Asymmetric Effects of Monetary Policy on the Armenian Economy

Whether inflation and output respond symmetrically or asymmetrically to the same size of contractionary and expansionary monetary policy shock has important policy implications. This paper shows the presence of asymmetric responses in Armenian inflation and output to positive and negative monetary policy shocks of the same size by employing econometric models. Contractionary policy decreases inflation less than expansionary policy increases it. Output reacts in the opposite way. An estimated small open economy DSGE model with sticky wages and investment adjustment costs explains about half of the asymmetry observed in the monetary policy transmission mechanism. This paper finds that the main part of inflation reaction asymmetry is a result of a highly convex Phillips curve for the importers. The nonlinearities of the internal economy explain the predominant part of the asymmetry in output reaction.


Introduction
Do positive and negative interest rate shocks of the same size have asymmetric effects on inflation and output? This is a relevant question from a monetary policy perspective. The size of the asymmetry represents the efficiency of monetary policy in managing inflation, though finding the factors affecting the creation of the asymmetry is important as well.
The literature presents evidence of asymmetric responses of economies to monetary policy shocks in different countries. This paper estimates the size of the asymmetry in Armenia using econometric techniques. Estimated residuals of a vol. 80 no. 1 forward-looking Taylor rule, which represent the stance of monetary policy, are used as regressors for the estimation of the impact of the policy stance on inflation and output growth. The results report that expansionary policy increases inflation more than contractionary policy decreases it. On the other hand, the decline in output is higher in response to tight policy. Then a nonlinear vector autoregressive (VAR) model is developed and estimated using Armenian data. Impulse response analysis shows the presence of significant asymmetric reactions in the variables to positive and negative monetary policy shocks of the same size.
However, such empirical models do not explain the sources of the asymmetries. Thus, this paper discusses a small open economy dynamic stochastic general equilibrium (DSGE) model with multiple frictions. The model economy is populated by households, which consume domestically produced and imported goods, invest in capital, hold domestic and foreign bonds, supply labour, and choose the utilisation rate of capital and lend it out to firms. They pay capital utilisation costs. The labour is heterogeneous, and households have the power to reset wages. There are investment adjustment costs in the model. Several types of firms operate in the economy. Prices are set via Calvo mechanism (Calvo, 1983). The model is estimated using 15 macroeconomic time series. The estimation results suggest that the prices of imported consumption goods are less sticky than domestic production.
Linearised DSGE models do not generate asymmetries. Asymmetries arise when nonlinearities are preserved. This paper uses second-order approximation. Simulations of the model show that inflation and output respond asymmetrically to monetary policy shocks. The asymmetry in the theoretical model is about half of the asymmetry in nonlinear VAR. Almost all the real variables react more strongly in response to contractionary policy compared to their reaction during expansionary policy. Then the paper estimates the contribution of specific frictions or model blocks in the creation of asymmetry in the monetary policy transmission mechanism. To show this, we apply a second-order approximation to a particular block and linearise the rest of the model. More than half of the asymmetry in inflation is explained by the nonlinear open economy blocks, which is a result of highly convex Phillips curves for importers. The labour market, the capital market, and the nonlinear Phillips curve of domestic producers each explain around 10% of the asymmetry in inflation. On the output side, 20% of the asymmetry in output is created through the nonlinear open economy blocks, while the remaining asymmetry is a result of the nonlinearities of the internal economy.
The paper finds asymmetric reactions of inflation and output during recessions and during growth. Furthermore, asymmetry arises with an increase in the size of the monetary policy shock. Monetary policy is more effective at preventing an inflation acceleration in a demand-driven expansion than at accelerating inflation in a demand-driven recession. When the economy is in a demand-driven expansion, an increase of contractionary monetary policy shock accelerates the decline in output but decreases the relative response of inflation. On the other hand, when the march 2021 economy is in a demand-driven recession, additional monetary stimulus accelerates inflation and diminishes the recovery of output, because the costs of attracting additional labour and capital increase. The deceleration in inflation is larger in a supply-driven recession compared to a supply-driven expansion. An increase in the size of contractionary monetary policy in a supply-driven expansion does not have a significant impact on inflation.
The rest of this paper is organised as follows. Section 2 provides a review of the literature on the asymmetric effects of monetary policy. Section 3 finds the presence of asymmetric effects of monetary policy on Armenian inflation and output. Section 4 develops the micro-founded theoretical model. Section 5 describes the data and the estimation process of the model. Section 6 discusses the sources of the curvatures in the model. Section 7 discusses the mixed equations approach. Section 8 analyses the asymmetries in the monetary policy transmission mechanism. Section 9 tests the ability of the model to reproduce the asymmetries observed in the Armenian data. Section 10 estimates the efficiency of monetary policy in demandand supply-driven recessions and expansions. Finally, Section 11 concludes.

