and production costs → domestic prices eventually decline;
  - imported good prices decline somewhat due to real exchange rate appreciation;
  - monetary authority responds to negative output and inflation effects by lowering the nominal interest rate, such that the policy interest rate rises by less than percent (policy adjustment dynamics described in source);
  - exchange rate appreciates then returns to equilibrium.

### Correspondence between model and observed data
- Approaches:
  - compare model’s estimated structural shocks with observed Armenian business-cycle patterns;
  - compare asymptotic distributional aspects implied by the model with observed data;
  - historical forecasting exercises.
- Historical shocks and fit:
  - overall: business cycle patterns largely explained by the model;
  - major deviations:
    - real exchange rate behavior from 2004Q3 to 2005Q2: sharp appreciation from rapid remittance growth from 2005Q3; model captures via increased risk premium and central bank smoothing — shocks affect economy for almost a year;
    - dedollarisation (2006Q3 to 2007Q4) identified as an exchange rate shock tied to declining risk premium and increased demand for domestic currency;
    - end-2006 onward: surge in global oil and food prices shown as shocks to home and imported good inflation.
  - interest-rate estimates deviate prior to inflation targeting; after 2006 adoption of inflation targeting, estimated interest rate closely tracks actual data except for last quarter of 2007.
- Second-moment and co-movement comparisons:
  - standard deviations: model largely captures relative variability; matches closely for home good inflation and real interest rate; less compelling for real exchange rate due to risk-premium shocks;
  - autocorrelations: model captures persistence in home and foreign good inflation, real exchange rate, and real interest rate reasonably well; understates persistence of output growth and real marginal cost of importer firms;
  - cross-correlations: model captures negative cross-correlations between real interest rate and output and home good inflation; matches co-movements between imported good inflation and real marginal cost of importer firms, output and real exchange rate, real interest rate and real exchange rate, remittances and real exchange rate. Correlation between home good inflation and output gap is low in the model (possible role of perfect-labor-market assumption).
- Historical simulations and forecasting performance:
  - model predicts overall movements in output gap and home and imported inflation well;
  - real exchange rate predictions align with observed business-cycle patterns although risk-premium shocks reduce forecasting accuracy in episodes of rapid remittance growth and dedollarisation;
  - interest-rate movements not well captured before inflation targeting; fit improves significantly after 2006 adoption of inflation targeting.

### Stylized numeric and methodological notes (from source)
- Data period: 2002Q4 to 2007Q4.
- Key calibrated numeric values (reiterated):
  - Government expenditure to GDP = 0.15.
  - Exports to GDP = 0.2.
  - Imported distribution sectors’ share in total demand = 0.1.
  - Imports to GDP = 0.38.
  - Ratio of private expenditures to GDP = 0.55.
  - Share of imported goods in consumption = 0.25.
- Simulation timing: inflation brought back to equilibrium 20 quarters later in domestic inflation shock experiment.
- Policy shock magnitude: one percent increase in the interest rate used for policy interest rate shock.
- Estimation methods: OLS for autoregressive coefficients; Bayesian estimation for behavioral parameters; bootstrap technique (resample 5000 times using wild bootstrap) used to construct observed characteristics from reduced-form VAR.

### Conclusion (paper’s contributions and applicability)
- Developed a DSGE small open economy gap model for Armenia capturing monetary policy transmission with country-specific features:
  - nominal rigidity in imported good sector via use of labor services in pricing decisions so domestic unit labor costs matter for imported-sector pricing;
  - remittances modeled as a negative preference shock for foreign households, capturing remittances’ influence on output and the real exchange rate via UIP and risk-sharing channels.
- Model demonstrates capacity to capture many observed features and policy responses in Armenian data and is useful for informing monetary policy questions, including adjustments following adoption of inflation targeting.

