structural versus matching estimation: transmission mechanisms in armenia

Economic Modelling 30 (2013) 136–148

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Economic Modelling

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Structural versus matching estimation: Transmission mechanisms in Armenia☆

Karen Poghosyan a, Otilia Boldea b,⁎a Central Bank of Armenia, Economic Research Department, Yerevan, Armeniab Department of Econometrics & Operations Research and CentER, Tilburg University, The Netherlands

☆ We are grateful to an anonymous referee and PavelHaan, Tobias Klein, Jan Magnus, Jenny Ligthart, Lorenzouseful comments. The second author acknowledges su415-11-001.⁎ Corresponding author.

E-mail address: [email protected] (O. Boldea).

0264-9993/$ – see front matter © 2012 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.econmod.2012.09.008

a b s t r a c t
a r t i c l e i n f o
Article history:Accepted 4 September 2012

JEL classification:E50E17C52F41

Keywords:Small open economyValid and relevant impulse responsesStructural and matching estimation

Opting for structural or reduced form estimation is often hard to justify if one wants to both learn about thestructure of the economy and obtain accurate predictions. In this paper, we show that using both structuraland reduced form estimates simultaneously can lead to more accurate policy predictions. Our findings arebased on new information criteria that allow us to pick for both estimates impulse responses that are validand relevant for prediction. We illustrate our findings in the context of analyzing the monetary transmissionmechanism for Armenia. Based on picking valid and relevant information from both structural and reducedformmatching estimation, our findings suggest that the interest rate targeting and the exchange rate channelare well specified and strongly reinforce each other in promoting the recent double-digit growth Armenia ex-perienced before the crisis.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

In the last decade, substantial advances in macroeconomic theoryand practice were fueled by the widespread use of dynamic stochasticgeneral equilibrium models (DSGE) — see interalia Clarida et al.(1999), Galí (2008), Rotemberg and Woodford (1997), Smets andWouters (2005, 2007) and Woodford (2003).

These models, known as new Keynesian models, have been usedintensively by central banks for modeling macroeconomic fluctua-tions and for prediction. Because they are derived from microeco-nomic foundations and incorporate key nominal rigidities, they arecapable of quantifying the key monetary transmission mechanismsand thus of guiding policy makers in implementing adequate macro-economic and monetary policies.

New Keynesian models can be estimated via direct or indirect in-ference. Direct inference refers to estimating the structural model viae.g. generalized method of moments (GMM), and using the resultingestimates directly to generate impulse response functions and predictthe macroeconomic reactions to various shocks. The indirect infer-ence approach is to generate from the structural model a reducedform, determining the implied theoretical impulse response functionswhich are then matched to the data via e.g. minimum distance

Čížek, Meltem Daysal, Jakob dePozzi and Damjan Pfajfar for

pport of the NWO VENI grant

rights reserved.

estimation (MDE). Various methods for direct and indirect inferencehave been implemented by interalia Altig et al. (2011), Boivin andGiannoni (2006), Braun (1994), Christiano et al. (2005), DiCecio(2005), Dupor et al. (2009), Jordà and Kozicki (2007) and Uribe andYue (2006).

Misspecification in the structural model as well as using too manyimpulse responses can lead to biased estimates and misleading policyconclusions for both methods. Hall et al. (2012) address this concernby proposing a method to pick impulse response functions (IRFs) thatare based on valid and relevant information. The picked IRFs not onlyprovide a more reliable estimator, but also indicate valid and relevantportions of the model, where validity and relevance refer to accuratedescription of the transmission of shocks into the economy.

This paper is, to our knowledge, the first study to use the methodsin Hall et al. (2012) in the context of both structural and reduced formestimation, with the scope of pin-pointing valid and relevant infor-mation for policy makers in terms of both economic structure andtransmission of shocks.

The methods proposed in Hall et al. (2012) are especially relevantfor developing countries, where one typically uses simpler models, asthere is not enough data for accurate estimation of a full-scalenonlinear DSGE model. An interesting example of a developing coun-try where such devices are valuable is Armenia. In the decade preced-ing the crisis, Armenia witnessed successful disinflation anddouble-digit economic growth. As pointed out by Mkrtchyan et al.(2009), the fiscal consolidation undertaken in the late 1990s playeda critical role in reducing inflation, and so did a recent much soundermonetary policy based on targeting inflation through interest ratesrather than monetary aggregates.

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137K. Poghosyan, O. Boldea / Economic Modelling 30 (2013) 136–148

As for most emerging economies, we find that for Armenia, the in-terest and exchange rate channels are the main policy transmissionchannels. The interest rate channel has strengthened due to the offi-cial introduction of inflation targeting in 2006, when monetary aggre-gates became increasingly difficult to target due to the large inflow ofcash remittances from Armenians living abroad. Via an open economyNew Keynesian model, our paper quantifies the inflation targetingmechanism and its effectiveness in conjunction with the large appre-ciation of the nominal exchange rate of dram.1

Most papers consider structural estimation or reduced form esti-mation, but not both. Our main contribution is to combine the twowith the scope of both learning about the structure of the economyand its responses to various shocks. We take advantage of economet-rically rigorous misspecification checks to identify the valid and rele-vant shock transmission mechanisms.

We start by introducing a small scale New Keynesian open econo-my model to quantify the exchange-rate pass-through to output andprices. We estimate the model both directly (structural estimation)and indirectly (reduced form matching estimation), and use thenew methods proposed by Hall et al. (2012) to check formisspecification. We find that inflation targeting, reinforced by asmall exchange-rate pass-through to prices, has been very successfulin Armenia in the recent decade. Our study is in line with the findingsof Bordon and Weber (2010), El-Ganainy and Weber (2010) andMkrtchyan et al. (2009), but due to picking valid and relevant IRFs,we are able to show that the exchange rate and interest rate shocksare well-specified in our model. Additionally, we find that eventhough agents are forward-looking and inflation targeting was suc-cessful in the last decade, the dynamics of output may be more subtle,possibly due to cash remittances and large monopolies in the importsector that prevent a higher exchange-rate pass-through. Inflationtargeting in conjunction with forward-lookingness are extremely rel-evant for the macroeconomic performance of Armenia in the recentcrisis period, but we find that more research is needed to uncoverthe true response of the economy to output and inflation shocks.

Our paper is organized as follows. Section 2 introduces the openeconomy New Keynesian model. In Section 3 we give a brief on Arme-nia and we summarize the construction of our data-set, which is thendetailed in Appendix A. Section 4 reports and interprets the estima-tion results for structural and IRF matching estimation. In Section 5,we check for misspecification via the methods in Hall et al. (2012),which we extend to structural estimation. This section also containsthe policy implications based on impulse response functions that con-tain valid and relevant information. Section 6 concludes. Appendix Ais a data appendix, and Appendix B contains graphs of our datasetand of the valid and relevant IRFs.

2 Note that supply shocks enter our model mainly through the Phillips curve. This

2. Structural model

Armenia is a small open economy — the population is of approxi-mately 3 million people and the trade openness degree was of about55%— in 2005 prices— during the last decade (PennWorld Table). Tounderstand the macroeconomic dynamics in Armenia, we use a sim-ple New Keynesian open economy model with rational expectations.As is common practice, the model we use is derived from arepresentative's agent intertemporal utility maximization problem,in the presence of external habit persistence, with staggered wagesand hybrid monetary policy (hybrid here means both forward andbackward looking). Cho and Moreno (2003) argue that such a parsi-monious model is rich enough so that the dynamic path of inflation,output gap and interest rate can be clearly explained in terms ofstructural parameters. We make no such claims, because asRuge-Murcia (2007) points out, structural and matching estimation

1 Dram is the national Armenian currency.

can suffer from misspecification, weak identification and/or stochas-tic singularity. We acknowledge that our model may be misspecified,but we start with it as a benchmark, then check which part of themodel may be misspecified. For modeling, we closely follow Berg etal. (2006).2

In the open economymodel, output gap depends on the real inter-est rate and the real exchange rate, as well as past and futureexpected output:

yt ¼ μEtytþ1 þ 1−μð Þyt−1−ϕrt þ κet þ �yt ð1Þ

where here rt is real interest rate, et is the real exchange rate (definedas units of home currency per one unit of foreign currency). Here, �ty isa demand shock with mean zero and variance σy

2. The key parametersof interest are the monetary transmission mechanism parameter ϕ,and the effect of competitiveness on home demand, κ. Here,μ∈(0,1), indicating that part of the households are forward looking,ϕ>0 indicating that a decrease in interest rates should have expan-sionary effects, and κ>0, signaling that increased competitivenessabroad should increase home demand. As mentioned in Berg et al.(2006), if (ϕ+κ) is small relative to (1−μ), we expect significantlags in the transmission of monetary policy, since the inertia in outputwill prevent monetary policy effectiveness. On the other hand, if it isrelatively high, the monetary policy transmission mechanism is swift.