Literature review
The asymmetric effects of monetary policy have drawn the attention of economists for the past three decades. There is large empirical literature which estimates the impacts of monetary policy on the economy. DeLong and Summers (1988) show that expansionary monetary policy has a greater effect on US output than a comparable tight policy. Cover (1992), using post-war US data, finds that an increase in the money supply is less effective in stimulating output compared to the effect of a decrease in the money supply. Morgan (1993), using the federal funds rate as the policy instrument, tests the same hypothesis and gets similar results. Ravn and Sola (1997) find no asymmetric impact between positive and negative monetary policy shocks. Instead, the authors find an asymmetry between the relative impacts of small and large shocks. Karras (1996) shows evidence of an asymmetry in the effect of the money supply on output for 18 European countries. Using the methodology of rolling VAR, Wong (2000) finds relatively higher responses in US output and price levels to positive monetary policy shocks. Garcia and Schaller (2002) test the impact of policy on output during recessions and expansions. They use a Markov switching model and find that monetary policy is more effective in recessions. Peersman and Smets (2001) use a multivariate extension of Hamilton's two-state Markov switching model and show that monetary policy is more effective in recessions in the Euro area. Kaufmann (2002) shows the relative efficiency of monetary policy in recessions using Austrian data. Weise (1999) shows the asymmetric reaction of the US economy to monetary policy employing a logistic smooth transition vector autoregressive (LSTVAR) model. Lo and Piger (2005) provide strong evidence of asymmetry in the business cycle by estimating an unobserved components model. Fehr and Tyran (2001) present evidence of asymmetric effects from expansionary and contractionary monetary policies as a result of money illusion.
Most theoretical models are constructed in a partial equilibrium framework. For example, Ball and Mankiw (1994) develop the model of menu costs, which leads to a convex supply curve. General equilibrium models are usually log-linearised, so the nonlinearities are lost, which result in the loss of the model's power to generate asymmetries. Literature related to the asymmetric effects of policy on the economy in general equilibrium is scarce. Wen and Wu (2011) show that first-order approximation of DGSE models results in the inaccurate capture of business cycle properties. Abbritti and Fahr (2011) introduce the mechanism of downward wage rigidities in a DSGE model with search and matching frictions, which enables the reproduction of the business cycle asymmetries observed in OECD countries. Ravn (2014) includes asymmetric monetary policy towards asset prices in a DSGE framework and creates nonlinearities in the economy. Castillo and Montoro (2008) consider intertemporal non-homotheticity in the preferences of agents and induce an asymmetry in the response of the economy to positive and negative monetary policy shocks.
To preserve the nonlinearities of the model, this paper applies second-order approximation. Second-order approximation of the policy function is extensively applied in economics in Judd (1998). Higher order perturbation methods are studied in Collard and Juillard (2001)

Empirical evidence of asymmetric effects of monetary policy in Armenia
The main data series used in macroeconomic analysis have asymmetric distribution around their mean values. The skewness of Armenian inflation and the interest rate are positive, and for the economic growth it is negative. The asymmetrical statistics of the main Armenian macroeconomic variables is presented in Table 1. The sample starts from 2004Q1 and ends in 2019Q4. Observed asymmetries are a result of higher order terms, such as price dispersion, investment adjustment costs, wage dispersion, or capital utilisation, which are not visible up to the first-order approximation.

Two-stage estimation
This part of the paper tests the presence of asymmetric effects of monetary policy on Armenian economic growth and inflation using the methodology proposed in Cover (1992). The logic of the methodology is as follows. The first stage estimates the Taylor rule to get residuals of the equation or the monetary policy stance. The second stage estimates the impact of policy stance on inflation and economic growth.
The central bank uses a forward-looking Taylor rule. It reacts to expected inflation and output gap with the following reaction function: where π t+ is the expected inflation on date t + , y t+ is the expected output gap on date t + , ρ is the persistence of the interest rate, and α and β are the reaction parameters of the interest rate to inflation expectations and the output gap, respectively. Following Clarida et al. (2000), Here E is the expectation operator and Ω t is the information set at the time the interest rate is set. Hence, the composite error term ε t is a linear combination of the forecast errors and is orthogonal to the variables in the information set. This provides the basis for the estimation of the parameters using the generalised method of moments (GMM) by imposing the orthogonality moment conditions implied by equation (3.1) and utilising instruments from the set of the information of the central bank, Ω t .
The data are quarterly time series covering the period from 2004Q1 to 2019Q4. The data are obtained from the Statistical Committee of the Republic of Armenia. The interest rate is the Armenian interbank rate. Inflation is expressed as a percentage change in the consumer price index (CPI) and the output gap is calculated running a Hodrick-Prescott (HP) filter (λ = 1,600) on seasonally adjusted quarterly GDP. The instrument set includes lags of the interest rate, inflation, the output gap, and the percentage change in real effective exchange rate. The latter is very important for small open economies like Armenia. k is set to one to represent one period expected inflation, and is set to zero to have the output gap at the current time in the Taylor rule. All the variables are demeaned by subtracting a sample average. In case of inflation, sample average is very close (less than 0.12 p.p.) to the Central Bank of Armenia target rate.
According to the estimation results (see Table 2), the persistence of the interest rate is high -0.914. The reactions of the central bank to inflation expectations and the output gap are 1.962 and 0.456, respectively. The results are close to the values observed in the literature. The next step estimates the responses of economic growth and inflation to expansionary and contractionary monetary policy. Residuals of the estimated Taylor rule represent the stance of monetary policy. The two following equations are estimated using Armenian data: where ∆y t is economic growth, π t is inflation, Policy t + represents contractionary monetary policy (positive residual from the Taylor rule) and Policy t expansionary policy (negative residual from the Taylor rule). The inclusion of four lags in the equations enables the smoothing of the volatility of the policy stance between periods, as well as the estimation of both the short-and long-term impacts of policy.
The results of the estimation are presented in Table 3. The cumulative impact of tight monetary policy on output growth (-0.955) is higher compared to the impact of easy policy (0.241). On the other hand, the four-lag cumulative effect of contractionary monetary policy on Armenian inflation is -0.61. The impact of expansionary policy on inflation is 0.905. The net impact of policy on inflation is 0.295, which is statistically significant, and the net impact on economic growth is negative (-0.714). 2 To test the robustness of the results, two other measures of monetary policy stance are used to estimate equations (3.2) and (3.3). The first measure of policy march 2021 stance is the quarterly change in the interest rate. 3 The second measure is the percentage deviation of the interest rate from its trend level calculated by the HP filter. The estimation results are given in Table 9 (Appendix A). As can be seen, the impacts of different measures of policy on economic growth and inflation are close to those reported in Table 3.  5 Wald test of the hypothesis that the sum of the coefficients of expansionary monetary policy equals zero, χ 2 . 6 t-statistics of the hypothesis that the sum of the coefficients of Policy + and Policyequals zero.