*Source: _wp0966 - 1. Long-Term Trends and Business Cycle Movements from Trends (PDF).*

### 1. Long-Term Trends and Business Cycle Movements from Trends ........................................8

### 1. Long-Term Trends and Business Cycle Movements from Trends

### Introduction
- Purpose: Extend a small open economy quarterly projections model (QPM) for Armenia into a New Keynesian-type DSGE model with microeconomic foundations to better analyze monetary policy transmission and responses to shocks.
- Model features emphasized:
  - Incorporates imperfect competition and nominal rigidities.
  - Captures deviations of main macro variables from long-term trends (“gap” model).
  - Explicitly models an LOP gap (wedge between world price in domestic currency and domestic price of same imported goods).
  - Assumes imported-goods distributors use domestic labor as an input, so domestic unit labor costs influence imported-goods pricing.
  - Models remittance inflows as a foreign consumption/preference shock that induces remittances and affects the exchange rate via uncovered interest parity.
- Calibration and evaluation:
  - Model is calibrated to the Armenian economy; impulse response functions and business-cycle pattern comparisons are used to assess model behavior.
- Paper organization:
  - Section II: Stylized facts about transmission mechanism and economy.
  - Section III: Model environment.
  - Section IV: Model responses to shocks and correspondence with data.
  - Section V: Conclusions.

### Stylized Facts about the Armenian Economy (2001–07)
- Macro context:
  - Successful disinflation and double-digit economic growth since 2001.
  - Fiscal and quasi-fiscal consolidation in late 1990s reduced inflation to single digits; a largely independent central bank supported tight monetary policy.
  - Since end-2003, large external shocks in the form of sizeable remittance inflows.
  - Shift toward implicit inflation targeting; since 2006 short-term inflation targets using the interest rate as instrument were adopted.

- Key long-term features and averages (2001–07):
  - GDP growth: 11.6 percent.
  - Consumption growth: 8.5 percent.
  - Productivity growth averaged: 12 percent.
  - Consumption share decline: from 92 percent in 2001 to 72 percent in 2007.
  - Remittances growth:
    - Grew on average by 20 percent in 2001–03.
    - Grew on average by 38 percent from 2004 onwards.
  - Inflation:
    - Average inflation: 3.4 percent during 2001–07.
    - Domestic inflation: 4.3 percent (average).
    - Imported good inflation: 1.7 percent (average).
  - Exchange rate movements:
    - Nominal exchange rate appreciated by more than 40 percent during 2004-2007 while imported good prices declined by less than 5 percent.
    - Real exchange rate: depreciated during 2002–03 (associated with large government expenditures), then permanent appreciating trend from second half of 2004 (linked to remittances).
  - Interest rates: declining trend associated with financial deepening, foreign bank entry, and increased bank capital.

- Structural interpretations relevant for modeling:
  - Low responsiveness (incomplete pass-through) of imported goods prices to exchange rate movements due to distribution/retailing frictions and inclusion of domestic unit labor costs in imported-goods pricing.
  - Demand for imported goods influences domestic output via labor demand in the imported-goods distribution sector (evidence: sustained exchange rate appreciation coincided with increased labor in imported-goods distribution at expense of export sector employment).
  - Remittances operate as capital inflows and stimulate domestic demand via modeled foreign-preference shocks.

### Business Cycle Fluctuations
- Methodology:
  - Business-cycle patterns examined via deviations of detrended data (HP filter) from long-term trends.
- Notable cyclical episodes and associations:
  - 2002Q4–2003Q4:
    - Positive output gap associated with large increase in government expenditures and a real exchange rate depreciation.
    - Home good inflation increased with the positive output gap.
    - Co-movement between imported good inflation and the nominal exchange rate depreciation over this period is very small — limited impact of exchange rate on imported good inflation.
  - 2004Q3–2005Q3:
    - Surge in private remittance inflows.
    - Associated with nominal and real exchange rate appreciation and a negative output gap.
    - Overall inflation declined; imported goods prices declined by significantly less than the nominal exchange rate appreciation — again indicating low correlation between imported good inflation and exchange rate fluctuations.
  - Since 2005:
    - Increasing dedollarisation further fueled appreciation pressures.
    - Real exchange rate appreciation contributed to a negative output gap and deflation during this period.
- Interest rate behavior:
  - Cyclical interest rate deviations suggest interest rates responded to output gap and inflation.
  - Prior to 2006 (monetary targeting era): monetary policy was largely countercyclical.
  - From 2006 (implicit inflation targeting): interest rate became the key policy lever and moved mainly in line with inflation developments.
- Additional cyclical correlations (visual inspection reference):
  - Negative relationship between consumption and the real interest rate — evidence of transmission from interest rates to consumption.
  - Real exchange rate impact on output gap evident, but weakened from 2005 onward, suggesting a changing role for the LOP gap over time.