Following Berg et al. (2006), we define the open economy NewKeynesian Phillips curve as depending on expected and lagged infla-tion, the output gap and the real exchange rate gap:

πt ¼ δEtπtþ1 þ 1−δð Þπt−1 þ λyt þ τ et−et−1ð Þ þ �πt ð2Þ

The presence of backward and forward components of inflation isjustified in Galí and Gertler (1999) and reflects a Calvo price-settingmechanism with sticky prices. Here δ∈(0,1), reflecting the fractionof firms that reset their prices based on expectations. Also, λ>0, indi-cating a positive trade-off over the cycle between inflation and outputgap. As found in several studies— see e.g. Galí and Gertler (1999) andZhang et al. (2008), this trade-off is weaker for recent decades, and sowe expect this coefficient to be small.

This Phillips curve is appropriate for Armenia, as it also reflects theidea that the fundamental role of monetary policy is to provide a nom-inal anchor for inflation; this is reflected in the fact that the backward-and forward-looking coefficients on inflation add up to one. The param-eter τ represents the real exchange rate pass-through to prices, whichwe expect to be low for Armenia: the nominal exchange rate appreciat-ed approximately 40% in 2004–2007, followed by only a 5% drop inimported good prices. This slow exchange rate pass-through is usuallyattributed to nominal rigidities in the imported good sector and arisesfrom inefficient distribution networks, but is also due to a large propor-tion of monopoly retailers that use domestic labor as an input, makingprices even less responsive to exchange rate movements — seeMkrtchyan et al. (2009). Thus, τ should be positive and small. As inBerg et al. (2006), we use the real exchange rate rather than the nomi-nal exchange rate; such an equation can be obtained from a consump-tion smoothing model with opening of the capital market — see e.g.Razin and Yuen (2002) for a theoretical justification. As before, �tπ de-notes an aggregate supply structural shock with mean zero and vari-ance σπ

2.The third equation specifies the exchange rate path. Unlike in Berg

et al. (2006), the real exchange rate dynamics is a linear expected ex-change rate rule, known as “partially uncovered interest parity” — seeDe Grauwe and Vansteenkiste (2007) and Plasmans et al. (1998). Fol-lowing Berg et al. (2006), we use the real exchange rate rather than

simplification is mainly employed for tractability, and several aspects of the supplyside could be introduced in a richer model.

138 K. Poghosyan, O. Boldea / Economic Modelling 30 (2013) 136–148

the nominal exchange rates, allowing for price disparities to bereflected in the error term. Unlike Mkrtchyan et al. (2009), we donot impose uncovered interest parity (UIP), as it would require per-fect capital mobility and complete financial markets, features thatare unlikely to hold for developing countries like Armenia. We as-sume that the real exchange rate depends on the expected and laggedreal exchange rate as well as the differences between home and for-eign real interest rate gap:

et ¼ φEt etþ1 þ 1−φð Þet−1−η rt−r�t� �þ �

et ; ð3Þ

where rt∗ is the international real interest rate and �te is a real exchange

rate structural shock with mean zero and variance σe2. Here, η>0, so

the expected real exchange rate gap is partly covered by the previousand expected future gaps — φ∈(0,1), and partly by the exchange ratedifference. Despite the widespread use of UIP, estimates for η are notequal to unity as UIP predicts, but usually small and quantitativelysimilar for OECD countries— Plasmans et al. (1998) and ASEAN coun-tries — Engwerda et al. (2012). We show in Section 5 that the ex-change rate dynamics is well-specified across most models andidentification strategies we use.3

We close the model by specifying monetary policy in Armenia viaa conventional Taylor rule, where the nominal interest rate, definedas it=rt+πt, is used as the main instrument for targeting bothexpected inflation and output:

it ¼ ρit−1 þ 1−ρð Þ βEtπtþ1 þ γyt� �þ �

it : ð4Þ

Here, �ti an interest rate shock with mean zero and variance σi2. The

parameter ρ∈(0,1) indicates the degree of interest rate smoothing.4

The model and all the data used for estimation in this paper referto monthly frequency. The next section details the construction of ourdataset and its main features.

3. Brief on Armenia and data

According to the CIA World Factbook, under the Soviet Union,Armenia developed a modern industrial sector, but since then hasswitched to placing emphasis on small-scale agriculture. It has intro-duced many economic reforms, including privatization, solid fiscalpolicies, price reforms, but its narrow export base and pervasive mo-nopolies in main business sectors make Armenia still vulnerable to aglobal downturn. Nevertheless, in the decade before the crisis, it hasbeen successful in slashing annual inflation to single digits and in pro-moting double-digit growth, due to sounder macroeconomic policies,in conjunction with a booming construction sector and the cash re-mittances from abroad. The sharp trade imbalance has been financedby international aid, and Armenia, joining the World Trade organiza-tion in 2003, has made large improvements in tax and customsadministration.

The central bank of Armenia, targeting first monetary aggregatesand the exchange rate, has switched in the last decade to inflationtargeting through interest rates, as managing the monetary aggregateshas been proved ineffective due to the large inflow of cash remittancesfrom abroad. Even though the inflation targeting was officially intro-duced in 2006, there is evidence that the central bank has beentargeting inflation much earlier — see e.g. El-Ganainy and Weber(2010). This motivates our use of a conventional Taylor rule

3 Alternatively, we could use models involving risk premia. We chose this model be-cause for developing countries, risk premia seem to introduce large volatilities that aremore difficult to tackle within a simple model.

4 As pointed out in Gorter et al. (2008) and Rudebusch (2002), the magnitude of thisparameter may be overstated if the errors are autocorrelated. We test and find no au-tocorrelation in the errors of all equations over the sample period, so the parameter es-timate for ρ can be legitimately interpreted as interest rate smoothing.

specification for inflation targeting. Alternatively, the official introduc-tion of inflation targeting in 2006 could be quantified via a trend shiftin interest rates and/or parameter changes on the right hand side ofthe Taylor rule, as in Bordon andWeber (2010). Our short data horizondoes not allow us to reliably identify potential change-points or trendshifts, so we stick to the conventional Taylor rule.

Concerning the target level, the annual inflation target was initial-ly 3% for 2006, and changed only once in 2007; from 2007 onward, itis set at an annual level of 4% with a confidence band of ±1.5% aroundit, reflecting the need to maintain credibility. The credibility of themonetary authority has been increasing over the recent years due toits successful policies. In this paper, we quantify the strength of themonetary transmission mechanisms through both structural and re-duced form estimation.

Our dataset comprises monthly data on Armenian key macroeco-nomic indicators, from January 2001 to December 2008, and it is com-puted using information provided publicly by the ArmenianStatistical Service Agency. We construct two monthly real GDP seriesthat are not publicly available but can be proxied using the data athand. To our knowledge, this is the first study that constructs anduses monthly data for Armenia. Our choice of monthly data is guidedby our desire to use larger samples and the availability of reliablemonthly data on GDP for different sectors; thus, we claim that ourstudy is less prone to small sample problems compared to e.g.Mkrtchyan et al. (2009).

Based on the available data, we construct two proxies for themonthly real GDP. The first proxy is computed using constant 2009prices as the base. The second measure adjusts the first for the im-plied official quarterly real GDP growth, reported at constant 2005prices. The computations of these two measures along with theother data below are detailed in Appendix A. The two measures arenot too different, as can be seen from Fig. 1 in Appendix B. There isa sharp drop in the last quarter of 2008 in the second measure com-pared to the first, but this has little impact on our estimation results,which are quite similar across the two measures.