Nonlinear VAR model
This section constructs and estimates the nonlinear VAR model, employing the methodology developed in Kilian and Vigfusson (2011). For the estimation of the vol. 80 no. 1 VAR, we use Armenian data for quarterly economic growth, inflation, and interest rates covering the period from 2004Q1 to 2019Q4. 4 Several lag length criteria support the inclusion of two lags.
The system is represented by the following three equations: The first equation is a standard in VAR. Censored variables R t + and R t are added in the output growth and inflation equations, which add nonlinearities to the system. They are given by: (3.7) (3.8) The censored variable in the economic growth equation, R t + , equals the interest rate (with subtracted sample average) when the interest rate is positive, and is zero otherwise. The censored variable R t is negative when the interest rate is negative, and is zero otherwise. The censored variable R t + is added in the economic growth equation (3.5) based on our previous finding, which shows that expansionary monetary policy increases output less compared to the decline in output as a result of the same size contractionary monetary policy. The same logic is applied to the inclusion of R t in the inflation equation (3.6).
Before estimating the whole system and getting the response of the economy to monetary policy shock, the presence of asymmetry is tested. This paper employs the slope-based asymmetry test proposed in Kilian and Vigfusson (2009). The advantage of this test is that it does not require the specification of the complete system. Equations (3.5) and (3.6) are estimated separately. Then, the hypotheses that coefficients of censored variables equal zero are tested: (3.9) march 2021 (3.10) This can be calculated by a Wald test with χ 2 distribution with two degrees of freedom. Table 4 reports the results of the test. The null hypothesis is rejected, with a significance level of 0.05 for both tests. The results of the slope-based tests support the inclusion of the censored variables in the VAR.  Then the system of equations (3.4)-(3.6) is estimated by the ordinary least squares (OLS) method. Figure 1 shows the response of the economy to a 1% increase and decrease in the interest rate. The responses to negative shock are shown as mirror images to facilitate the comparison. Simulation of the estimated model for Armenia shows that the response of output to contractionary monetary policy is stronger than that to expansionary policy. On the other hand, a low interest rate is more powerful in creating inflation and a high interest rate is less efficient at decreasing inflation. The degree of asymmetry in economic growth is higher than the asymmetry in inflation. Figure 1 shows 90% confidence bands as well. The asymmetric responses of inflation and economic growth to positive and negative monetary policy shocks are statistically significant.
This finding is consistent with the convex Phillips curve theory. A graphical illustration is presented in Figure 2. The equilibrium point of the economy is given by the interaction of the demand and supply curves with the equilibrium levels of output (y * ) and inflation (π * ). In this experiment, we abstract from the nonlinearities of the demand curve. The interest rate, controlled by the central bank, shifts the demand curve. A decrease of the interest rate from R * to R 1 stimulates demand. Firms, facing growing demand for their production, increase their hiring of labour and capital to produce additional goods. In the short term, the production capacities of the economy are limited, so firms put more pressure on prices but increase output relatively less. In the opposite case, when the central bank increases the interest rate from R * to R 2 (the size of interest rate change is symmetric), firms decrease production more than prices because of downward price rigidities. A graphical illustration of the convex Phillips curve demonstrates that contractionary and expansionary monetary policies of the same magnitude impact output and inflation asymmetrically. On the other hand, with a linear Phillips curve, output and inflation react symmetrically to positive and negative shocks of the same size. This can be graphically illustrated by a simple framework of aggregate supply and demand curves ( Figure 3). The only difference from the above example (convex supply curve) is the linear Phillips curve. An increase of the interest rate from R * to R 2 shifts the aggregate demand to the left and a new equilibrium is reached with output level y 2 and inflation π 2 . Expansionary monetary policy of the same magnitude increases output to y 1 and inflation to π 1 . In the linear economy, the increase and decrease of output are of equal size. The change in inflation is symmetric as well.

Small open economy DSGE model
The empirical models discussed in the previous section are quite powerful tools to estimate asymmetries in the data. However, the empirical models are unable to explain the sources of the asymmetries. Theoretical models fill that gap.
This section presents a micro-founded small open economy model. The representative household consumes both domestically produced and imported consumption goods. Each household is specialised in a particular type of labour, has some power to negotiate over wages, and supplies its labour to a labour packager. The labour packager combines heterogeneous labour into a homogeneous package and supplies it to domestic firms, which operate in a monopolistic competitive environment. The discussion of the labour packager is a modelling technique to introduce wage stickiness into the model. Households hold capital stock and invest in capital accumulation by purchasing domestically produced and imported investment goods. Households, choosing the utilisation rate of capital, supply it to domestic firms, which produce intermediate goods. They use a Cobb-Douglas production function by combining technology, labour, and capital. The representative firm combines varieties of intermediate inputs into a homogeneous good. Then, the homogeneous good is used in the consumption, investment, government expenditures, or export sector. Three types of importer operate in the vol. 80 no. 1 economy. They import consumption goods, investment goods, and goods used in the export sector. Importers import differentiated goods and set prices following the mechanism proposed in Calvo (1983). The central bank operates via the Taylor rule. The domestic economy is small and does not affect the foreign economy, so the external sector's variables are exogenous.
In contrast with models of this type developed in the literature, 5 this paper does not discuss the growing path of technology, and the variables are not scaled by unit-root technology. There are two explanations for this. Firstly, the growing path of the model is not a significant feature affecting the asymmetry. Secondly, there is a problem of linking data to the model for developing countries because of deviation from the balanced growth path. A schematic representation of the model is presented in Figure 4.

