BIS Working Papers
Monetary policy spillovers, global commodity prices and cooperation
by Andrew Filardo, Marco Lombardi, Carlos Montoro and Massimo Ferrar
Monetary and Economic Department
JEL classification: F36, F41, G20
Keywords: global value chains, dollar invoicing, global liquidity
This publication is available on the BIS website (www.bis.org).
© Bank for International Settlements 2017. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated.
ISSN 1020-0959 (print)
ISSN 1682-7678 (online)
Monetary policy spillovers, global commodity prices and cooperation
Andrew Filardo , Marco Lombardi , Carlos Montoro and Massimo Ferrari
How do monetary policy spillovers complicate the trade-offs faced by central banks face when responding to commodity prices? This question takes on particular relevance when monetary authorities find it difficult to accurately diagnose the drivers of commodity prices. If monetary authorities misdiagnose commodity price swings as being driven primarily by external supply shocks when they are in fact driven by global demand shocks, this conventional wisdom – to look through the first-round effects of commodity price fluctuations – may no longer be sound policy advice.
To analyse this question, we use the multi-country DSGE model of Nakov and Pescatori (2010) which breaks the global economy down into commodity-exporting and non-commodity-exporting economies. In an otherwise conventional DSGE setup, commodity prices are modelled as endogenously changing with global supply and demand developments, including global monetary policy conditions. This framework allows us to explore the implications of domestic monetary policy decisions when there is a risk of misdiagnosing the drivers of commodity prices.
The main findings are: i) monetary authorities deliver better economic performance when they are able to accurately identify the source of the shocks, ie global supply and demand shocks driving commodity prices; ii) when they find it difficult to identify the supply and demand shocks, monetary authorities can limit the deterioration in economic performance by targeting core inflation; and iii) the conventional wisdom approach of responding to global commodity price swings (as external supply shocks when they are truly global demand shocks) results in an excessive procyclicality of global inflation, output and commodity prices. In light of recent empirical studies documenting a significant role of global demand in driving commodity prices, we conclude that the systematic misdiagnoses inherent in the conventional wisdom applied at the country level have contributed to destabilising procyclicality at the global level. These findings support calls for greater attention to global factors in domestic monetary policymaking and highlight potential gains from greater monetary policy cooperation focused on accurate diagnoses of domestic and global sources of shocks.
Keywords: commodity prices, monetary policy, spillovers, global economy.
JEL classification: E52, E61.
We thank conference participants at the Central Bank of Brazil’s XVII Annual Inflation Targeting Seminar, CEMLA’s XX Annual Meeting and CEBRA’s 2017 Annual Meeting. We also thank seminar participants at the Bank for International Settlements, the Bank of Canada and Bank of Japan for their comments. The views expressed here are those of the authors and do not necessarily reflect those of the Bank for International Settlements, the Central Reserve Bank of Peru.
Over the past decade, global commodity prices have experienced wide swings, reaching historically high levels in the run-up to the Great Recession before plummeting as the global economy collapsed. Prices subsequently rebounded with the global economic recovery but, more recently, commodity prices have fallen again amid significant policy concerns. While challenging, this type of volatility is not a new environment for policymakers. Even though most commodity prices remained broadly stable during the so-called Great Moderation, they were quite volatile in the 1970s amid geopolitical tensions that pushed oil price volatility to then unprecedented levels.
It was the experience of the 1970s that forged the conventional wisdom about how monetary authorities should respond to commodity price fluctuations. Commodity price fluctuations were seen largely as the result of exogenous supply shocks; in such an environment, the conventional wisdom that emerged was that, when facing such swings, monetary authorities should look through the first-round price effects and only respond to the second- round effects on wage and inflation expectations. In practice, this suggested a monetary policy focus on core inflation.