As for prices, we use monthly inflation in the CPI index, whose cal-culation can be found in Appendix A. The plots in Fig. 1 indicate thatinflation has been kept down to single digits quite successfully duringthe recent decade.

The Central Bank of Armenia main policy instruments is themonthly repo interest rate on repurchase agreements of over90 days of maturity.5 Real exchange rates (in dollars per Armeniandram) and nominal interest rate data are published by the Central Bankof Armenia. Plots of the interest rate and real exchange rate gap dataare in Fig. 1. We work with detrended interest rates but chose not todetrend inflation, so that its path with respect to the target can be easieranalyzed. While detrending interest rates but not inflation is in generallikely to distort the relationship between the two and affect the conclu-sions about the effectiveness of monetary policy,6 we maintain that thispractice is innocuous for our sample, as the inflation trend is very closeto zero over the sample period.

We restrict our attention to the sample period 2001–2008 for tworeasons. First, as Dabla-Norris et al. (2007) show (see their Fig. 2), CPIinflation was very high and volatile before 2000, reaching annuallevels of approximately 25% in 1998. Greater exchange rate flexibilitywas introduced only around 2000, allowing to bring down annual in-flation to single digits, and a commitment to price stability has notbeen officially made until the previous decade. This indicates that aTaylor rule may be inappropriate before 2001, which motivates thestart of our dataset. We end our dataset in 2008 due to the fact thatthe onset of the financial crisis and the presence of large fluctuations

5 See www.cba.am, Monetary and Financial Statistics.6 We would like to thank an anonymous referee for pointing this out.

http://www.cba.am


in real quarterly GDP (53% in the first quarter of 2012 compared toprevious quarter), compound with spillovers from the Eurozone cri-sis, have driven the Central Bank of Armenia to interest rates ofaround 8% in May 2012 (see Minutes of June 2012 meeting, www.cba.am). Intuition from the recent crisis indicates that such high in-terest rates cannot be rationalized with sensible inflation targeting.Moreover, annualized inflation in May 2012 was around 0.5%, whilethe current annual inflation target is 4% with ±1.5% confidencebands. Thus, if we estimated a model extending our dataset to the re-cent periods, the evaluation of inflation targeting may be erroneous,so we chose to end our sample in 2008.

All time-series except inflation are in percentage deviation fromtheir gaps, and so have been de-trended using the Hodrick–Prescottfilter. Using the above described data set, we quantify the monetarytransmission mechanisms in the next sections.

4. Estimation results

4.1. Structural estimation by GMM

Based on the two output gap measures, we estimate the openeconomy model in Eqs. (1)–(4) via iterated GMM.

A possible pitfall of using GMM with lags of variables as instru-ments is that they may be weak — see e.g. Fuhrer and Rudebusch(2004) for concerns about the output equation, and Ma (2002) andMavroeidis (2004) for concerns about the Phillips curve. We assessvarious instruments sets via the Cragg and Donald (1993) statisticusing Stock and Yogo (2005) critical values. We chose the set of in-struments which is strongest according to Stock and Yogo (2005)test, z′t ¼ yt−1; yt−2; yt−3; πt−1;πt−2;πt−3; et−1; et−2; it−1; it−2ð Þ.7

Thus, the moment conditions are E[�t⊗zt]=0, with ⊗ denotingthe Kronecker product, and t=(�ty,�tπ,�te,�ti)′. We assume rational ex-pectations, implying that zt, reflecting the information set at timet-1, is uncorrelated with future expectations of variables, namelyEtπt+1, Etyt+1, Etet+1. Hence, the moment conditions can be writtenin terms of the original variables rather than expectations; for exam-ple, the moment conditions for �ty can be written as:

E½�yt zt � ¼ E yt−μEtytþ1− 1−μð Þyt−1 þ ϕrt−κet� �

zt

¼ E yt−μytþ1− 1−μð Þyt−1 þ ϕrt−κet� �

zt ¼ 0:

The results in Table 1, first two columns, are very similar acrossthe two different measures of real GDP, despite the sharp drop inthe second measure of GDP at the end of the period. Some of the pa-rameter estimates are closely in line with those of other developed ordeveloping countries, others reveal unique features of the Armenianeconomy. The strong significance of ϕ for real GDP 2 indicates thatthe interest rate in Armenia does influence output directly. The esti-mate is not large, but much larger than usually found for US — seeCho and Moreno (2003), indicating that even if the objective of mon-etary policy is mostly inflation targeting, as seen from the interestrate equation estimates, there is potential for the monetary policy tostabilize output as well.

For the output equation, we find that the intertemporal elastic-ity of substitution in consumption, according to the estimatesbased on real GDP 2, is — see Cho and Moreno (2003) for formuladerivation — 1/σ=ϕ/μ∼0.05/0.5=0.1. This implies that Armenianconsumers are impatient, in line with the majority of populationhaving small wages — see Guvenen (2006). Also, habit persistenceh, defined as 1/ϕ=σ(1+h)−h — see Cho and Moreno (2003), is

7 Results with various instrument combinations with first, first up to second, andfirst up to third lags of are available upon request from the authors. We also test for au-tocorrelation in the errors and find no further evidence of autocorrelation in our data,indicating that the moment conditions are likely to be well specified for zt.

approximately h~1.11. This implies that people's consumptionschoices are strongly enrooted in habit, unlike findings for someEU members — see e.g. Flavin and Nakagawa (2008).

The estimate of λ indicates a flat Phillips curve. This flatness is awell-known finding for many economies — see e.g. Galí and Gertler(1999) for US, Mihailov et al. (2011) for Poland, Hungary, Slovakia, Lat-via, Lithuania, Cyprus, Malta, Czech Republic, Slovenia, Bulgaria; for thelatter countries, some estimates are even negative. Galí and Gertler(1999) argue that output gap is not proportional to real marginal cost,but real marginal cost better accounts for direct productivity gains oninflation, and so it should replace output gap in the Phillips curve. Onthe other hand, realmarginal cost is also unobserved, and other authors,e.g. Rudd and Whelan (2005) argue that the current practice of replac-ingmarginal costwith average unit labor cost has little theoretical foun-dations. We do not use marginal cost proxies here due to datalimitations.

El-Ganainy and Weber (2010) estimate a slightly different specifi-cation for the open-economy Phillips curve for Armenia, and find thatoutput gap is significant; their results might be influenced by the lessefficient single equation estimation and by the use of data from therecent financial crisis. They also find that inflation is mostly backwardlooking, while we find that the success story of Armenia in reducinginflation to single digits is attributable to inflation targeting combinedwith forward-looking behavior. However, our results show that thebackward looking component is almost equally important. Similarfindings can be found in Berg et al. (2006) for Canada, and Zhang etal. (2008) for US. Mkrtchyan et al. (2009) calibrate the forward-looking parameter to 0.65, assuming slightly less inflation inertiabut the IRFs are qualitatively comparable to ours, reinforcing the ef-fectiveness of inflation targeting through forward-lookingness.

As for the interest rate, even though inflation targeting is not ex-plicit until 2006, our large and significant estimate for β across thetwo real GDP measures implies that inflation targeting is activelyemployed over the period, whether explicitly or implicitly. We noticethat despite the inflation targeting, the interest rate exhibits high in-ertia. This is not surprising, as policy makers maintain credibility bynot spooking the markets with large interest rate swings. We findthat the objective of price stability precedes that of output stability.Output stability is relatively less important, but also seems to play arole; this finding is in line with the Armenian central bank beingforced to dampen the effect of large cash remittances from abroad,part of the measured GDP.

As for competitiveness, the parameter κ is close to zero, eventhough significant for real GDP 2. This implies that the direct compet-itiveness has a small impact on output. On the other hand, the esti-mates for τ are significant and slightly larger, indicating that theexchange rate pass-through to prices does happen but is incomplete.This is in line with the fact that during 2004–2007, the nominal ex-change rate appreciated by more than 40% but was accompanied bya less than 5% decline in imported good prices; thus, most importingArmenian firms take into account domestic unit labor costs in theirpricing decisions. According to Karam and Pagan (2008), Canada ex-hibits an incomplete pass-through of almost the same magnitude.