Final consumption and investment goods
The consumption basket of the representative household is given by the following functional form: where C H,t and C F,t are home-produced and imported consumption goods, respectively, γ c is the share of imported goods in the household consumption basket, and η c is the elasticity of substitution between the two groups of goods. march 2021 Aggregate investment goods I t are a function of the domestically produced I H,t , imported I F,t and investment goods used in capital services ( ( t )K t ), given by the following equation: where γ In is the share of imported investment goods, η I is the elasticity of substitution between domestic and imported investment goods, K t is the stock of capital, and ( t ) is the capital utilisation cost represented by the following functional form: where t is the utilisation rate of capital and and b are parameters of the function. This function is very convenient for analysis because it goes to zero in a steady state.

Households
The representative household maximises its utility function, given by: where E t is the expectation operator conditional on information available at time t, ξ t c and ξ t N are consumption preference and labour supply shocks, β denotes the discount factor, h b is the parameter for the habit of consumption, φ is the inverse of the Frisch elasticity of labour supply, and ( ) t represents the -th type of labour supplied by the household. The maximisation problem is subject to the following budget constraint written in terms of domestic goods: The left-hand side represents household expenditures. Each period, it purchases consumption goods C t , investment goods I t , and domestic B t and foreign F t bonds. It also faces capital utilisation costs ( t ) and pays taxes T t . E t denotes the vol. 80 no. 1 effective nominal exchange rate. The right-hand side of the constraint represent the household's income. The household receives nominal wage W( ) t for the -th type of labour. R t k is the rate of return on installed capital. Households receive interest payments for previously purchased domestic (R t-1 B t-1 ) and foreign bonds (R* t-1 E t F t-1 ). Π t denotes the dividends of firms. Households hold capital, and its accumulation is represented by the following: where δ is the depreciation rate of capital and Ψ t is the shock to the marginal efficiency of investments. denotes the investment adjustment cost function, which has the following functional form: The household maximises its utility subject to the budget constraint and capital accumulation. The first-order conditions of the household problem are given in Appendix B (equations 1, 2, 3, 8, 11, and 12).

Production
There is a continuum of intermediate goods producers, which use a Cobb-Douglas production function of the form: (4. 8) where K ser (j) t represents the capital services rented by the j-th firm, N(j) t is the labour hired by the firm, α represents the share of capital and Z t is the stationary productivity process available for all firms. Φ denotes the fixed cost of production. 6 The j-th firm has monopolistic power to produce a differentiated good. Following Calvo (1983), the firm receives a signal to change the price with probability (1 -θ ) in each period. Otherwise, it keeps the price unchanged with probability θ . The optimal price chosen in the current period is denoted by P(j) t * . The j-th firm maximises its expected profit: subject to the demand function. Λ t,t+j denotes the stochastic discount factor. The nonlinear Phillips curve is derived from the solution of the optimisation problem (Appendix B, equations 16-19).

Importers and exporters
Three types of importers operate in the economy: importers of consumption goods, importers of investment goods, and importers of goods used in the production of final export goods. They have monopolistic power and repackage a homogeneous good from the foreign sector into a specialised good and supply it to domestic retailers. Domestic retailers combine a continuum of specialised goods into a homogeneous imported good using a Dixit-Stiglitz function: (4.10) where ∈ (C, I, E ) is for consumption, investment, and export sector goods. I t is the aggregated import and ε is the elasticity of substitution between varieties of goods. The domestic aggregator is competitive and takes the price (P t ) of I t and price (P t (j)) of I t (j) as given.
The real marginal cost of importers is given by the expression: (4.11) where τ t ,I is the mark-up on marginal costs and P t * is the foreign price. Importers solve a profit maximisation problem similar to the domestic producer's problem. As a result, three nonlinear Phillips curves are derived from these problems (Appendix B, equations 20-23, 26-29, and 32-35). Because of the presence of price dispersion in the model, total imports concentrated for the consumption, investment, and export sectors ∈ (C, I, E ) are the following: (4.12) Foreign demand for domestically produced goods is represented by the following: where export is an increasing function of foreign demand Y t * and relative prices. η f is the elasticity of exports and P t E is the export price in domestic currency. Equations describing the export sector are given in Appendix B (38-43). vol. 80 no. 1

Labour market
The representative household supplies labour to the labour packager. The latter combines differentiated labour into a homogeneous labour package via a constant elasticity of substitution (CES) technology: (4.14) A household has the monopolistic power to set wages. Following Calvo (1983), a (1 − θ w ) share of households is able to optimise wages. A θ w share of households sets wages looking at inflation, so the non-optimising household updates its wage according to the following formula: where π c t,t+s is cumulative inflation from period t to period t + s. The j-th household chooses optimal wage W t * in the current period, considering the flow of future (non-optimised, but updated by (4.15)) wages. So, the problem becomes dynamic and is represented by the following discounted utility function. (4.16) The nonlinear Phillips curve of wages is represented by equations 55-60 in Appendix B.

Aggregation
Aggregation of the production function gives the following: On the other hand, production is divided into consumption, investment, government expenditures, and exports. The interest rate has some persistence ρ R and reacts to inflation expectations μ π and to the deviation of output from its steady state μ g .

