We are grateful to John Rogers, Ken West, two anonymous referees, seminar participants at the JMCB/Fed Conference on “International Influences on Domestic Prices,” the CCBS Conference on “New Developments in Dynamic Factor Modeling,” and especially to our discussants, Marc Giannoni and Thomas Laubach, for very useful comments and suggestions. The views expressed in this work are those of the authors and do not necessarily reflect those of the Bank of England or the Monetary Policy Committee.

# The Transmission of International Shocks: A Factor-Augmented VAR Approach

Version of Record online: 22 JAN 2009

DOI: 10.1111/j.1538-4616.2008.00199.x

© 2009 Crown Copyright

Issue

## Journal of Money, Credit and Banking

Volume 41, Issue Supplement s1, pages 71–100, February 2009

Additional Information

#### How to Cite

MUMTAZ, H. and SURICO, P. (2009), The Transmission of International Shocks: A Factor-Augmented VAR Approach. Journal of Money, Credit and Banking, 41: 71–100. doi: 10.1111/j.1538-4616.2008.00199.x

#### Publication History

- Issue online: 22 JAN 2009
- Version of Record online: 22 JAN 2009
- Received October 31, 2007; and accepted in revised form July 23, 2008.

- Abstract
- Article
- References
- Cited By

### Keywords:

- E52;
- F41

- international transmission;
- FAVAR;
- open economy anomalies;
- large information;
- identification

### Abstract

- Top of page
- Abstract
- 1. AN OPEN-ECONOMY FAVAR
- 2. RESULTS
- 3. THE EXCHANGE RATE AND FORWARD DISCOUNT PUZZLES REVISITED
- 4. SUBSAMPLE ANALYSIS
- 5. CONCLUSIONS
- Appendices
- LITERATURE CITED

The empirical literature on the transmission of international shocks is based on *small*-scale VARs. In this paper, we use a *large* panel of data for 17 industrialized countries to investigate the international transmission mechanism, and revisit the anomalies that arise in the empirical literature. We propose a factor augmented VAR (FAVAR) that extends the model in Bernanke, Boivin, and Eliasz (2005) to the open economy. The main results can be summarized as follows. First, the dynamic effects on the UK economy of an unanticipated fall of short-term interest rates in the rest of the world are: real house price inflation, investment, GDP and consumption growth peak after 1 year, wages peak after 2 years, and CPI and GDP deflator inflation peak during the third year. Second, a positive international supply shock makes the distribution of the components of the UK consumption deflator negatively skewed. Third, in response to a domestic monetary shock, we find little evidence of the exchange rate and liquidity puzzles and little evidence of the forward discount and price anomalies.

Understanding the international transmission of structural shocks is important for identifying the best policy response to international developments. In a world economy that has experienced a steady increase in goods, capital, and financial markets integration, the international dimension of the transmission mechanism has become an essential ingredient of the policy discussion.

A long-standing empirical literature, pioneered by Eichenbaum and Evans (1995) and Grilli and Roubini (1995), has used *small-scale* vector autoregressions (VARs) to identify the dynamic effects of foreign and domestic monetary policy shocks. The research program on the empirics of the international transmission mechanism has delivered a few open-economy anomalies such as the exchange rate and the forward discount puzzles.

Together with other anomalies such as the price and liquidity puzzles, already apparent in closed economy studies, these facts pose a serious challenge to our ability of isolating correctly a monetary shock. In an effort to improve identification, a number of contributions have proposed alternative schemes, ranging from nonrecursive to sign restrictions, which, however, have had mixed success in rationalizing the puzzles. A sample of important contributions include Cushman and Zha (1997), Kim and Roubini (2000), Faust and Rogers (2003), and Scholl and Uhlig (2005).

In this paper we approach this identification issue from another perspective. In particular, we examine the role played by the limited information set used in previous studies in generating various puzzles. Central banks across the world monitor (and possibly respond to) a far wider information set than typically assumed in small-scale VARs. To the extent that the additional information processed by central banks are not reflected in small-scale VARs, the measurement of policy innovations is likely to be contaminated: what appears to the econometrician to be a policy shock is, in fact, the response of the monetary authorities to the extra information not included in the VAR. This identification problem associated with omitted variables is well recognized in econometrics. In the empirical literature on the international transmission mechanism, the issue can only be more severe as the number of variables (and countries) that are relevant for policy analysis increases rapidly when moving from closed to open-economy investigations.