There is widespread empirical evidence that the uncovered inter-est parity does not hold — see the comprehensive surveys of Engel(1996), Froot and Thaler (1990) and Lewis (1995). We reconfirmthis finding for Armenia, where the expected exchange rate differen-tials seems to be partially uncovered by the interest rate differentialsand predominantly by their previous values.

Overall, we find that the central bank places a large weight ontargeting inflation, and that the exchange rate pass-through to outputand prices is incomplete, but the exchange rate rule acts to reinforceinflation targeting as a monetary policy decision. These findings areconsistent across the two measures of real GDP. The monetary trans-mission mechanism, while slow, seems to work well for Armenia. Theresults in Table 2 also indicate that while individual tests can suggest

http://www.cba.am

http://www.cba.am

Table 1GMM and MDE estimates.

GMM MDE Specification 1 MDE Specification 2

GMM1 GMM2 Type MDE1 MDE2 Type MDE1 MDE2

Output equation (1)μ 0.5483⁎⁎⁎ 0.5677⁎⁎⁎ c 0.5483 0.5677 e 0.6324⁎⁎⁎ 0.6512⁎⁎⁎

ϕ 0.0162 0.0432⁎⁎⁎ f 0.1345⁎⁎⁎ 0.0545 f 0.1025⁎⁎⁎ 0.0945⁎⁎⁎

κ 0.0002 0.0012⁎ f 0.0510⁎⁎⁎ 0.0112 f 0.0124 0.0158Phillips curve (2)

δ 0.5678⁎⁎⁎ 0.5661⁎⁎⁎ c 0.5678 0.5661 e 0.6102⁎⁎⁎ 0.6312⁎⁎⁎

λ 0.0073 0.0044 f 0.0450 0.0350⁎⁎⁎ f 0.0120 0.0251τ 0.0319⁎⁎⁎ 0.0331⁎⁎⁎ c 0.0319 0.0331 e 0.0874⁎⁎⁎ 0.0902⁎⁎⁎

Exchange rate rule (3)φ 0.5597⁎⁎⁎ 0.5359⁎⁎⁎ c 0.5597 0.5359 e 0.5841⁎⁎⁎ 0.5642⁎⁎⁎

η 0.1879⁎⁎⁎ 0.1416⁎⁎⁎ e 0.1100⁎⁎⁎ 0.1000⁎⁎⁎ e 0.2514⁎⁎⁎ 0.2132⁎⁎⁎

Interest rate rule (4)ρ 0.6444⁎⁎⁎ 0.7870⁎⁎⁎ c 0.6444 0.7870 e 0.4856⁎⁎⁎ 0.5123⁎⁎⁎

β 2.2341⁎⁎⁎ 2.0544⁎⁎⁎ f 1.8250⁎⁎⁎ 2.2500⁎⁎⁎ f 1.8546⁎⁎⁎ 2.1241⁎⁎⁎

γ 0.0836⁎⁎⁎ 0.0165⁎⁎⁎ f 0.1500⁎⁎⁎ 0.0450 f 0.1524⁎⁎⁎ 0.1245⁎⁎⁎

Here, the ⁎, ⁎⁎ and ⁎⁎⁎ superscripts are used to denote significance at 10%, 5% and 1% level; the subscripts 1,2 indicate estimation using real GDP 1 or 2, and c, e and f stand for cal-ibrated nuisance parameters, estimated nuisance parameters, respectively focus parameters.


weak identification given our instrument set, the more rigorous over-all test indicate strong identification.

Our results are based on a parsimonious model, which is poten-tially misspecified. In the next sections, we perform IRF matching es-timation to provide misspecification checks via picking valid andrelevant impulse response functions.

4.2. IRF matching estimation

IRF matching estimation is frequently used with different methodsof estimation — see Ruge-Murcia (2007) for a detailed account. Here,we consider one of the most popular matching estimation proce-dures, the vector autoregression (VAR) based IRF matching. The pa-rameter estimates are obtained by minimizing the distance betweenthe sample IRFs obtained by fitting a VAR(1) to the actual data andthe theoretical IRFs generated by the New Keynesian model. We usea VAR(1) because this arises as the rational expectations solution ofour model.

In two recent papers, Dridi et al. (2007) and Hall et al. (2012)present a comprehensive statistical framework for estimating param-eters of a structural model by matching moments using a bindingfunction obtained from a reduced form model. Using their terminolo-gy here, the New Keynesian model is the structural model, theVAR(1) is the reduced form model, and the IRFs are the binding func-tions. They allow for model misspecification and group parametersinto three categories: focus parameters (those we are interested in),estimated nuisance parameters and calibrated nuisance parameters.Since the structural model may be misspecified, an important ques-tion is whether it partially or fully encompasses the reduced formmodel, meaning that even in the presence of misspecification, theminimum distance estimation based on the binding function never-theless yields consistent estimators of the focus parameters.

This paper focuses on the monetary transmission mechanism forArmenia as an open economy. We thus take the open economymodel, and define the focus parameters to be (ϕ,κ,λ,β,γ), describing

Table 2Weak instrument diagnostics.

F statistic real GDP 1 Rejec

Output equation (1) 22.5 YesPhillips curve (2) 16.5 YesExchange rate rule (3) 6.33 NoInterest rate equation (4) 0.62 NoSystem (1)–(4) 14.9 Yes

the influence of interest rates and exchange rates on output, theslope of the Phillips curve whose structural estimate might sufferfrom misspecification bias, and the relative weights monetary policysets on price and output stability. While the focus parameters areclearly defined in terms of the researcher's interest, it is less clearwhether the rest of the parameters should be calibrated or estimated.In general, the estimated nuisance parameters should be the onesthat the researcher finds problematic to be kept fixed. Since ourmodel involves a relatively novel UIP formulation, we first considerη as a nuisance parameter, that we have to estimate to confirm theUIP violation; the rest of the parameters (μ,δ,τ,φ,ρ) are regarded ascalibrated nuisance parameters and set equal to their structural esti-mates. We call this Specification 1. We also consider an alternativespecification (Specification 2) with the same focus parameters, butwith all non-focus parameters (η,μ,δ,τ,φ,ρ) treated as nuisance pa-rameters to be estimated. In both cases, for simplicity we set the var-iance of MDE errors as it is implied by the structural estimates σy

2, σπ2,

σe2 and σi

2.By matching all the impulse response functions at a horizon of

20 months using minimum distance estimation, we obtain the esti-mates for the focus and estimated nuisance parameters; the resultsare in Table 1, last four columns.

One of the most striking results in Table 1 is that ϕ is much largerfor the reduced form estimates, indicating that monetary policy mayhave a (much) larger influence on output than the initial structuralmodel estimates indicates. The Phillips curve seems to be less flat ifwe match impulse response functions, and the trade-off between in-flation and output even becomes significant under Specification 1,MDE 2. Inflation targeting is consistently the primary objective ofmonetary policy. Most MDE estimates imply a significant weight onoutput stability, indicating that this is the second monetary policygoal.

Most results are qualitatively the same across different estimates,but their quantitative differences indicate that some parts of themodel may be misspecified, and finding such misspecifications is

t 10% level F statistic real GDP 2 Reject 10% level

19.6 Yes16.3 Yes11.0 Yes0.41 No13.4 Yes

Table 3VIRSC values for GMM and MDE generated IRFs.

c GMM MDE Specification 1 MDE Specification 2

GMM1 GMM2 MDE1 MDE2 MDE1 MDE2

1,0,0,0 0.449 64.301 1.209 66.293 2.121 60.1240,1,0,0 0.067 16.412 0.560 21.122 0.962 18.5210,0,1,0 −0.003 0.044 0.034 0.057 0.021 0.0420,0,0,1 −0.002 0.374 0.001 0.689 0.004 0.4271,1,0,0 0.204 0.927 11.112 2.857 9.111 1.8271,0,1,0 0.289 31.297 0.365 34.640 0.245 29.5421,0,0,1 0.303 17.680 2.415 14.745 1.584 11.2040,1,1,0 0.011 37.824 0.036 42.313 0.021 38.2140,1,0,1 0.463 60.981 1.031 85.308 0.994 80.2140,0,1,1 0.059 2.655 0.030 3.257 0.020 2.1051,1,1,0 0.204 0.195 4.211 0.570 3.124 0.4151,1,0,1 0.050 0.139 15.989 2.986 12.243 2.1651,0,1,1 0.419 6.529 0.966 5.610 0.758 6.1240,1,1,1 0.082 113.587 0.157 143.219 0.114 138.3241,1,1,1 0.049 0.096 7.051 0.975 8.012 1.025

Here, VIRSC stands for the Valid Impulse Response Selection Criterion, whose valuesdepend on c. The 4×1 selection vector c has jth value equal to one if the correspondingIRF (w.r.t. to a shock to y, π, e or i) is included in the VIRSC calculation, and zero other-wise (j=1, …, 4).


important for accurate policy recommendation. Having potentialmisspecification may imply that the parameters we fixed may be bi-ased. To check this, we consider Specification 2, where all nuisanceparameters are estimated rather than fixed. We see that the parame-ter estimates of focus are largely the same for the two specifications.The nuisance parameters are not very different either, except that η islarger and ρ smaller in Specification 2. This could be a flag for calibrat-ing the wrong parameters, but the next section shows that preciselybecause our method is able to detect valid and relevant impulse re-sponses functions regardless of wrong calibrations, the IRFs pickedare the same across most specifications: the exchange rate IRF orthe interest rate IRF.