Foreign economy
The rest of the world is exogenous to the small open economy. Foreign demand, interest rates, and inflation follow first-order autoregressive processes: (4.20) where ρ y* , ρ R* and ρ π* ∈ (0,1) are persistence coefficients and σ t Y* , σ t R* , and σ t π* are independently and identically distributed shocks with zero mean. Y *,ss , R *,ss , and π *,ss are the steady states of foreign demand, foreign interest rates, and foreign inflation, respectively.

Shocks
The model is driven by fifteen structural shocks: consumption preference (ξ t c ), labour supply (ξ t ), marginal efficiency of investments (Ψ t ), government spending (G t ), risk premium (Ω t ), stationary productivity (Z t ), mark-up on domestically produced goods (τ t ), mark-up on imported consumption goods (τ t c,I ), mark-up on imported investment goods (τ t I ,I ), mark-up on imported goods used in the export sector (τ t E ,I ), mark-up on exported goods (τ t E ), monetary policy (σ t R ), foreign demand (Y t * ), foreign inflation (π t * ), and foreign interest rates (R t * ).
All the equations of the model are given in Appendix B.

Estimation
This section estimates the model developed in the previous section using the Bayesian technique.

Data
For the estimation of the DSGE model, twelve macroeconomic time series for Armenia and three for the foreign economy are used as observables. The sample covers the period from 2004Q1 to 2019Q4. Data for real GDP (GDP t ), private consumption (Co s t ), private investment (I t ), government expenditures (Go t ), exports (E port t ), and imports (I port t ) are from the system of national accounts of the Statistical Committee of the Republic of Armenia. The real effective exchange rate (REER t ) is calculated by the Central Bank of Armenia and published on its website. The real wage (W ge t ) is calculated by dividing the nominal wage by the CPI. The interest rate (I tR te t ) is the interbank repo rate. Inflation (dlCPI t ) is the quarterly percentage change in the CPI. As a proxy for the prices of domestically produced goods, the quarterly percentage change in the GDP deflator (dlGDPDefl t ) is used. The price of investment goods (INVDefl t ) is the investment deflator from the system of national accounts. Foreign inflation (dlCPISt r t ) and GDP (GDPSt r t ) are calculated as the weighted average of those of Armenia's trading partners. The foreign interest rate (I tR teSt r t ) is the average of the USA, euro area, and Russia's values. All the time series are seasonally adjusted using the X12 algorithm. The corresponding measurement equation is: where and stand for log and log difference, respectively. Figure 5 in Appendix E presents the model input data.

Calibration
The discount factor β is calibrated to 0.99, implying a 4% annual real interest rate. Inflation target π target is 1.00 97, which corresponds to the quarterly 0.97% inflation. This is the average for the estimation sample. Following a wide range of literature (see, for example, Adolfson et al., 2007, and Christiano et al., 2011, etc.), the elasticities of substitution between varieties of domestically produced (ε ), imported consumption (ε c,I ), imported investment (ε I ,I ), imported input in the export sector (ε E ,I ), and exported (ε E ) goods are calibrated to 6, which results in a 20% mark-up. The depreciation rate of capital δ is calibrated to 0.025, which is a commonly used value in business cycle literature.
The parameters capturing the shares are calculated from the data. They represent the average of the estimation sample. The share of government expenditures in GDP G ss is 0.165. The share of labour in production (1 -) is calculated by dividing the nominal wage of all employed by the nominal GDP, which is 0.43. The share of imported goods in the consumption basket is 35% (γ c = 0.35). The share of imported investment goods in aggregate investments γ I is 0.3. Finally, for the production of final export goods, the sector uses 30% of imported goods (γ E = 0.3). Table 10 in Appendix E summarises the calibration.

Prior distributions
The rest of the parameters are estimated using the Bayesian technique. Beta distribution is applied to the parameters that lie between zero and one. The parameters, restricted to be positive, follow a gamma distribution. The means of the standard deviations of structural shocks follow an inverse gamma distribution.
The prior means and standard deviations of the structural parameters are presented in Table 11 (Appendix E). Following much of the literature, all five Calvo price stickiness parameters (θ , θ c,I , θ I ,I , θ E ,I , and θ E ) and the wage stickiness parameter θ w have beta distributions with 0.75 prior means and 0.075 standard deviations to match yearly price and wage durations.
The prior mean of the inverse of the Frisch labour supply elasticity parameter φ is calibrated to 2 and has standard deviation 0.3. This calibration of labour supply elasticity is a commonly used value in the literature (see, for example, Gali et al., 2011, Grabek and Kłoset, 2013, etc.).
Following Beltran and Draper (2008), the prior means and standard deviations of the elasticities of substitution between home-produced and imported consumption η c and investment η I goods are 2 and 0.45, respectively. The same prior distribution is applied to the elasticity of exports η f and the vol. 80 no. 1 elasticity of substitution between domestic and imported goods used in the export sector η .
Habit persistence in the utility function has a beta distribution with prior mean 0.5 and standard deviation 0.2, which is the average value used in Chetty and Szeidl (2016). The prior distribution of the investment adjustment costs parameter follows a gamma distribution with mean 9 and standard deviation 2.8. The prior of the parameter in the capital utilisation function follows a gamma distribution with mean 0.2 and standard deviation 0.075. This prior is from Smets and Wouters (2007) and Christiano et al. (2011).
The prior mean of persistence in the interest rate ρ R has a beta distribution with mean 0.7 and standard deviation 0.12. In addition, the responses of the interest rate to inflation expectations μ π and GDP deviation from its steady state μ g follow a gamma distribution with mean values 1.5 and 0.25, respectively.
There is a problem in the identification of the mark-up on wages λ w parameter, so we take the average of the values used in Smets and Wouters (2007) Table 12 in Appendix E).
All the standard errors of structural shocks follow an inverse gamma distribution (see Table 13 in Appendix E). The prior means of the labour supply shock and markup shock are higher compared to the rest of the shocks.