In this paper, we attempt to solve the limited information problem associated with small-scale empirical models by proposing an open-economy factor augmented VAR (FAVAR). We extract international and UK-specific common components from a large panel of data covering 17 industrialized countries and around 600 price, activity, and money indicators. We use the FAVAR to model the interaction between the UK economy and the rest of the world, which we treat as the “foreign” block.

The contribution of the paper is twofold. First, we quantify the dynamic effects on a wide variety of UK aggregate and disaggregate variables of a common shock to short-term interest rates and to real activity in the foreign block. Second, we assess the extent to which the open-economy anomalies documented in earlier empirical contributions can be explained by the limited information in small-scale VARs.

The main results are as follows. In response to a deviation from the systematic component of monetary policy across the rest of the world, the nominal exchange rate peaks within 1 year, implying that we find scant evidence of delayed overshooting. An unanticipated monetary expansion in the rest of the world exerts its maximum impact on real house price inflation, investment, GDP growth, and consumption growth after 1 year, on wages after 2 years, and on CPI and GDP deflator inflation during the third year. A positive international supply shock makes the sectoral distribution of UK consumption deflators negatively skewed. A domestic monetary policy shock in the UK is associated with little evidence for the exchange rate and liquidity puzzles; furthermore, the forward discount and the price anomalies are very modest and short-lived.

This work extends the FAVAR approach developed by Bernanke, Boivin, and Eliasz (2005) to the open economy. Other contributions using large panel of international data include Miniane and Rogers (2007), Laganá and Mountford (2005), Rüffer and Stracca (2006), and Sousa and Zaghini (2007). These papers, however, focus on the role of capital controls and excess global liquidity. Boivin and Giannoni's (Forthcoming) analysis is most similar in spirit to our paper: they use a FAVAR to gauge the evolution of the impact of the international factors on the U.S. economy. The two analyses, however, differ in a number of dimensions, including the structure of the FAVAR model, the identification strategy, the estimation method and the country analyzed in the empirical application.

An interesting alternative to the FAVAR approach is the global VAR model introduced by Dees et al. (2007). The global VAR incorporates an explicit model for all countries in the sample, which are linked via a set of observed and unobserved international factors. The global VAR is particularly convenient when the goal is to examine the impact of shocks that originate in *specific* foreign countries (rather than the rest of the world as in our FAVAR). On the other hand, the FAVAR is particularly convenient when the goal is to estimate the dynamic responses of a large number of home variables to foreign shocks. Furthermore, the FAVAR allows one to incorporate a large amount of information in the model in a very simple manner.

The paper is organized as follows. Section 1 presents a FAVAR model for open economies, discusses the identification, and briefly describes the wide set of international variables used in the empirical investigation. Section 2 reports the dynamic effects of an unexpected fall in world interest rates, an unexpected increase in world activities, and a positive international supply shock on selected UK variables. The exchange rate and forward discount puzzles are revisited in Section 3 where we present the impulse response functions to a UK monetary policy shock. The appendices provide details on the data and the identification.

### 1. AN OPEN-ECONOMY FAVAR

- Top of page
- Abstract
- 1. AN OPEN-ECONOMY FAVAR
- 2. RESULTS
- 3. THE EXCHANGE RATE AND FORWARD DISCOUNT PUZZLES REVISITED
- 4. SUBSAMPLE ANALYSIS
- 5. CONCLUSIONS
- Appendices
- LITERATURE CITED

A large empirical literature has investigated the international transmission of monetary and nonmonetary shocks using small-scale structural VAR. The correct identification of the systematic component of monetary policy has been widely recognized as crucial to trace out the dynamic effects of the shocks of interest.

Several contributions have proposed alternative identification structures including, among others, the recursive schemes in Grilli and Roubini (1995), Eichenbaum and Evans (1995), and Faust and Rogers (2003); the nonrecursive schemes in Cushman and Zha (1997), Kim and Roubini (2000), and Kim (2001); and the sign restrictions in Canova (2005) and Scholl and Uhlig (2005).

Despite the differences in identification, these contributions share two important features. First, the VARs are based on a few variables, rarely exceeding 14 at the very end of the spectrum. Second, the empirical results show evidence of open-economy anomalies, and it is difficult, for instance, to solve the delayed exchange rate overshooting and the forward discount puzzles simultaneously.