Views about the drivers of global commodity price swings have been evolving, especially in recent years, as a growing body of statistical evidence points to a new interpretation of commodity price swings. Kilian (2009), for example, finds evidence that oil price fluctuations have been increasingly influenced by demand from commodity-hungry emerging market economies (EMEs). The most recent literature has not challenged this view: Kilian and Baumeister (2016) argue that the oil price decline in 2015 should also be ascribed to a slowdown in global economic activity; and Stuermer (2017) and Fukei et al (2018) emphasises the role of demand shocks in a historical perspective. In a similar vein, Sussman and Zohar (2017) report that commodity price fluctuations can be taken as a proxy for global demand. In a broader context, Filardo and Lombardi (2013) note the growing prominence of these global demand shifters for EME inflation dynamics. This new evidence raises doubts about the relevance of the conventional wisdom and may even suggest that the exogenous supply shock view is not only misleading but actually contributing to global economic and financial instability.
The prominence of endogenous commodity price swings has important implications for monetary policy, given the central role of monetary policy in influencing aggregate demand. The relationship between monetary policy decisions and endogenous commodity prices implies an important two-way link. Monetary policy decisions influence aggregate demand and hence commodity prices. Indeed, Filardo and Lombardi (2013) and Anzuini et al report evidence that loose monetary policy has had an impact on commodity prices via the global demand channel.5 At the same time, commodity price swings influence price stability and hence monetary policy decisions.
This two-way relationship can operate to stabilise the economy under certain conditions and de-stabilise the economy under others. For example, when monetary authorities around the world correctly diagnose the nature of the shocks driving commodity prices and internalise the monetary policy spillovers across national borders, monetary policy can be stabilising. However, when monetary authorities systematically misdiagnose the nature of the shocks driving commodity prices and largely ignore the spillover effects of their collective actions, monetary policy at the global level can be excessively procyclical.
The misdiagnosis risk is particularly high in a world of many central banks with purely domestic monetary policy mandates. Individual countries may think that because they are sufficiently small, they can reasonably ignore the impact of their own policy decisions on the rest of the world. This would be the case if all economies were hit by uncorrelated idiosyncratic shocks.
However, global shocks imply that central banks are likely to respond in a correlated way. So, in the case of a global demand shock, country-level monetary policy responses highlight the potential for a fallacy of size, ie when monetary authorities respond in a similar way to global shocks, the collection of monetary authorities effectively act as if they were a large monetary authority.
The fallacy of size and the potential role of misdiagnosing the drivers of commodity prices also cast light on the shortcomings of the current international monetary system. In this context, questions are being raised about whether monetary authorities are sufficiently internalising monetary policy spillovers and spillbacks. The failure to do so would contribute to both economic and financial stability concerns (Rajan (2014) and Caruana et al (2014)).
From a modelling perspective, this discussion suggests the importance of developing monetary policy models encompassing endogenous commodity prices and monetary authorities that are subject to misdiagnosis risk. To date, the bulk of the theoretical literature has stayed clear of models with endogenous commodity prices (see eg Leduc and Sill (2004), Carlstrom and Fuerst (2006), Montoro (2012), Natal (2012) and Catao and Chang (2015)). Moreover, this literature has generally focused on how a monetary authority should respond to exogenous movements in oil prices, eg whether it is optimal to target core or headline inflation and whether commodity price movements have far-reaching implications for the trade-off between stabilising output and controlling inflation. For example, Blanchard and Gali (2010) have gone so far as to argue that an increase in commodity prices driven by foreign demand can still be treated by a domestic monetary authority as an external supply shock. Such a conclusion is less tenable in models of endogenous commodity prices and correlated monetary policy reaction functions.
Various theoretical papers have addressed the endogeneity of commodity prices in small-scale DSGE models (eg Backus and Crucini (1998),
Bodenstein et al (2011) and Nakov and Nuno (2013)). However, these models have generally ignored monetary policy, focusing instead on oil price determination and the frictions affecting it. Nakov and Pescatori (2010) is an early attempt to characterise monetary policy trade-offs in a DSGE model in which oil prices are determined endogenously. Another important contribution to this literature is Bodenstein et al (2012), who highlight, as we do, the importance of identifying the nature of the shocks hitting the economy.