The next subsection explains the notion of valid and relevant IRFs,and uses the methods in Hall et al. (2012) to pick those among allIRFs. This section also discusses the implications of these choices formonetary policy.

5. Selecting valid and relevant IRFs

The motivation for checking for misspecification via selection ofvalid and relevant IRFs in MDE is best seen by drawing a parallel toGMM moment selection. When we perform GMM estimation, we im-plicitly assume we have “right” moments: those that are valid, mean-ing that the population moment condition holds, and relevant,meaning that they add new information, thus contributing to moreefficient estimators. Otherwise, one can pick the valid and relevantmoments via moment selection criteria — see Hall et al. (2007).

Similarly, Hall et al. (2012) propose information criteria for pick-ing valid and relevant IRFs to estimate the focus and nuisance param-eters. They pick IRFs that are valid, meaning they are correct eventhough some calibrated (fixed) nuisance parameters are misspecified,and relevant, meaning that they increase the efficiency of the focusparameter estimators.

In this paper, we do not attempt to pick IRFs across horizons as weassume that the central bank has a certain fixed horizon length H=20 for prediction. This is reasonable for a developing country like Ar-menia. We focus on picking the valid and relevant IRFs to variousshocks. In the open economy model (1)–(4), we have four equations,thus four shocks, which can be taken one, two, three at a time or allfour together. For each of these, we calculate the valid impulse re-sponse selection criterion (VIRSC) and the relevant impulse responseselection criterion (RIRSC).

To define VIRSC and RIRSC, we need to introduce some notation.Let nY=4 be the number of shocks (equations) in the open economymodel. Define α=g(θ,η∗,ψ) to be the nY

2H×1 vector of impulse re-sponse functions implied by the set of structural parameters(θ,η∗,ψ), where θ are the focus parameters, η∗ the nuisance parame-ters to be estimated, and ψ the calibrated nuisance parameters fromthe structural model (1)-(4). Thus, in Specification 1, θ=(ϕ,κ,λ,β,γ),η∗=η and ψ=(μ,δ,τ,φ,ρ), while in Specification 2, θ=(ϕ,κ,λ,β,γ),η∗=(η,μ,δ,τ,φ,ρ), and ψ is the empty set. The VAR(1) OLS-estimatedimpulse response functions α are then matched to α=g(θ,η,ψ) viaMDE estimation.

To check for misspecification, we allow for the possibility that notall nY2H×1 IRFs are valid and relevant for MDE estimation, and we doso for both specifications. In both the implicit theoretical impulse re-sponses, α, and the estimated impulse responses, α , the nuisance pa-rameters that are not estimated are fixed at their estimated structuralvalues, ψ ¼ �ψ; for Specification 2, ψ contains no parameters and thusno parameters are fixed.

For selecting the valid and relevant IRFs, as in Hall et al. (2012), letc, an nY×1 selection vector, index the IRFs that are included for MDEfor each horizon. Denote α cð Þ ¼ g θ;η� �;ψ; c

� �the selected theoretical

IRFs, and α cð Þ their estimated counterparts. Then, if the nth elementof c equals one, and the rest are zero, this implies that only the nth el-ement of α(c), respectively α cð Þ, is included in the MDE.

Using this notation and letting T be the sample size, the MDE esti-mator for selected IRFs can be defined as:

θ cð Þ; η� cð Þ� �

¼ argminθ;η�QT θ;η�; c� �

where:

QT θ;η�; c� � ¼ α cð Þ−g θ;η� �;ψ

� �� ′ΩT cð Þ α cð Þ−g θ;η� �;ψ� ��

with ΩT cð Þ being an estimate of the inverse of the covariance matrixof the IRFs that were selected through c.

We select the valid impulse response functions by minimizing:

VIRSCT θ cð Þ; η� cð Þ; c� �

¼ QT θ cð Þ; η� cð Þ; c� �

− cj jln Tð Þ

over all c. This information criterion picks the minimum number ofvalid impulse response functions needed to minimize the MDE objec-tive function.

The relevant impulse response functions are selected by minimiz-ing:

RIRSCT θ cð Þ; η�cð Þ; c

� �¼ ln det W T θ cð Þ; η�

cð Þ; c� ��

þ cj j lnTð Þ=ffiffiffiT

p

where W T θ cð Þ; η� cð Þ; c� �

is the 5×5 left upper corner sub-matrix ofthe estimate of the long-run covariance matrix of the selected theo-retical IRFs (long-run variance of the focus parameters), ln denotesthe natural logarithm and det(A) stands for the determinant of thematrix A. This criterion picks the upper left 5×5 covariance matrixrelevant for our focus parameters; we want to minimize a penalizedversion of its determinant to pick the smallest and thus the most effi-cient covariance matrix with the minimum number of shocks.

The penalties for both information criteria are imposed assuggested in Hall et al. (2012) to yield consistent estimators of c forrespectively the valid and the relevant impulse response functions.

Subject to the existence of a minimizing selection vector for bothcriteria, one notices that their asymptotic properties in terms of pick-ing the valid, respectively the relevant information criteria, dependonly on having consistent estimates of the parameters θ, η∗ andtheir asymptotic variance. In other words, they do not depend onthe method used for estimating θ, η∗, and one can also use thesecriteria by plugging in GMM estimates for θ, η∗ instead of their MDEcounterparts. Because our model is linear, the asymptotic properties

Table 4RIRSC values for GMM and MDE generated IRFs.

c GMM MDE Specification 1 MDE Specification 2


1, 0, 0, 0 −14.0 −19.7 −12.2 −9.3 −10.2 −10.20, 1, 0, 0 −4.0 −6.8 −8.2 −9.2 −7.2 −8.10, 0, 1, 0 −21.8 −20.1 −16.3 −14.3 −14.1 −13.10, 0, 0, 1 −10.6 −8.8 −11.9 −12.7 −10.8 −12.61, 1, 0, 0 0.5 −4.7 −6.4 −6.5 −5.9 −6.21, 0, 1, 0 −14.7 −22.2 −13.1 −10.3 −12.5 −9.41, 0, 0, 1 −3.5 −4.5 −10.6 −7.4 −9.6 −6.20, 1, 1, 0 −6.1 −6.2 −8.5 −9.4 −7.5 −8.80, 1, 0, 1 −2.2 −5.1 −7.6 −6.7 −8.6 −7.90, 0, 1, 1 −15.6 −9.2 −14.2 −9.4 −12.1 −6.81, 1, 1, 0 0.1 −6.8 −6.1 −8.9 −7.3 −9.41, 1, 0, 1 1.7 −1.4 −8.7 −6.1 −6.5 −3.31, 0, 1, 1 −4.2 −5.6 −11.3 −9.6 −12.4 −10.50, 1, 1, 1 −3.4 −2.8 −8.3 −6.2 −7.2 −5.91, 1, 1, 1 1.5 −2.5 −8.3 −10.3 −7.3 −9.1

Here, RIRSC stands for the Relevant Impulse Response Selection Criterion, whose valuesdepend on c. The 4×1 selection vector c has jth element equal to one if the correspond-ing IRF (w.r.t. to a shock to y, π, e or i) is included in the RIRSC calculation, and zero oth-erwise (j=1, …, 4).