Posterior estimates
The posterior means and 90% credible set of the estimated parameters are in the fourth, fifth, and sixth columns, respectively in Tables 11-13 (see Appendix E). The estimation is obtained by running three parallel chains of the Metropolis-Hastings algorithm with 600,000 draws. The acceptance rates for the three chains are 26.33%, 27.17%, and 27.58%. Figure 7 in Appendix E shows the convergence diagnostics of the model's likelihood function. The blue line captures the 80% interval range based on the pooled draws from all sequences. The orange line shows the mean interval range based on the draws of individual sequences. The second (m2) and third (m3) rows show the estimation of the same statistics for the second and third central moments. Convergence is achieved when two lines are stabilised horizontally and should be close to each other. Figure 6 (Appendix E) shows the prior and posterior densities of the estimated parameters. The data are quite informative in obtaining the posterior distribution. 7 The posterior mean of the price stickiness coefficient of domestically produced goods is 0.91, which corresponds to a price duration of eleven quarters. The price stickiness parameter of exported goods is estimated to be 0.65, capturing a price duration of three quarters. On the other hand, the estimated posterior means of imported consumption goods, investment goods, and imported goods used in the export sector are 0.62, 0.52, and 0.45, respectively. The estimation shows that the prices of imported goods are adjusted more frequently compared to domestic prices. Castillo and Montoro (2008) show that the convexity of the second-order approximated Phillips curve increases with a decrease of price stickiness. The posterior estimation of the Calvo wage stickiness parameter is 0.82, which is a little bit higher than its prior mean. The estimated elasticity of substitution between varieties of labour is 6, reporting a 1.22 mark-up on wages.
The estimated mean of the investment adjustment costs parameter is 5.13. The posterior mean of the parameter in the cost function of capital utilisation is estimated to be 0.15, which is smaller compared to its prior mean. The value of this parameter identifies the concavity of the utilisation function. The small value of this parameter means less concavity of the utilisation function, which decreases the asymmetric adjustment of the utilisation rate based on the function's properties.
The persistence parameter in a Taylor rule has posterior mean 0.69. The posterior mean of the reaction to inflation expectations is 1.59. The central bank reacts to deviation of output from its steady state with coefficient 0.18. Figure 8 in Appendix E presents the historical decomposition of Armenian cyclical GDP based on the posteriors of the estimated model. According to the decomposition, the decline in GDP during the financial crisis in 2008-2009 was mostly the result of the marginal efficiency of investment, consumption preference, and productivity shocks. The marginal efficiency of investment represents the transformation of technology investment goods into capital. This transformation decreases during crises and increases in times of high growth. One of the components of this shock is the functioning of financial markets. Models with financial frictions take on the part of the shock. Households increase precautionary savings, which is reflected in the negative contribution of consumption preference shock to the GDP decline during the 2008-2009 crisis. The crisis also yields the structural decline in GDP, represented by the fall in productivity. The main positive contribution to Armenian GDP during the crisis was the huge increase in government spending through borrowing. There was some contribution from the monetary policy side to the recovery of the economy.

Sources of curvatures in the model
The theoretical model has several sources of asymmetry. The first group of curvatures are the Phillips curves for domestically produced and imported goods. The nonlinear Phillips curve for domestically produced intermediate good is expressed by equations 16-19 in Appendix B. Calvo price setting frictions make the Phillips curve convex, which means that the trade-off between output and prices changes along the supply curve. When the growth of the economy accelerates, more inflation is created. This trade-off decreases when output is below its equilibrium level (see Figure 2 for illustration). First-order approximation or log-linearisation of the Phillips curve yields a linear New Keynesian Phillips curve of the following form: When the economy is described by a linear supply curve, the trade-off between aggregate output and inflation is constant (see Figure 3). This linearisation cancels a potential source of the asymmetry in the model. In addition, price dispersion, visible in the second-order approximation, increases the amount of capital and labour needed to produce a given level of output.
The second-order approximated Phillips curve is convex. This creates a nonlinear trade-off between inflation and output. Additionally, the convexity of the Phillips curve with Calvo price setting frictions increases with a decrease in the price stickiness parameter. 8 The estimation of the structural parameters reports that the prices of domestically produced goods are highly sticky. The Calvo parameter of domestically produced goods is 0.91. High price stickiness decreases the convexity of the curve. This is because a higher price stickiness parameter decreases the responsiveness of a firm's prices in optimal equilibrium to its marginal costs.
The next sources of asymmetry are from the import sector's price setting. The estimated Calvo parameters of imported consumption, investment, and goods used in the export sector are 0.62, 0.52, and 0.45, respectively, which make the import sector Phillips curves more convex. As a result, the trade-off between prices and imports increases more compared to domestic production.
The next friction is the investment adjustment cost function given by the following: (6.2) The first-order Taylor approximation of this function around the deterministic steady state is always zero (for more details, see Appendix C). Asymmetry becomes visible in higher order approximations. Actually, the function is symmetric, but it generates asymmetries in the business cycle by accelerating the relative decrease or increase in capital stock.
The next nonlinearity comes from the convex wage curve (Appendix B, equations 55-60). During recessions, households tend to decrease employment rather than nominal wages. In a growing economy, the wealth effect is dominant over the substitution effect, and households work relatively less, putting pressure on nominal wages to increase. The prior belief about the elasticity of substitution between varieties of labour is 4. The posterior estimated value of this parameter is 6, which results in a higher elasticity of substitution. Castillo et al. (2007) show that an increase in the elasticity of substitution between varieties of goods increases the convexity of the Phillips curve. This high convexity results in the highly asymmetric behaviour of the labour market in response to shocks (see Appendix F).