Our model extends this class of models by considering the policy challenges facing a monetary authority when it tries to infer the source of commodity price shocks. Namely, there is a risk that a monetary authority may misdiagnose a commodity price swing as being driven by an external supply shock when it is, in fact, driven by an endogenous global demand shock, and vice versa. In our model, the commodity price is endogenously determined in equilibrium by the interplay of global demand from a commodity-importing country (or region) and commodity supply from two types of commodity-exporting country - one competitive and one monopolistic. In this setting, the optimal monetary policy response to commodity price swings depends on the perception of the underlying drivers of the swings. Unable to fully know the nature of the drivers, the monetary authority infers them via signal extraction, leaving open the possibility of systematic misdiagnosis. The nature and implications of misdiagnosis risk are addressed.
The modelling exercise highlights several policy-relevant implications. First, it is important to distinguish between global demand and supply shocks when a monetary authority responds to commodity prices. The optimal responses to global demand and supply shocks are different. On the one hand, the optimal response to demand shocks is to lean against them fully, a result consistent with a standard New Keynesian closed economy model. On the other hand, the optimal response to commodity supply shocks (ie a decrease in commodity prices) is to look through them.
Second, by looking through the impact on headline inflation, monetary policy does not perfectly stabilise core inflation. In other words, the conventional wisdom of looking through the first-round effects of commodity price swings is not optimal in our model. This is because our model breaks the "divine coincidence" between inflation and output gap stabilisation (eg Blanchard and Gali (2007)), which is a standard feature of DSGE models with exogenous commodity prices. In part, the breaking of such a divine coincidence comes from the assumption of a monopolistic commodity exporter that sets prices by assuming a downward sloping demand curve.
Third, misdiagnosis risk matters in monetary policy. In the case where the monetary authority misinterprets supply-driven increases in commodity prices as demand-driven, the contraction in both output and core inflation is larger than in the case of an accurate diagnosis. This outcome indicates another reason for the breakdown of the divine coincidence in this model (even if the dominant exporter acts as a price taker). This finding underscores the importance of correctly diagnosing the underlying sources of commodity price swings when setting monetary policy. For example, when commodity price fluctuations are driven by global demand shocks, a monetary authority that consistently misdiagnoses them as external supply shocks amplifies cyclical fluctuations and, as a result, destabilises the economy.
Of course, in any uncertain environment, there is a risk that shocks will be misdiagnosed. But in the case of correlated global shocks and domestically- oriented monetary policy mandates, the risk is particularly high. When facing global commodity price swings, there is a natural tendency for a given monetary authority - even in a relatively large country - to treat them as if they were exogenously-determined external supply shocks. Clearly, one lone monetary authority has little, if any, impact on global prices. However, if a sufficient number of monetary authorities were to act in a similar (and uncoordinated) way, their joint behaviour would result in procyclical effect that could destabilise the global economy. This coordination failure supports the case for greater central bank cooperation in a world experiencing wide endogenous commodity price swings.
II. The model
We present a global economic model in which commodity prices are determined endogenously, in the spirit of Nakov and Pescatori (2010).7 The global economy is split into commodity importers and exporters. The commodity-importing region is treated as one representative country (but this can be extended to a group of importing countries without loss of generality). The commodity-importing country does not produce the commodity itself but uses it both as a consumption good and as an input into the production of final goods. Final goods producers in the commodity- importing country are subject to monopolistic competition and nominal rigidities, and the central bank sets monetary policy using a linear policy rule a la Taylor (1993).
The commodity-exporting region is made up of a dominant commodity- exporting country and a fringe of smaller competitive exporters. These countries produce the commodity using final goods sold by the commodity- importing region. In addition, the commodity-exporting countries buy final goods for their consumption from the commodity-importing country.