Table 6Available data*.

Abbreviation Description Frequency

Nominal GDP (2009)NGDP2009:M1 nominal GDP industry (mln drams) monthlyNGDP2009:M2 nominal GDP agriculture (mln drams) monthlyNGDP2009:M3 nominal GDP construction (mln drams) monthlyNGDP2009:M4 nominal GDP services (mln drams) monthly


of c are the same across estimates, so all the smoothness assumptionsin Hall et al. (2012) are satisfied.

We thus report the information criteria for both GMM and MDEestimates of the two specifications. Tables 3 and 4 report the VIRSC,respectively RIRSC for different selection vectors c. Table 5 reportsthe corresponding selected IRFs group-wise for responses to one,two, three shocks and overall.

The main message of Table 5 is that the selected IRFs, similaracross different output gap measures and different estimates, arethe responses to exchange rate or interest rate shocks. This impliesthat the impulse responses to an exchange rate or interest rateshock and their transmission into the economy are both valid and rel-evant despite the fixed parameters �ψ which may or may not bemisspecified. Even in the absence of calibrated parameters (Specifica-tion 2), the valid and relevant impulse responses picked are largelythe same. Since both GMM and MDE largely agree as to the strengthof the interest targeting policy in Armenia and its high effectivenessin the last decade, our findings imply that the monetary policy isquite effective when reinforced by the exchange rate channel. Sincethe exchange rate and interest rate shock responses are picked asvalid or relevant or both, our results imply that the exchange ratechannel reinforces the interest rate channel in the transmissionmechanism. On the other hand, we see that the responses to inflationare almost never valid or relevant, implying that the expectations arenot entirely anchored as described by a Phillips curve even thoughthe interest rate and exchange rate shocks may influence inflationas described, through indirect channels. The exclusion of the

Table 5Valid and relevant shocks.

No. shocks valid/relevant GMM Specification 1 Specification 2


1 valid e e i e i erelevant e e e e e e

2 valid π, e y, π e, i y, π e, i y, πrelevant e, i y, e e, i y, e y, e y, e

3 valid y, π, i y, π, i y, e, i y, π, e y, e, i y, π, erelevant y, i, e y, π, e y, i, e y, i, e y, i, e y, i, e

all valid e e i e i erelevant e y, e e e i e

Note: The symbols y, π, e, i indicate that the IRFs of all variables that have been pickedw.r.t. to a shock to y, π, e and i, respectively.

responses to inflation shocks from the valid and relevant IRFs is a ro-bust finding across the GMM and MDE estimates for both specifica-tions, suggesting that a potential misspecification does not refer tocalibrated parameters, but possibly to the richness of the structuralmodel. Our results are useful for policy makers as they imply thateven though policies are effective, more credibility may be neededto increase forward-lookingness.

Moreover, picking the overall valid and relevant IRFs allows themonetary policy makers to be better informed about the policy trans-mission mechanism and its duration. Appendix B contains the IRFs ofall variables to a positive shock in the interest rate and the exchangerate, based on our six estimates (GMM, MDE, for Specifications 1,2,with two measures each).

Figs. 2–7 show that an increase in the interest rate reduces outputthrough intertemporal substitution. The real exchange rate drop (ap-preciation) implies less domestic demand, reducing equilibriumprices and inflation. The monetary policy makers respond to thelower demand and production by reducing the interest rate, whichthen increases consumption and output, depreciating the real ex-change rate. The real exchange rate partial uncovered parity impliesfurther depreciation of the real exchange rate, which returns to theequilibrium but slower than the other real variables. Our findingsare qualitatively similar to those in Mkrtchyan et al. (2009), Fig. 8,pp. 29. We find that for the MDE estimates using the second specifica-tion, the time it takes for the interest rate shocks to have maximumimpact is shorter; this can be best explained by noting that the inter-est rate parity η is almost double for the second specification, facilitat-ing a quicker pass through to exchange rates and output. In additionto Mkrtchyan et al. (2009) IRFs, we report the IRFs from a shock inthe real exchange rate — see Figs. 8–13. We find that a depreciationin the exchange rate has a small but steady impact in changing do-mestic demand, output and prices; the effect is slightly larger forthe second specification, which is expected given the higherpass-through coefficients. The monetary authority responds to theoutput increase by increasing the interest rate, which in turn reducesoutput, causing it to gradually return to equilibrium.

Even though the IRFs are different for the two specifications, thevalid and relevant IRFs picked are invariably for the exchange rateor interest rate shocks, indicating less misspecification in the trans-mission mechanisms for these two.

Production price indexes (2009)P2009:M1 price index industry (% compared to previous month) monthly

P2009:M2 price index agriculture (% compared to previous

month)monthly

P2009:M3 price index construction (% compared to previous

month)monthly

P2009:M4 price index services (% compared to previous month) monthly

Real GDP (2001–2009)RgGDPY:M real growth of total GDP (% compared to previous year) monthlyRGDPQY:Q real GDP at constant 2005 average prices quarterly

Rest of data (2001–2008)CPIY:M consumer price index monthlyRY:M nominal interest rate on repurchase agreements monthlyeY:M real exchange rates monthly

⁎ The data in this table are freely available from the Armenian Statistical Service Agencyat http://www.armstat.am/en/.

http://www.armstat.am/en/

8 Finding the optimal constant would be interesting, and we leave this to futureresearch.


6. Conclusions

Opting for structural or reduced form estimation is often hard tojustify in the light of potential misspecification. Since both estima-tions are based on a larger structural model that is unknown, bothmodels can be misspecified, and either can be worse in terms of pol-icy recommendation depending on data at hand — see Ruge-Murcia(2007). In this paper, we do not pick one path, but show that marry-ing the two can lead to important conclusions about the type ofmisspecification. To that end, we use the method in Hall et al.(2012) for picking valid and relevant impulse response functions.We extend the use of their method to structural parameter estimates,and point to the origins of the possible misspecification for a datasetpertaining to Armenia.

Our small-scale model for Armenia does not include the large cashremittances from abroad and the impressive boom in the construc-tion sector, because such features are uncommon for developed coun-tries and thus not part of any standard model. Instead of attemptingto model such features which would be subject to small-sample esti-mation issues, we show by means of picking relevant and valid infor-mation that a Phillips curve and the open-economy aggregatedemand equation may both be misspecified, especially with regardto modeling expectations. But more importantly, we show that, de-spite the misspecification, the interest rate targeting works throughthe direct transmission channel, and the exchange rate mechanism,suffering from partial uncovered interest parity, still influences aggre-gate demand through a small but significant partial pass-through tooutput and prices.

Picking valid and relevant information is thus useful in highlight-ing the monetary policy aspects of the Armenian economy that havebeen solid over the previous decade. We postulate that such methodsare useful for policy makers in different countries, because they canpin-point to the source of the misspecification and thus make moreaccurate policy recommendations, while using information fromboth structural and reduced form models when both are identified.

Appendix A

This Appendix details the data construction at monthly frequency,based on the available data listed in Table 6. To describe the construc-tion of our monthly GDP measures, we use Y:M to denote years withcorresponding months, Y=2001, 2002, …, 2008, 2009, and M=M1,M2, …, M12. We denote by Y:Q years followed by the correspondingquarters Q1, Q2, …, Q4.

The first measure of monthly real GDP, RDGPY:M(1), for 2001:M1−2008:M12, is constructed ignoring the official releases of quar-terly real GDP, while the second measure of monthly real GDP,RDGPY:M(2), is adjusted to reflect the official quarterly real GDPgrowth. The construction of RDGPY:M(1) is detailed below.