Mixed equations approach and models for simulations
To preserve the nonlinearities of the structural model, this paper uses a secondorder approximation of the policy function. 9 This technique is widely used in DSGE literature for studying the nonlinear implications of the model. The presence of nonlinearities enables the determination of the asymmetric responses of the economy to expansionary and contractionary monetary policies of the same magnitude. However, a second-order approximated full model does not allow the estimation of the contribution of specific frictions or specific sectors to the creation of asymmetry.
This paper applies a mixed equations approach to show the contribution of specific frictions in the creation of asymmetric responses of the economy to shocks. To show the relative importance of a specific sector in the creation of asymmetry, we apply second-order approximation to that sector and keep the rest of the model linearised.
To analyse the relative importance of a specific nonlinearity in the creation of asymmetric reactions of the economy to positive and negative monetary policy shocks, the following six specifications of the model are simulated using posterior estimated coefficients for Armenia. A second-order perturbation method makes the approximation stable. However, it generates explosive sample paths, which are the result of additional fixed points. The additional fixed points in the system are the result of terms of higher order than 2. This paper uses pruning to avoid the generation of explosive sample paths. 10 vol. 80 no. 1

Asymmetries in the monetary policy transmission mechanism
This section presents the responses of the economy to positive and negative monetary policy shocks of the same size in six models in steady states. 11 The models are calibrated based on the estimated posterior values of the parameters. Figure 11 in Appendix G shows the impulse response functions to 1% positive and negative monetary policy shocks in the second-order approximated model. The reaction of inflation to expansionary policy is higher than its reaction to contractionary policy. On the other hand, a 1% contractionary monetary policy decreases GDP by more than a stimulating policy of the same size increases it. The high asymmetry in inflation is created mostly by the imported consumption goods sector. The Phillips curve of imported consumption goods is more convex because the Calvo stickiness coefficient of importers is small, which means that importers tend to increase prices more in response to increasing demand than decrease prices during falling demand. The same tendency is observed in the domestic sector, but the relative size of the asymmetry is less compared to the import sector because the prices of domestically produced goods are stickier, which results in a less convex Phillips curve. Real variables, such as consumption, investment, export, and employment, react more to tight policy than to easy policy. The asymmetric reaction of investment creates asymmetries in investment adjustment costs, which further accelerates the asymmetric response of the capital stock. Households react to this by changing the utilisation rate asymmetrically and in the opposite direction. When investments decrease and price dispersion creates more loss in productivity, households tend to increase the utilisation rate of capital. As a result, utilised capital declines relatively less during contractionary monetary policy, preventing further loss in output. Positive monetary policy shock results in more reduction of employment and less fall in nominal wages. Figure 12 in Appendix G presents the results of the same simulation using Model 2, where the main nonlinearities of the model are linearised. Some standard nonlinear parts are not enough to explain the asymmetries, and we have a symmetric response from the economy to tight and easy policies of the same size. Figures 13-16 (Appendix G) show the responses of inflation and output from simulations of Models 3, 4, 5, and 6. 12 Table 6 summarises the contribution of a specific sector or friction in the creation of asymmetry in the monetary policy transmission mechanism. The asymmetry is calculated as follows. We calculate the differences of the responses to positive and negative shocks. Then the absolute value of the sum of the first four quarters of the simulation is taken as the size of the asymmetry. 13 11 The simulations are implemented within the Dynare software platform. 12 Generalised impulse response functions (GIRFs) of the extended set of variables are available upon request. 13 Calculations are based on the 0 to 3 period for the DSGE models, and on the 1 to 4 period for VAR. march 2021 The asymmetries in inflation and output growth from a nonlinear VAR are 0.62 and 0.75, respectively. The second-order approximated DSGE model explains around half of the asymmetry estimated by the VAR. Most of the asymmetry in inflation is a result of the highly convex Phillips curves of importers (0.17 of 0.28). Both nonlinear labour and capital markets create a 0.025 asymmetry in inflation, while the domestic price setting frictions create 0.03. The sum of the components (0.25) is smaller than the asymmetry from the full second-order approximated model (0.28), because the joint inclusion of parts in the system creates additional asymmetry. The estimated asymmetry in the change of output is mostly a result of the domestic economy's frictions (0.08 + 0.12 + 0.105). Open economic parts create a 0.08 asymmetry in GDP growth.

Third-order empirical moments of simulated models
As reported in Section 3, economic growth in Armenia is negatively skewed, while the skewness of inflation and interest rates is positive. This section tests whether our theoretical model generates the asymmetries observed in the data. Table 7 presents the third-order theoretical moments of inflation, output growth, and the interest rate, which are calculated from simulations of six models. Skewness is calculated from 25,000 simulations, which are based on the estimated posterior values of the parameters and all the structural shocks. The second-order approximated model generates skewness, the directions and degrees of which are close to those observed in the Armenian data. The skewness of inflation, GDP growth, and the interest rate are 0.33, -0.95, and 0.57, respectively. When the main nonlinearities are absent from the model (Model 2), it generates almost symmetrical data. The presence of even one nonlinear block enables a skewed simulation. The high degree of asymmetry in economic growth is a result of internal economy frictions. But even the presence of these nonlinearities in the internal economy results in the generation of skewed inflation very close to the actual data. A nonlinear labour market yields a higher skewness of the interest rate (0.25). Nonlinear specifications of open economy parts generate 0.27 skewness in inflation and negative skewness of economic growth (-0.33).