On the supply side, the dominant commodity-exporting country has market power and sets prices above marginal cost. The fringe of small exporting countries is similar in structure to the dominant exporting country but operates competitively, taking commodity prices as given. Note that nominal rigidities are absent in the commodity-exporting countries, thereby simplifying the modelling of monetary policy trade-offs; in this model, there is only a role for a monetary authority to conduct countercyclical policy from the perspective of the commodity-importing country.
The rest of this section provides the modelling details.
II.1. Commodity-importing countries
II.2. Commodity-exporting countries
The commodity industry is modelled as comprising a dominant commodity exporter and a fringe group of competitive commodity exporters. The relative market share of the imperfectly competitive dominant exporter vis-à-vis the competitive fringe is important because it will influence the transmission channel of monetary policy. Market share can be varied to study the impact 14 of the degree of competitive. That is, the market share of the dominant commodity exporter can range from zero to one, which corresponds to a range of market dynamics from perfect competition to a monopoly situation.
II.2.1 Dominant commodity exporter
III. Characterising optimal monetary policy
Monetary policy in the commodity-importing country is modelled as a linear Taylor-type rule determined by deviations from model-based benchmarks for output, inflation and the interest rate. In this section, the benchmarks are defined and the implications of alternative policy rules are analysed.
III.1. Output gap benchmarks
Benchmark output gaps can be derived by substituting the equations for labour demand (2.28), labour supply (2.6), aggregate demand (2.50) and commodity demand for production (2.29) into the aggregate production transfers to households are funded by taxing final good producers. 20 function (2.30). The level of output in terms of marginal costs, the dispersion of prices, productivity and the real commodity price is:
III.4. Analysing monetary policy rules
This section explores the model dynamics under alternative monetary policy rules, highlighting the differential responses to demand and commodity supply shocks. The baseline policy rule assumes that the monetary authority responds to core inflation and the efficient output gap.17 It is of the form:
where the relative weights on core inflation and the output gap determine the trade-off between core inflation and output gap stabilisation. The benchmark interest rate also influences the optimal policy setting. We additionally assume that the monetary authority is able to observe inflation and output with a one period lag - hence the presence of the expectations operator - whereas commodity prices are available in real time. Therefore, the central bank uses the forecast (ie the expectation based on the information set available in the previous period) of inflation and output to conduct monetary policy and the observed (contemporaneous) change in the commodity price Aq.
For most structural parameters, the calibration is in line with those found in the literature (Table 1). For the parameters associated with the commodity market, the choice is a bit more arbitrary owing to the less conventional view of the literature. The share of the commodity in the consumption basket is set to 10%, which roughly matches the share of primary commodity inputs in the
As commonly found in the DSGE literature, a markup shock can be fully neutralised by monetary policy: the increase in the policy rate completely offsets any impact on the key macroeconomic variables as well as on those associated with the commodity market. So, we also introduced a more traditional type of demand shock - ie an exogenous shift in aggregate demand. This is displayed in Graph 1: due to the nature of the shock, a change in the interest rate is not sufficient to offset it, and a positive output gap remains open for around six quarters.
Similarly, the monetary authority is unable to offset a commodity supply shock (Graph 2). The policy rate response as well as the macroeconomic impacts are, however, very modest. This confirms the conventional wisdom that monetary authorities should look through the first-round effects of commodity supply shocks.