• We start by calculating the monthly real GDP in each sector in 2009,dividing nominal GDP by monthly measures of 2009 prices. Forconstructing the latter, let monthly and average 2009 prices foreach sector j=1, …, 4, PM2009:M

j , respectively PA2009j , be:

PMj2009:M ¼ ∏

2009:M

t¼2009:M1Pjt ; PAj

2009 ¼ 112

X2009:M12

t¼2009:M1

PMjt ;

for M=M2, …, M12. Then the monthly 2009 prices are (PM2009:Mj /

PA2009j ), and so the monthly real GDP in each sector in 2009,

RGDP2009:Mj , is:

RDGPj2009:M ¼ NGDPj2009:M

PMj2009:M=PA

j2009

:

• We add the real GDP in each sector in 2009 to obtain the monthlyreal GDP for the economy in 2009:

RGDP2009:M ¼X4j¼1

RGDPj2009:M :

• From RGDP2009:M and the monthly cumulative real GDP growthrates with respect to the previous year from 2001:1 to 2009:12,RgGDPY:M, we can construct the real GDP in eachmonth RGDPY:M(1):

RGDPY:M 1ð Þ ¼ RGDP2009:MRgGDP2008:M � RgGDP2007:M �…� RgGDPYþ1:M

:

Here Y:M=2001:M1−2008:M12.

This proxy is a sensible monthly GDP measure, but it ignores theofficial releases of quarterly real GDP, RGDPQY:Q. We construct a sec-ond proxy that brings the first one closer to the published quarterlyGDP, as follows:

• We first add the real GDP proxies RGDPY:M(1) for each month of thequarter to obtain a measure of the quarterly GDP, e.g.

RGDPQ2008:Q1 1ð Þ ¼ RGDP2008:M1 1ð Þ þ RGDP2008:M2 1ð Þ þ RGDP2008:M3 1ð Þ:

• Note that RGDPQY:Q(1) is computed with respect to average 2009prices, while the officially released real GDP is reported with respectto 2005 average prices. However, the growth rates of the officiallyreleased real GDP are by definition independent of prices. We firstcompute these growth rates, with respect to the previous quarter,say RgGDPY:Q∗ , as:

RgGDP�Y :Q ¼ RGDPQY:Q

RGDPQY:Q−1:

• Finally, we compute the second measure of real GDP, RGDPY:M(2),with initial values the same as the first measure for 2001:M1−2001:M3, and for the rest, using the growth rates RgGDPY:Q∗ forward.For example,

RGDP2001:M4 2ð Þ ¼ RGDP2001:M4 1ð Þ � RgGDP�2001:Q1RGDP2001:M5 2ð Þ ¼ RGDP2001:M5 1ð Þ � RgGDP�2001:Q1RGDP2001:M6 2ð Þ ¼ RGDP2001:M6 1ð Þ � RgGDP�2001:Q1:

Note that this last calculation appropriately uses quarterly growthrates rather than monthly growth rates, because then the first and thesecond measure of GDP appropriately differ by the official quarterlygrowth rates:

RGDPQ2001:Q2 2ð Þ ¼ RGDP2001:M4 2ð Þ þ RGDP2001:M5 2ð Þ þ RGDP2001:M6 2ð Þ

¼ RgGDP�2001:Q1

X2001:M6

t¼2001:M4

RGDPt 1ð Þ" #

¼ RgGDP�2001:Q1 � RGDPQ2001:Q2 1ð Þ:

To obtain the output gap yt, we take logs, seasonally adjust the twomeasures of real GDP, and detrend the resulting measures using theusual Hodrick–Prescott (HP) filter with the program TRAMO/SEATS,and the default monthly constant 14400.8


Regarding the Consumer Price Index (CPI), data are disseminated byNational Statistical Service Agency as a modified Laspeyres index with2005 as a base year. The index is the weighted average monthly changein prices of 470 commodities. It is calculated for Yerevan and other 11most densely populated regions. We seasonally adjust the log CPI in thesame way as the log GDP, and compute our measure of inflation πt asthe difference of log CPI from previous month.We do not detrend the in-flation rate for two reasons: first, as the plot indicates, its in-samplemeanis approximately zero, and the inflation gaps will be approximately thesame as inflation; second, for checking effectiveness of inflation targeting,it is more useful to work with levels.

2001:1 2003:1 2005:1 2007:1 2008:12−12

−10

−8

−6

−4

−2

0

2

4Real GDP gap measures

2001:1 2003:1 2005:1 2007:1 2008:12−10

−5

0

5

10Real exchange rate gap

GDP1

GDP2

Fig. 1. Monthly Ar

Interest rate

0 10 20 30 40−0.25

−0.2−0.15

−0.1−0.05

y

0 10 20 30 40−2

−1.5−1

−0.50

e

Fig. 2. IRFs for an interes

The Central Bank of Armenia main policy instruments is the repo(repurchase agreement) interest rate, Rt. The real interest rate iscomputed from the nominal interest rate, subtracting inflation rt=Rt−πt. Following Berg et al. (2006), we HP-detrend the nominal in-terest rate first, in the same way as log GDP. Real exchange ratesare official releases, in log nominal exchange rates in units of Arme-nian drams per US dollar, times the US dollar foreign price level perArmenian dram domestic price level. We HP-detrend the real ex-change rates in the same way as log GDP. As usual in the literature,the real exchange rates and interest rates are not seasonallyadjusted.

Appendix B

2001:1 2003:1 2005:1 2007:1 2008:12−1.5

−1

−0.5

0

0.5

1

1.5Inflation with respect to previous month

2001:1 2003:1 2005:1 2007:1 2008:12−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5Nominal interest rate gap

menian data.

shock: GMM1

0 10 20 30 40−0.1

−0.050

0.050.1

π

0 10 20 30 400

0.20.40.60.8

1i

t rate shock GMM 1.

Interest rate shock: MDE1

0 10 20 30 40−0.5

0

0.5

1i

0 10 20 30 40−0.4−0.2

00.20.4

e

0 10 20 30 40−0.3−0.2−0.1

00.1

π

0 10 20 30 40−1

−0.5

0

0.5y

Fig. 3. IRFs for an interest rate shock MDE 1: specification 1.

Interest Rate Shock: MDE1

0 10 20 30 400

0.20.40.60.8

1i

0 10 20 30 40−1

−0.8−0.6−0.4−0.2

0e

0 10 20 30 40−0.2−0.1

00.10.2

π

0 10 20 30 40−0.8−0.6−0.4−0.2

0y


Interest rate shock: GMM2

0 10 20 30 400

0.20.40.60.8

1i

0 10 20 30 40−3

−2

−1

0e

0 10 20 30 40−0.2−0.1

00.10.2

π

0 10 20 30 40−1

−0.8−0.6−0.4−0.2

0y

Fig. 5. IRFs for an interest rate shock GMM 2.

Interest rate shock: MDE1

0 10 20 30 40−0.5

0

0.5

1i

0 10 20 30 40−0.4−0.2

00.20.4

e

0 10 20 30 40−0.3−0.2−0.1

00.1

π

0 10 20 30 40−1

−0.5

0

0.5y

Fig. 6. IRFs for an interest rate shock MDE 2: Specification 1.


Interest Rate Shock: MDE2

0 10 20 30 400

0.20.40.60.8

1i

0 10 20 30 40−0.8−0.6−0.4−0.2

0e

0 10 20 30 40−0.15−0.1

−0.050

0.05π

0 10 20 30 40−0.8−0.6−0.4−0.2

0y


Exchange rate shock: GMM1

0 10 20 30 40−0.06−0.04−0.02

00.020.04

i

0 10 20 30 400

0.51

1.52

2.5e

0 10 20 30 40−0.05

0

0.05

0.1

0.15π

0 10 20 30 400

0.05

0.1

0.15

0.2y

Fig. 8. IRFs for an exchange rate shock GMM 1.

Exchange rate shock: MDE1

0 10 20 30 40−0.1

00.10.20.3

i

0 10 20 30 40−1

0

1

2e

0 10 20 30 40−0.05

00.05

0.10.15

π

0 10 20 30 40−0.2

00.20.40.6

y

Fig. 9. IRFs for an exchange rate shock MDE 1: specification 1.

Exchange Rate Shock: MDE1

0 10 20 30 40−0.2

−0.15

−0.1

−0.05

0i

0 10 20 30 400

0.5

1

1.5

2e

0 10 20 30 40−0.2

−0.1

0

0.1

0.2π

0 10 20 30 400

0.2

0.4

0.6

0.8y



Exchange rate shock: GMM2

0 10 20 30 40−0.04

−0.02

0

0.02i

0 10 20 30 400

0.51

1.52

e

0 10 20 30 40−0.05

00.050.1

0.15π

0 10 20 30 400

0.10.20.30.4

y

Fig. 11. IRFs for an exchange rate shock GMM 2.