### Modeling Implications and Emphasis for Policy Analysis
- Model must capture:
  - Incomplete exchange rate pass-through in imported goods sector, amplified by domestic unit labor cost considerations.
  - Remittances as a source of demand shocks and capital inflows (foreign preference shocks).
  - Interaction between imported-goods demand and domestic labor allocation across sectors.
  - Changing transmission properties over time (e.g., weakening real exchange rate effect post-2005, dedollarisation).
- Use of the model:
  - Provide qualitative impulse response analysis to shocks (imported-good inflation shocks, home-good inflation shocks, productivity shocks, remittances shocks, foreign output shocks, policy interest rate shocks).
  - Assess the model’s ability to replicate key business cycle patterns observed in Armenian data for 2001–07.

*Source: _wp0966 - 1. Long-Term Trends and Business Cycle Movements from Trends (PDF).*

### Section III) is an endogenous variable and has an influential impact on the transmission

### _wp0966 - Section III) is an endogenous variable and has an influential impact on the transmission

### Exchange rate pass-through and pricing implications
- The limited role of the exchange rate in affecting imported good inflation in Armenia implies that exchange rate pass-through is muted.
- Key mechanism: distributive trade accounts for an important share of retail imported goods because of the need for local labor-intensive distribution services; domestic unit labor costs therefore influence importer pricing behavior.
- As a result, even if imported goods prices were flexible and distribution networks efficient, incomplete exchange rate pass-through would hold due to the movement of nominal marginal costs.
- Implication for modeling: to capture short-term dynamics of monetary policy transmission in Armenia, the model must account for domestic nominal marginal costs in the import distribution sector.

### Model environment — overview and extensions
- The structural equations are derived from Gali and Monacelli (2005) and Monacelli (2005), with enriched dynamics by allowing for adjustment costs, habit formation, and indexation of prices (as in Furher (2000), Justiano and Preston (2004), Svensson (2000)).
- Representative household maximizes expected discounted utility (equation label (1) present in source).
- Composite consumption index of foreign and domestically produced goods defined in (2) with:
  - γ ∈ [0,1] as the degree of openness (import share in consumption) and as the elasticity of substitution between home and imported goods.
- CES aggregation across varieties with elasticity w.

### Households — first-order conditions and foreign household remittance preference
- Budget constraint in period form given (3); prices m_jt and P_t denote domestic and foreign good prices (expressed in domestic currency).
- Demand functions and allocation between domestic and imported goods given by equations (4) and (5); overall CPI defined in (6).
- First-order conditions: Euler equation (8) and labor condition (9).
- Foreign household modified utility to capture remittances: equation (10) introduces ξ_t as an exogenous consumption/investment preference parameter for the foreign household; ξ_t captures motive to remit or invest in domestic economy.
  - Negative sign implies foreign household derives utility from remitting/investing at expense of its own consumption.
- Foreign Euler equation and foreign demand for imported goods given in (11).

### Linearized system — log-linear approximations
- Log-linear approximations of (2), (5)-(6), FOCs (8)-(9), and (11) yield equations (12)–(18) (labels preserved from source).
- Lower case variables denote percentage deviations from steady state; π_t = ln p_t − ln p_{t−1} is CPI inflation as in source.