III.4.1 A note on the natural benchmark
To simplify the discussion, we do not report the impulse responses for the natural policy rule. It is useful to note, however, that the dynamics associated with a commodity supply shock generate similarities and differences compared to the efficient rule. For both the natural and efficient benchmarks, a negative supply shock increases the commodity's price, boosts headline inflation and reduces the amount of the commodity supplied by the exporters. The levels of natural and efficient output both decline, with the level of efficient output falling more. In the efficient case, the decline in the level of efficient output partially offsets the increase in the commodity's price via a reduction in the markup. The trade-off between inflation and output are different in the two cases. Core inflation and the output gap are completely stabilised in the natural benchmark case. But in the efficient benchmark case, the efficient output gap rises and core inflation declines. This indicates that a monetary authority following an efficient policy rule partially offsets the effects of the higher commodity price on headline inflation with lower core inflation.
III.4.2 Welfare calculations
The performance of the efficient policy rule in equation (3.13) is also assessed in terms of the welfare of the representative household (ie from the commodity-importing country), along with two alternative policy rules that take the general form:
For policy rule (3.14), the monetary authority responds only to core inflation. For policy rule (3.15), the response is to headline instead of core inflation.
Table 2 reports the welfare losses associated with a commodity supply shock, in terms of steady state consumption, using the efficient policy rules. The first column corresponds to the baseline policy rule (3.13), while columns 2 and 3 corresponds to two alternative calibrations of the efficient policy rule calibration for column 5 is meant to capture the notion that a monetary authority may consider responding somewhat more strongly to the commodity price than a conventional Taylor-type rule would suggest.
The optimal policy rule (column 1) assumes jy = 0 and jcom = 0, ie there is no response to the efficient output gap and to commodity prices. It provides a welfare loss that can be compared with the other specifications.
In columns 2, 3, 4 and 5, the policy rules that respond directly to the commodity's price and headline inflation generate larger welfare losses than the policy rule in column 1. This is because the policy rule of column 1 already takes into account the effects of the commodity's price; the additional responses to changes in the commodity price and headline inflation in the alternative policy rules simply generate more volatile interest rates than is optimal. These results highlight the importance of monitoring and responding to core inflation rather than headline inflation. Note, however, that a moderate response to commodity prices (column 4) reduces welfare losses compared to the optimal policy (3.14).IV. Incomplete information, misdiagnosis and monetary policy spillovers
In practice, monetary authorities do not know in real time which shocks are affecting their jurisdictions: all they can observe are movements in the international prices of commodities. Moreover, the readings on inflation and output will not be available in real time. Given that the optimal responses to demand and supply shocks differ, this complicates the formulation of an appropriate monetary policy reaction,. On top of this, a supply shock would affect the efficient output benchmark, while a demand shock would not, which would generate additional uncertainty on the output gap.
This section considers the challenges arising from misdiagnosis, ie the risk that a monetary authority misinterprets the source of the shocks driving commodity price fluctuations. The optimal monetary policy response to demand and supply shocks differs: the optimal response to demand shocks is to fully neutralise their effects on output and inflation, so that the commodity's price is stabilised. By contrast, the optimal response to negative commodity supply shocks is to partially offset their effects on headline inflation by a reduction in both core inflation and the output gap. As a consequence, misdiagnosis of the source of the shocks will lead to a deterioration in economic outcomes.
IV.1. Monetary policy under incomplete information
As pointed out in Section III, the source of the shocks matters for the determination of the benchmark output gap and natural rate. This complicates the real-time problem that policymakers face, ie the inability to observe output and inflation in real time. In practice, policymakers observe commodity prices in a timely fashion but only observe output and inflation with a lag. So there is the risk that a monetary authority will misdiagnose the state of the economy in real time. In this section, we highlight the monetary policy challenges under two types of learning: the first is a classical signal extraction problem in which the monetary authority bases its assessment of commodity demand and supply shocks on past data; and the second in which the monetary authority updates its assessments of the source of the shocks with information about how the economy responds to its monetary policy actions.