Exchange rate shock: MDE1

0 10 20 30 40−0.1

00.10.20.3

i

0 10 20 30 40−1

0

1

2e

0 10 20 30 40−0.05

00.050.1

0.15π

0 10 20 30 40−0.2

00.20.40.6

y


Exchange Rate Shock: MDE2

0 10 20 30 40−0.1

−0.050

0.050.1

i

0 10 20 30 400

0.51

1.52

e

0 10 20 30 40−0.1

00.10.20.3

π

0 10 20 30 400

0.20.40.60.8

y



References

Altig, D., Christiano, L., Eichenbaum, M., Lindé, J., 2011. Firm-specific capital, nominalrigidities and the business cycle. Review of Economic Dynamics 14, 225–247.

Berg, A., Karam, P., Laxton, D., 2006. A practical model-based approach to monetarypolicy analysis: overview. IMF Working Papers No. 80.

Boivin, J., Giannoni, M., 2006. Has monetary policy become more effective? The Reviewof Economics and Statistics 88, 445–462.

Bordon, A., Weber, A., 2010. The transmission mechanism in Armenia: new evidencefrom a regime switching VAR analysis. IMF Working Papers No. 270.

Braun, A.R., 1994. Tax disturbances and real economic activity in the postwar UnitedStates. Journal of Monetary Economics 33, 441–462.

Cho, S., Moreno, A., 2003. A structural estimation and interpretation of the NewKeynesian macro model. University of Navarra Working Paper No. 14.

Christiano, L., Eichenbaum, M., Evans, C., 2005. Nominal rigidities and the dynamic ef-fects of a shock to monetary molicy. Journal of Political Economy 113, 1–45.

Clarida, R., Galí, J., Gertler, M., 1999. The science of monetary policy: a new Keynesianperspective. Journal of Economic Literature 37, 1661–1707.

Cragg, J., Donald, S., 1993. Testing identifiability and specification in instrumental var-iable models. Econometric Theory 9, 222–240.

Dabla-Norris, E., Kim, D., Zermeño, M., Billmeier, A., Kramarenko, V., 2007. Modalities ofmoving to inflation targeting in Armenia and Georgia. IMF Working Papers No. 133.

De Grauwe, P., Vansteenkiste, I., 2007. Exchange rates and fundamentals: a non-linearrelationship? International Journal of Finance & Economics 12, 37–54.

DiCecio, R., 2005. Comovement: it's not a puzzle. FRB of St. Louis Working Paper No.2005-035A.

Dridi, R., Guay, A., Renault, E., 2007. Indirect inference and calibration of dynamic sto-chastic general equilibrium models. Journal of Econometrics 136, 397–430.

Dupor, B., Han, J., Tsai, Y., 2009. What do technology shocks tell us about the NewKeynesian paradigm? Journal of Monetary Economics 56, 560–569.

El-Ganainy, A., Weber, A., 2010. Estimates of the output gap in Armenia with applica-tions to monetary and fiscal policy. IMF Working Papers No. 197.

Engel, C., 1996. The forward discount anomaly and the risk premium: a survey of re-cent evidence. Journal of Empirical Finance 3, 123–192.

Engwerda, J., Boldea, O., Michalak, T., Plasmans, J., Salmah, 2012. A simulation study ofan ASEAN monetary union. Economic Modelling 29, 1870–1890.


Flavin, M., Nakagawa, S., 2008. A model of housing in the presence of adjustment costs:a structural interpretation of habit persistence. The American Economic Review 98,474–495.

Froot, K., Thaler, R., 1990. Anomalies: foreign exchange. The Journal of Economic Per-spectives 4, 179–192.

Fuhrer, J., Rudebusch, G., 2004. Estimating the Euler equation for output. Journal ofMonetary Economics 51, 1133–1153.

Galí, 2008. Monetary Policy, Inflation and the Business Cycle: An Introduction to theNew Keynesian Framework. Princeton University Press, Princeton, NJ, U.S.A.

Galí, J., Gertler, M., 1999. Inflation dynamics: a structural econometric analysis. Journalof Monetary Economics 44, 195–222.

Gorter, J., Jacobs, J., De Haan, J., 2008. Taylor rules for the ECB using expectations data.The Scandinavian Journal of Economics 110, 473–488.

Guvenen, F., 2006. Reconciling conflicting evidence on the elasticity of intertemporalsubstitution: a macroeconomic perspective. Journal of Monetary Economics 53,1451–1472.

Hall, A., Inoue, A., Jana, K., Shin, C., 2007. Information in generalized method of mo-ments estimation and entropy-based moment selection. Journal of Econometrics138, 488–512.

Hall, A., Inoue, A., Nason, J., Rossi, B., 2012. Information criteria for impulse responsefunction matching estimation of DSGE Models. Journal of Econometrics 170,499–518.

Jordà, Ò., Kozicki, S., 2007. Estimation and inference by the method of projection min-imum distance. Bank of Canada Working Paper.

Karam, P., Pagan, A., 2008. A small structural monetary policy model for small openeconomies with debt accumulation. IMF Working Paper No. 64.

Lewis, K., 1995. Puzzles in International Financial Markets. In: Grossman, G., Rogoff, K.(Eds.), Handbook of International Economics. Elsevier, Amsterdam, pp. 1913–1949.

Ma, A., 2002. GMM estimation of the new Phillips curve. Economics Letters 76,411–417.

Mavroeidis, S., 2004. Weak identification of forward-looking models in monetary eco-nomics. Oxford Bulletin of Economics and Statistics 66, 609–635.

Mihailov, A., Rumler, F., Scharler, J., 2011. The small open-economy new KeynesianPhillips curve: empirical evidence and implied inflation dynamics. Open Econo-mies Review 22, 317–337.

Mkrtchyan, A., Dabla-Norris, E., Stepanyan, A., 2009. A New Keynesian model of the Ar-menian economy. IMF Working Papers No. 66.

Plasmans, J., Verkooijen, W., Daniëls, H., 1998. Estimating structural exchange ratemodels by artificial neural networks. Applied Financial Economics 8, 541–551.

Razin, A., Yuen, C.-W., 2002. The ‘New Keynesian’ Phillips curve: closed economy ver-sus open economy. Economics Letters 75, 1–9.

Rotemberg, J., Woodford, M., 1997. An optimization-based econometric model for theevaluation of monetary policy. NBER Macroeconomics Annual 12, 297–346.

Rudd, J., Whelan, K., 2005. Does labor's share drive inflation? Journal of Money, Credit,and Banking 37, 297–312.

Rudebusch, G., 2002. Term structure evidence on interest rate smoothing and mone-tary policy inertia. Journal of Monetary Economics 49, 1161–1187.

Ruge-Murcia, F., 2007. Methods to estimate dynamic stochastic general equilibriummodels. Journal of Economic Dynamics and Control 31, 2599–2636.

Smets, F., Wouters, R., 2005. Comparing shocks and frictions in US and euro area busi-ness cycles: a Bayesian DSGE Approach. Journal of Applied Econometrics 20,161–183.

Smets, F., Wouters, R., 2007. Shocks and frictions in US business cycles: a BayesianDSGE approach. The American Economic Review 97, 586–606.

Stock, J., Yogo, M., 2005. Testing for weak instruments in linear IV regression. In:Andrews, D., Stock, J. (Eds.), Identification and Inference for Econometric Models: Es-says in Honor of Thomas Rothenberg, Lecture Notes in Computer Science. CambridgeUniversity Press, pp. 80–108.

Uribe, M., Yue, V., 2006. Country spreads and emerging countries: Who drives whom?Journal of International Economics 69, 6–36.

Woodford, M., 2003. Interest and Prices: Foundations of a Theory of Monetary Policy.Princeton University Press, Princeton, NJ, U.S.A.

Zhang, C., Osborn, D., Kim, D., 2008. The new Keynesian Phillips curve: from sticky in-flation to sticky prices. Journal of Money, Credit, and Banking 40, 667–699.

structural versus matching estimation: transmission mechanisms in armenia

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