Efficiency of monetary policy in growing economies and recessions
This section estimates the efficiency of monetary policy during expansions and recessions. Both supply and demand shocks are important forces driving Armenian output. This paper divides the 15 structural shocks of the model into demand, supply, and monetary policy shocks. Demand shocks drive inflation and output in the same direction. Inflation and output move in opposite directions in response to supply shocks. Next, this paper generates supply-and demand-driven expansions and recessions using the posterior values of the structural parameters and the standard deviations of shocks. Here, expansion is defined as a state of the economy where GDP is 5% above the steady state, and recession is a state where GDP is 5% below the steady state level. Figure 17 in Appendix H shows the reaction of inflation and output to a modest monetary policy shock in demand-driven expansion and recession. In a demandgrowing economy, firms attract additional labour and capital and put pressure on inflation. Aggregate demand intersects aggregate supply in a steeper region. On the other hand, there is unemployment and unutilised capital in a recession, and demand intersects the supply curve in a flatter region. So, expansionary policy stimulates more demand in a recession than contractionary policy decreases it in an expansion. Inflation reacts oppositely. In recession, firms react to expansionary policy by producing more goods and put less pressure on prices because they can easily attract labour and capital. An increase of monetary stimulus in a recession changes the trade-off between output and inflation, which results in a smaller reaction of output and accelerating inflation (Figure 18 in Appendix H). Movement in the direction of equilibrium constrains firms more in hiring extra labour and capital, and they increase prices relatively more. In demand-driven expansion, an increase in the size of contractionary policy accelerates the decline of output and decreases the marginal decline in inflation (Figure 19 in Appendix H).
The next simulations apply contractionary monetary policy shocks in supplygenerated expansions and recessions. Tight monetary policy impacts the real economy stronger in a supply-driven recession because no additional labour or capital resources are attracted for the expansion of GDP (Figure 20 in Appendix H). On the other hand, the aggregate supply curve intersects aggregate demand in a steeper region in a supply-driven recession. As a result, firms decrease labour and capital inputs less. Instead, they put relatively more pressure on inflation. An increase in the size of monetary policy shock during expansion moves the demand curve into a flatter region of supply and accelerates the decline of output. On the march 2021 other hand, aggressive policy does not have a significant marginal effect on inflation (Figure 21 in Appendix H). In a supply-driven recession, aggressive monetary policy results in a decrease in the reaction of inflation and an increase in the response of output (Figure 22 in Appendix E). Table 8 summarises the policy simulations in supply-and demand-driven recessions and expansions. The responses are calculated as the absolute value of the average of the first three periods of the simulation. Responses to aggressive policy are rescaled for comparison.

Conclusion
This paper empirically shows the presence of asymmetries in the monetary policy transmission mechanism in Armenia. Two-stage estimation reports that inflation reacts stronger to expansionary monetary policy than to contractionary policy. On the other hand, the estimation shows an opposite response from output. To observe the empirically dynamic responses of inflation and output, a nonlinear VAR is constructed and estimated for Armenian economy. The results show that the economy reacts asymmetrically to positive and negative monetary policy shocks of the same size.
Next, this paper constructs a small open economy DSGE model to explain the sources of the asymmetries in the monetary policy transmission mechanism. There is a number of nonlinearities in the model, such as the convex Phillips curves of importers, domestic producers and wages, and capital adjustment costs and capital utilisation costs. The model is estimated for Armenian economy using 15 macroeconomic parameters. The estimation's diagnostic measures indicate the good quality of estimation. The estimation reports high stickiness of prices for domestic goods and high flexibility of prices for imported goods. As a result, the Phillips curve of importers is highly convex.
To preserve the nonlinearities of the model, a second-order approximation technique is applied. The theoretical model generates half of the asymmetry in inflation estimated with the empirical model. On the other hand, the DSGE explains more than half of asymmetry of output estimated with nonlinear VAR. Most of inflation asymmetry is a result of the highly convex Phillips curve of importers, but the nonlinearities of the open economy blocks explain around 20% of the asymmetry in output. Much of the asymmetry is a result of the frictions vol. 80 no. 1 of the internal economy. Policy simulations show that the efficiency of monetary policy in managing inflation in demand-driven recession is high. In addition, the model matches the directions and sizes of the skewness of Armenian inflation and output growth.
A number of extensions of the DSGE model could introduce additional nonlinearities and, as a result, generate more asymmetry, closer to those estimated with empirical models. march 2021 Appendices Appendix A. Robustness of empirical results Table 9. Estimation of the output growth and inflation equations  Appendix C. First order approximation of investment adjustment cost Investment adjustment cost function is given by the following form: First order approximation of the f(I t , I t-1 ) function is calculated by the following: where f(I ss , I ss ) is the value of function in steady state, f It (I ss , I ss ) is the first order derivative of function f(I t , I t-1 ) with respect to I t at I t = I ss and I t-1 = I ss . f(I t-1 )(I ss , I ss ) is the derivative of f(I t , I t-1 ) with respect to I t-1 . [O 2 ] includes second and higher order terms. At the first order, we assume that the higher order terms are zero.
We apply the above formula of the first order Taylor approximation to the investment adjustment cost function used in the model. Some simplification yields to the following: Further simplification gives: march 2021 All terms cancel each other, and we have zero value of investment adjustment costs by applying the first order approximation.

Appendix D.
Input data for the estimation of DSGE       Appendix H.

Monetary policy in growing economies and recessions
GIRFs at 5% above and below steady state level of GDP based on the average of 25,000 simulations. 1,000 periods in simulations are dropped as burn-in. Modest response is 1% interest rate shock, aggressive response is 2% shock.