IV.2. The signal-extraction problem
In the previous section, the degree of uncertainty faced by the monetary authority is limited to shocks to the benchmarks. In this section, we consider the decision-making problem faced by the monetary authority when it does not observe the supply and demand shocks ( zt and y ) driving the commodity's price. The monetary authority can only infer the shocks from past behaviour. To model this, we assume the commodity price takes the form:
Given this informational structure, the monetary authority infers the sources of commodity price fluctuations by solving a signal-extraction problem using a Kalman filter, ie:
Three cases of equation (4.3) help to shed light on the trade-offs facing the monetary authority. In the first case (type A), when x ^ 0, the volatility of the commodity supply shock is high relative to that of the commodity market markup. In this case, the monetary authority attributes nearly all of the fluctuations to the commodity price markup. That is:
In the last case (type C), the monetary authority attributes commodity price fluctuations partially to each component of the commodity price, taking into account the relative volatility and correlation the components, as in equation (4.4). Given the monetary authority's inference of the drivers of commodity price fluctuations, Etna(zt) and E™(y), the monetary authority uses the policy benchmarks, Etna(rtss) and En^y™), in the policy rule (3.13).
where j and j capture the relative weiqht of stabilising inflation and the welfare-relevant output gap. Given E’nyzt) and E^yy) , the monetary authority can form expectations based on the inferred origin of the shock driving the change in commodity prices Aq. If the monetary authority fails to correctly identify the shocks driving the commodity price fluctuation, a policy error arises. That is:
corresponds to a misdiagnosis error, which is an endogenous variable, and E™- denotes the expectations under the incorrect diagnosis on the source of the shock. Note that when the monetary authority imputes the change in commodity prices to the wrong type of shock, its estimates of endogenous variables will be incorrect, leading to persistent errors in the interest rate setting.23 To see this, we augment our dynamic system with equation (4.6) and analyse the implications for the impulse responses.
If the monetary authority correctly identifies the source of the shock, the error is zero.
Graph 3 shows the impulse responses to a commodity supply shock in the misdiagnosis case A. Even though the commodity price is driven by a supply shock, the monetary authority misdiagnoses it as a traditional demand-driven commodity shock. If the monetary authority fails to recognise that an increase in the commodity price is driven by external supply conditions, the consequence is overly tight monetary policy accompanied by an excessive drop in both output and inflation. The commodity price rises less than in the baseline case because of tighter monetary policy. Core and headline inflation both fall because of the economy's slowdown.
Graph 4 shows the impulse responses to a conventional aggregate demand shock in the case of misdiagnosis type B, in which the rise in the commodity's price is mistakenly attributed to a negative commodity supply shock. In this case, the easier monetary policy associated with an attempt to look-through the rise in the commodity price results in higher output and inflation. This type of policy misdiagnosis induces a very procyclical increase in the commodity price.
Graphs 5 and 6 report the results for the case of a misdiagnosis of type C, in which the monetary authority implements an optimally weighted response to the commodity price rise based on the historical correlation of commodity demand and supply shocks as per equation (4.4). The standard deviations of the supply and demand shocks for the Kalman filter are calibrated to the empirical estimates by Filardo and Lombardi (2013), which yields a ratio (x in equation (4.4)) of about 1.5. Consistent with the general conclusions from misdiagnosis types A and B, the monetary authority responds excessively to supply shocks and insufficiently to demand shocks: hence, monetary policy turns out overall to be excessively procyclical.