### Inflation, real exchange rate, and terms of trade (TOT)
- Terms of trade (TOT) defined as price of foreign good per unit of home good (label from source).
- Log-linearized relationships linking domestic goods inflation, CPI inflation, and changes in the TOT shown in (19) and (20).
- Equation (19) implication: difference between overall CPI and domestic goods inflation is proportional to change in TOT; strength of relationship increases with openness γ.
- Law of one price (LOP) assumption:
  - LOP holds for export sector; incomplete pass-through in import sector (LOP gap).
  - Rationale: export prices set in international markets; on import side, monopolistic retail distribution and local labor-intensive distribution services allow domestic retail import prices to deviate from world prices.
  - Model introduces nominal marginal costs of domestic economy into importers’ pricing, producing incomplete pass-through.
- LOP gap and real exchange rate definitions given by (21) and (22). Log-linearized forms provided in (23) and (24).
- Equation (23) implication: LOP gap is positively related to the real exchange rate and negatively related to international competitiveness.

### International risk sharing and uncovered interest parity
- Under complete international financial markets and perfect capital mobility, expected nominal returns from risk-free bonds must equate (equation in source).
- Remittance preference ξ_t enters international risk sharing condition; foreign household’s remittance bias follows AR(1): ξ_t = ρ ξ_{t−1} + ε_t^ξ with 0 ≤ ρ_ξ ≤ 1 and ε_t^ξ i.i.d (as specified).
- Rearranged risk sharing condition given in (26); equilibrium relation linking consumption and asset positions in (27); log-linearized form in (28).
- Domestic consumption linked to world consumption, real exchange rate, and remittances (as per (28)).
- Uncovered interest parity (real) condition (29) relates domestic CPI-based real interest rate to foreign real interest rate and includes remittance inflows term akin to an exogenous stochastic risk premium.

### Firms, production, and real marginal costs
- Continuum of identical monopolistically-competitive firms with production function in (30); productivity follows AR(1).
- Aggregate production log-linearized in (31).
- Real marginal cost derived from cost minimization; log-linearized result in (32).
  - Equation (32) shows LOP gap reduces the influence of the real exchange rate on firms’ real marginal costs.
  - Real marginal costs increase with domestic output and decrease with labor productivity.

### Price-setting behavior and incomplete pass-through
- Domestic firms set prices in Calvo-staggered manner: fraction able to reset each period; optimizing price p_t^* and aggregate price evolution described in source.
- Optimal (log-linear) price-setting rule for domestic producers given in (33), where real marginal cost deviation and β appear; adjustment costs and habit formations introduce partial price adjustment and backward-looking inflation components.
- Importer pricing: similar Calvo mechanism with fraction of importers able to change prices; imported goods distribution requires domestic labor input, so importer costs depend on domestic nominal marginal costs.
- Importer cost function and nominal marginal cost result in equation (35), introducing wedge between world and domestic import prices due to:
  - (i) inefficiencies in distribution and monopolistic retailers (LOP gap),
  - (ii) importer costs depending on domestic nominal marginal costs.
- First-order condition for import-setting and log-linearized imported inflation equations given in (36) and (37).
  - Share (1−γ) ψ is the employee compensation share in total cost of imported good distribution sector.
  - Imported price-setting implies retailers care about future imported inflation, LOP gap, and domestic nominal marginal costs — producing short-run incomplete pass-through.
- Model extension relative to Monacelli (2005) and Liu (2006): introduction of domestic nominal marginal costs into importers’ cost function, leading to even more gradual impact of world import prices on domestic economy.

### Aggregation, goods market clearing, and monetary policy rule
- Goods market clearing: domestic output equals sum of domestic and foreign consumption of home goods (exports) and consumption of distribution services; equation (38).
  - Distribution service specification: imported goods consumption includes domestically-produced distribution service purchased together with the imported good.
- Linearized goods market condition expressed (39) and simplified into form (40) in terms of the real exchange rate q_t.
- Monetary policy: central bank sets endogenously determined interest rate via a reaction function distinguishing responses to home and imported good inflation, following Benes et al. (2007).
  - Reaction function stated in (41) with parameters for interest rate smoothing and relative weights on home and imported goods inflation.