On the policy implication side, the difference between equations (3.9) and (4.6) implies a failure to stabilise core inflation in the short run (as is verified in Graphs 3-6). As a consequence, and to the extent to which the monetary authority cannot infer the nature of the shocks perfectly, the policy reaction will inherently tend to amplify fluctuations in commodity prices and the macroeconomy more generally. In the case where the monetary authority misinterprets a rise in the commodity price as supply-driven, the contraction in both output and core inflation would be larger than in the full information case. And, in the case where commodity price fluctuations are driven by global demand, the monetary authority would amplify cyclical fluctuations and, as a result, destabilise the economy. These results underscore the importance of correctly identifying the underlying nature of commodity price shocks. A corollary of this is that if monetary authorities can and do take efforts to learn about the true nature of the shocks, they can improve macroeconomic outcomes. Finally, the results suggest that a monetary authority focused on core inflation would help to stabilise the economy more actively in the presence of misdiagnosis risk than one focused on headline inflation.IV.4. Cooperation and monetary policy spillovers
This section considers the possibility - if not a natural tendency - of monetary authorities in small economies to treat global demand shocks as external supply shocks. It follows that if all monetary authorities were to misdiagnose the nature of the shocks and respond in a similar manner, their responses would be highly correlated across countries and potentially result in unintended destabilising feedbacks of the type discussed in the previous section, ie this would result in systematically procyclical monetary policy at the global level. A key question is, how strong is the incentive to treat global demand shocks as external supply shocks (ie deliberately misdiagnose the nature of the shock)? In our model, that incentive turns out to be significant.
To assess the relevance of the misdiagnosis incentive, consider a world of incomplete monetary policy cooperation in which monetary authorities act in
a manner that is consistent with a Nash policy equilibrium, ie taking the actions of the other countries as given and assuming no monetary policy spillovers. Without loss of generality, also assume that the size of commodity- importing economies is identical. Let one group comprising N-1 commodity- importing economies follow the optimal monetary policy rule from Section.
Formalising this logic, assume there are N commodity-importing countries indexed by i such that they face a problem similar to that discussed in Section III. The efficient policy rule for each N-1 monetary authorities takes the form found in equation (3.13):
The extent of the incentive to deviate from the group can be evaluated, in terms of monetary policy implications, by examining the coefficients in the policy rule. For coefficients that are close, the incentive to deviate is small. For large deviations, the incentive is correspondingly large.
See appendix F for a complete derivation of the impact of the demand from one single country i on the global commodity price.
As noted above, if one country had an incentive to deviate from the consensus, then each country facing the same situation would have a similar incentive to deviate, which would have implications for the whole group. Moreover, there is a "first mover" advantage, which by itself reinforces the likelihood of non-optimal group behaviour. That is, the incentive for each to deviate implies that the group is likely to collectively act as if it were misdiagnosing the true nature of the shock. The result is procyclical monetary policy at the global level. By ignoring monetary policy spillovers and spillbacks, this tendency to act as if global demand shocks were exogenous means that external supply shocks naturally open up potential gains from policy coordination.V. Learning from past mistakes
In this section, we allow the policymaker to learn from the economy's reaction to its policy decision.25 This is in contrast to the more elaborate information set in the Section IV, where, the monetary authority diagnosed the nature of the shock at t=1 and conditioned the subsequent monetary policy responses on its initial (mis-)diagnosis. For example, if it diagnosed the shock to be a supply shock (even though it was a demand shock), the monetary authority would respond without ever updating its initial diagnosis about the nature of the shock. In this section, the monetary authority is assumed to be able to learn about the initial source of the shock over time and therefore updates its initial diagnosis about the source of the shock. In this way, the impulse responses may converge faster over time to those associated with the full information impulse responses.
The rate of learning will depend on the full range of shocks at the time of the commodity price shock, as well as all the subsequent shocks that may potentially obscure the origins of the commodity price shock. We model this dynamic with Bayesian learning. The setup is as follows. On impact (t=1), the monetary authority has a prior about the source of the shock and makes an inference about it. For our illustrative exercise, the mass of the prior distribution is centered well away from the true shock distribution.