*Source: _wp0966 - Section III) is an endogenous variable and has an influential impact on the transmission*

### Appendix A provides a summary of the linearized model consisting of equations for the

### _wp0966 - Appendix A provides a summary of the linearized model consisting of equations for the

### Model calibration and estimation
- Data sample: 2002Q4 to 2007Q4 for Armenia.  
- Data treatment: All variables are re-scaled to have a mean of zero and can be interpreted as an approximate percentage deviation from the mean.  
- Parameter groups and methods:
  - Steady-state values of observed macroeconomic variables: parameterized using Armenian data.
  - Autoregressive coefficients and stochastic-process parameters: estimated using OLS.
  - Behavioral parameters: estimated using a Bayesian approach; priors guided by Armenian structural characteristics and similar research; standard deviations of priors and shocks adjusted to match Armenian business cycle properties and historical forecast fit.
- Specified steady-state parameter values and related calibrations (as presented in the text):
  - Ratio of government expenditure to GDP = 0.15 (based on observed fiscal ratios during the period 2002-2007).
  - Ratio of exports to GDP = 0.2 (same period).
  - Imported good distribution sectors’ share in total demand = 0.1 (in line with ratio of retail trade employment in total employment).
  - Ratio of imports to GDP = 0.38 (period 2002-2007).
  - Coefficient of the share of nominal marginal costs in total costs of the importing firms derived as , or  .
  - Ratio of private expenditures to GDP = 0.55 (determined from above).
  - Share of imported goods in consumption = 0.25 (calculated from the CPI basket).
- A summary of the parameter values is provided in Table 1 (table not reproduced here).

### Impulse response findings (Model properties — impulse responses)
- Method: Dynamic simulation with a temporary shock (unit increase in first period); simulations conducted with the Iris-toolbox.
- Domestic inflation shock:
  - Initial effect: worsens domestic competitiveness via real exchange rate appreciation.
  - Central bank response: raises interest rates, generating further appreciation.
  - Real effects: reduced output via decline in export demand and consumption and substitution toward imported goods.
  - Role of LOP gap: changes in imported good prices are less responsive to exchange rate movements.
  - Outcome: central bank increases interest rate by more than with complete pass-through; domestic output and consumption decline; exchange rate appreciation helps bring inflation back to equilibrium 20 quarters later.
- Imported inflation shock:
  - Initial effect: improves domestic competitiveness (expenditure switching to domestic goods) but raises overall inflation via higher import prices and production costs.
  - Central bank response: raises interest rates → consumption falls and real exchange rate appreciates.
  - Net effect: the negative effects outweigh initial competitiveness gains → output reduction.
- Productivity shock:
  - Temporary productivity increase reduces real marginal cost, allowing lower prices of domestic goods → improved competitiveness and substitution into home-produced goods.
  - Consumption is higher on impact; output initially increases by less than productivity increase due to substitution between work and leisure.
  - Inflation falls initially; monetary authority lowers interest rates modestly.
  - Lower interest rates generate exchange rate depreciation; imported inflation only limitedly affected due to rigidities.
  - Positive output gap reduces deflation in the future as interest rates gradually rise.
- Remittance shock:
  - Nominal and real exchange rate appreciate on impact → worsened competitiveness and initial output decline.
  - Rigidities in imported goods sector weaken import-price response to appreciation; domestic prices fall slightly with lower output.
  - Monetary authority lowers interest rates in response to deflation → nominal depreciation follows.
  - Remittances increase consumption via income effect; exchange rate appreciation partially damps consumption increase.
- Foreign output shock:
  - Increases foreign and domestic consumption via risk sharing → higher real marginal costs and domestic inflation.
  - Higher foreign output raises export demand → nominal and real exchange rate appreciate; import-price response initially weakened by rigidities.
  - Central bank raises interest rates; nominal exchange rate appreciates on impact but eventually depreciates due to permanent positive interest rate differential.
  - Positive real interest rate and appreciation reduce output and lower inflation during stabilization.
  - Contrast with remittances shock: foreign output shock yields higher domestic output and consumption in the first period because it affects exports and divides higher foreign output between foreign and home consumption; remittances act as direct income with smoother intertemporal effects and stronger initial exchange-rate appreciation via UIP.
- Policy interest rate shock:
  - A one percent increase in the interest rate reduces consumption (intertemporal substitution) and sharply appreciates nominal and real exchange rates.
  - Resulting substitution out of domestically-produced goods lowers demand; firms reduce nominal wages and production costs → domestic prices eventually decline.
  - Imported good prices decline somewhat due to real exchange rate appreciation.
  - Monetary authority responds to negative output and inflation effects by lowering the nominal interest rate, such that the policy interest rate rises by less than percent.  
  - Exchange rate appreciates then returns to equilibrium.

### Correspondence between model and observed data
- Approaches used:
  - Compare model’s estimated structural shocks with observed Armenian business-cycle patterns.
  - Compare asymptotic distributional aspects implied by the model (given parameterization and shocks) with observed data.
  - Historical forecasting exercises (sample forecasts and simulations starting at various points).
- Analysis of historical shocks and fit:
  - Overall: business cycle patterns in observed data are largely explained by the model.
  - Major deviations:
    - Real exchange rate behavior from 2004Q3 to 2005Q2: rapid increase in remittance inflows from 2005Q3 caused sharp appreciation; preceding trend depreciation meant households expected depreciation, muting appreciation in observed data. Model captures this via increased risk premium (interpreted as exchange rate shock) and central bank interventions smoothing volatility; such shocks affect economy for almost a year.
    - Period of rapid dedollarisation (2006Q3 to 2007Q4) identified as an exchange rate shock tied to declining risk premium and increased demand for domestic currency.
    - End-2006 onward: surge in global oil and food prices shown as shocks to home and imported good inflation.
  - Interest-rate estimates deviate prior to adoption of inflation targeting; after inflation targeting implementation in 2006, estimated interest rate closely tracks actual data except for last quarter of 2007 when commodity-price shocks induced different central bank responses than model implies.
- Second-moment and co-movement comparisons:
  - Standard deviations: model largely captures relative variability of observed series; matches closely for home good inflation and real interest rate; less compelling for real exchange rate due to risk-premium shocks.
  - Autocorrelations: model captures persistence in home and foreign good inflation, real exchange rate, and real interest rate reasonably well; understates persistence of output growth and real marginal cost of importer firms.
  - Cross-correlations: model captures negative cross-correlations between real interest rate and output and home good inflation; matches co-movements between imported good inflation and real marginal cost of importer firms, output and real exchange rate, real interest rate and real exchange rate, remittances and real exchange rate. Correlation between home good inflation and output gap is low in the model (possible role of perfect-labor-market assumption).
- Historical simulations and forecasting performance:
  - Model predicts overall movements in output gap and home and imported inflation well.
  - Real exchange rate predictions align with observed business-cycle patterns, although risk-premium shocks reduce forecasting accuracy in episodes of rapid remittance growth and dedollarisation.
  - Interest-rate movements not well captured before inflation targeting; fit improves significantly after 2006 adoption of inflation targeting.

### Stylized numeric and methodological notes (as presented)
- Data period: 2002Q4 to 2007Q4.
- Key calibrated/shown numeric values:
  - Government expenditure to GDP = 0.15
  - Exports to GDP = 0.2
  - Imported distribution sectors’ share in total demand = 0.1
  - Imports to GDP = 0.38
  - Ratio of private expenditures to GDP = 0.55
  - Share of imported goods in consumption = 0.25
- Simulation timing: inflation brought back to equilibrium 20 quarters later in domestic inflation shock experiment.
- Policy shock magnitude: one percent increase in the interest rate used for policy interest rate shock.
- Estimation methods: OLS for autoregressive coefficients; Bayesian estimation for behavioral parameters; bootstrap technique (resample 5000 times using wild bootstrap) used to construct observed characteristics from reduced-form VAR.