We first focus on the case of a supply shock misinterpreted as a demand shock (similar to misdiagnosis A). We start by setting the monetary authority's prior probability of a demand shock at P0(D)=0.99 and for a supply shock Po(S)=0.01. At the end of the period, the monetary authority observes output and inflation. Since additional shocks may have occurred, the central bank attaches a probability distribution to the outcomes it expects to observe. In other words, the prior probability placed on the D scenario (originating shock was demand) induces a prior for the outcomes for output and inflation. As the authorities thought the originating shock was from the demand side, such prior probability distribution is centered around the outcomes that would have occurred if the originating shock was indeed a demand shock, ie around the baseline response of Graph 1. Instead, the originating shock was actually a supply shock, and the actual outcome is the combination of the originating supply shock and the monetary policy shock induced by the misperception. So, the outcomes are drawn from a distribution that is centered around the responses of the misperception A exercise in Graph 3. As the monetary authority observes values of output and inflation that are far from their prior beliefs, it updates its inferences about the initial shock according to the likelihood of what they have observed under the D scenario: more formally, the posterior probability at time t=1 is:
where L(D|ni,yi) and L(S|n1,yi) are, respectively, the likelihood of an originating demand or supply shock based on observed output and inflation.
This is visualised in Graph 7, which reports the prior distributions for core inflation, the output gap, the likelihood of the observed outcomes and the resulting posterior distribution as well as the implied probability distribution of the policy rate.
The posterior distribution at time t=1 is used as the protoprior for the period t=2 and gets, in turn, updated by the new observations. In general, the updating follows the following recursive equation:
This produces a sequence of posterior probabilities that the monetary authority attaches to the original nature of the shock as new information becomes available.
We summarise results up to t=3 for the misperception case A in Graph 7. At time t=1, a supply shock hits the economy but the central bank treats is as a demand shock. The first row of Graph 7 shows the distribution of inflation under the two scenarios. As the likelihood and the prior are still well distinguished, the posterior distribution turns out to be bi-modal. Yet the distribution of the output gap (second row) is less precise and the posterior distribution is not bimodal.
At time t=2, the prior and the likelihood are closer to each other, as the monetary authority starts learning about the initial misdiagnosis and responds optimally. The posterior distribution becomes more unimodal. Note, however, that some of the convergence is also due to fairly rapid convergence of the impulse responses under the baseline and the case of misperception A. As a consequence, the interest rate response (bottom row) is somewhere between the prior and the likelihood.
Results for the case of misperception B (Graph 8) also show the benefits of learning. In this case, the initial monetary policy response turns out to be excessively loose. As the monetary authority learns about the mistake and eventually corrects its stance, the resulting policy is procyclical with output and inflation more volatility than if the shock had been diagnosed correct.
This Bayesian exercise suggests that it may be very difficult in real time for a monetary authority to infer an initial misdiagnosis. Of course, if the commodity price shock is very large relative to the other shocks hitting the economy, the learning will be faster as the economy's reaction to the true shock will show through more prominently in the posterior distribution. But for run-of-the-mill shocks of the type calibrated in this paper, the ability of a monetary authority to learn from past mistakes may be constrained by looking simply at the macroeconomic consequences of its policy actions. This exercise suggests that efforts to uncover the initial shocks exploiting microeconomic and the cross-country data would be useful and suggests that better international cooperation and information sharing could prove welfare enhancing.VI. Conclusions
The main findings of this paper are that: i) monetary authorities deliver better economic performance when they are able to accurately identify the source of the shocks, ie global supply and demand shocks, driving commodity prices; ii) when it is difficult to identify the supply and demand shocks, monetary authorities can limit the deterioration in economic performance by targeting core inflation; and iii) as a cautionary note, if monetary authorities face a risk of misdiagnosing commodity price fluctuations, ie as a result of external (or exogenous) supply shocks when they are truly driven by global demand shocks, their policy actions can contribute unwittingly to increased procyclicality of global inflation, output and commodity prices.
These findings argue for greater prominence to be given to global factors in domestic monetary policymaking. They also support calls for greater monetary policy cooperation, if only to institutionalise the sharing of information about the nature of shocks hitting economies. In the case where all monetary authorities initially see shocks hitting their respective economies as arising from external sources, such cooperation might lead to a useful pause and a reality check before acting.
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