### Conclusion (paper’s summary of contributions and applicability)
- The paper develops a dynamic stochastic general equilibrium model for the Armenian economy based on a standard small open economy gap model that captures monetary policy transmission.
- Country-specific features incorporated:
  - Nominal rigidity in the imported good sector via use of labor services in pricing decisions → domestic unit labor costs matter for imported-sector pricing; aggregate prices, wages, and real marginal costs are less responsive to real exchange rate movements than in standard models.
  - Remittances modeled as a negative preference shock for foreign households, capturing remittances’ influence on output and the real exchange rate via uncovered interest parity and risk-sharing channels.
- Model demonstrates capacity to capture many observed features and policy responses in Armenian data and is useful for informing future monetary policy questions, including adjustments following adoption of inflation targeting.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0966.pdf*

### Appendix A: Model Equations

### _wp0966 - Appendix A: Model Equations

### Core model equations (headings listed in source)
- Consumption equation
- Good market clearing condition
- Uncovered interest parity
- Nominal exchange rate and the LOP gap
- Domestic inflation
- Imported inflation
- Overall inflation
- Real marginal cost of the domestic firm
- Real marginal cost of importers
- Monetary policy rule
- Exogenous processes:
  - Domestic productivity
  - Foreign variables
  - Foreign household preferences (Remittances)

### Notes on consumption equation
- The consumption equation is obtained by substituting equation (28) for consumption at time t+1 into the Euler equation (17).
- Page reference in source: 18

### Data description (model estimation and simulations)
- Sample period: quarterly data for the Armenian economy from 2002Q4 to 2007Q4.
- Data treatment: all variables are in the form of detrended seasonally adjusted deviations from their dynamic trends.
- Variables used (as listed in source):
  - Log of real gross domestic product  •
  - Log of private sector expenditures •
  - First difference of the log of imported consumer price index. The date is created by the Statistical Department of the Central Bank of Armenia •
  - First difference of the log of home good consumer price index. This is calculated as a residual taking into account the fact that the overall consumer price index is a geometric average of the home good and imported good price indices.
  - Log of the real exchange rate •
  - Interbank repo action interest rate •
  - Log of government expenditures •
  - Log of private transfers •
  - Log of foreign real Gross Domestic Product. We take the weighted average of the data for the United States and the EU. The weights are calculated using trade weights for the USA and EU weights with Armenia.  •
  - First difference of the log of Foreign Consumer Price Index. This is the weighted average of the data for the United States and the EU, using the above mentioned method. •
  - Foreign interest rate. This is the weighted average of the discount rate of FED and Refinancing rate of ECB, using the above mentioned method.

### References (selected items as listed in source)
- Acosta, P., E. Lartey, and F. Mandelman, 2007, “Remittances and the Dutch Disease,” Federal Reserve Bank of Atlanta Working Paper 2007-08.
- Benes, J., M. Castello Branco, and D. Vavra, 2007, “A Simple DGE Model for Inflation Targeting,” IMF Working Paper 07/197 (Washington: International Monetary Fund).
- Burstein, A., J. Neves, and S. Rebelo 2003, "Distribution Costs and Real Exchange-rate Dynamics During Exchange Rate-based Stabilizations,” Journal of Monetary Economics, Vol. 50, pp. 1189-1214.
- Christiano, L., M. Eichenbaum, and C. Evans, 2005, “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy, Vol. 113, pp. 1-45.
- Clarida, R., J. Galí, and M. Gertler, 1999, “The Science of Monetary Policy: A New Keynesian Perspective,” Journal of Economic Literature, Vol. 37, pp.1661-1707.
- Dabla-Norris, E., K. Daehaeng, M. Zermeno, A. Billmeier, and V. Kramarenko, 2007, “Modalities of Moving to Inflation Targeting in Armenia and Georgia,” IMF Working Paper 07/133 (Washington: International Monetary Fund).
- Fuhrer, J., 2000, “Habit Formation in Consumption and Its Implications for Monetary-Policy Models,” American Economic Review, Vol. 90, pp. 367–89.
- Galí J., and T. Monacelli, 2002, “Monetary Policy and Exchange Rate Volatility in a Small Open Economy,” Review of Economic Studies, Vol. 72, pp. 707-34.
- Monacelli, T., 2005, “Monetary Policy in a Low Pass-through Environment,” Journal of Money, Credit, and Banking, Vol. 37, pp. 1047-66.
- Smets, F., and R. Wouters, 2004, “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area,” Journal of the European Economic Association, Vol. 1, pp. 1123-75.
- Walsh, C., 2003, Monetary Theory and Policy, (Cambridge, Massachusetts: MIT Press, 2nd ed.)

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0966.pdf*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0966.pdf_