In analogy to the closed-economy contribution by Bernanke, Boivin, and Eliasz (2005), we ask whether the use of a wide information set, relative to earlier studies, can improve our understanding of the *international* transmission of policy and nonpolicy shocks and shed new lights on long lasting puzzles in international macroeconomics.

This section proposes an open-economy FAVAR model in which a large international panel of macroeconomic variables is used to identify an unanticipated fall in the interest rates of the rest of the world, an unanticipated expansion in world real activity, and a domestic monetary policy shock.^{1}

#### 1.1 The Empirical Model

The model consists of two blocks, one for the UK, which is named “domestic,” and one for the rest of the industrialized world, which is named “foreign” and it is ordered first. The information about the UK and rest of the industrialized world are summarized by *K* unobserved factors, *F _{t}*=[

*F**

_{t}

*F*]′ where asterisks denote the foreign economies. The UK short-term interest,

^{uk}_{t}*R*, is the only observable factor, and together with the unobserved common components it forms a dynamic system that evolves according to the following transition equation:

_{t}- (1)

where *B*(*L*) is a conformable lag polynomial of finite order *p*, and *u _{t}*=Ω

^{1/2}

*e*with the structural disturbances

_{t}*e*∼

_{t}*N*(0,

*I*) and Ω=

*A*

_{0}(

*A*

_{0})′.

The unobserved factors are extracted by a large panel of *N* indicators, *X _{t}*, which contain important information about the fundamentals of the economy. The factors and the variables in the panel are related by an observation equation of the form:

- (2)

where Λ^{F} and Λ^{Y} are *NxK* and *N*× 1 matrices of factor loadings, and *v _{t}* is a

*N*× 1 vector of zero mean disturbances.

The system 1–2 is the FAVAR model proposed by Bernanke, Boivin, and Eliasz (2005). Our main innovation relative to them is the introduction of a block for the rest of the world.

We assume that the foreign block *F**_{t} consists of four factors, *F**_{t}={Δ*Y**_{t}, Π*_{t}, Δ*M**_{t}, *R**_{t}}, where Δ*Y**_{t} represents an international real activity factor, Π*_{t} denotes an international inflation factor, Δ*M**_{t} is an international liquidity factor, and *R**_{t} denotes comovements in international short-term interest rates. These international factors are identified through the upper *N*× 4 block of the matrix Λ^{F}, which is assumed to be block diagonal. For instance, we extract the international real activity factor from all international real activity series in our panel. Similarly, the international inflation factor is identified as the only factor that is loaded by all international inflation series. The other international factors are identified accordingly.

The dynamics of the UK variables are captured by *k* domestic factors *F*^{uk}_{j,t}={*F*^{1,uk}_{t}, *F*^{2,uk}_{t}, … , *F*^{k,uk}_{t}}. The domestic factors are extracted from the full panel of UK series. In other words, the bottom *N*×*k* block of Λ^{F} is a full matrix. The reason for this choice comes from recognizing that the dynamics of the variables in *X _{t}* depends on the structure imposed on the factor loadings. If all domestic prices shared a single domestic inflation factor, then the domestic prices would also share the dynamics of that common component, up to a scale factor pin down by the loading. Our goal is to investigate any possible heterogeneity in the responses of domestic prices and activities across sectors, and therefore it would be unsatisfactory to impose a tight constraint on the dynamics of the individual series.

As in Bernanke, Boivin, and Eliasz (2005), we treat *R _{t}* as the monetary policy instrument (for the domestic economy). The dynamics of each domestic series is a linear combination of all UK factors, which are linked to the international factors via the transition equation (1). This implies that the response of any underlying UK variable in

*X*to a shock in the transition equation (1) can be calculated using the estimated factor loadings and equation (2).

_{t}The specification of our (reduced-form) model is related to the FAVAR in Boivin and Giannoni (Forthcoming). However, Boivin and Giannoni do not impose zero restrictions on the factor loadings in the international block of the VAR. This is important in our application as it allows us to identify different foreign shocks using a number of alternative identification strategies.

The model is subject to the rotational indeterminacy problem, and without a normalization it is econometrically unidentified. We follow Bernanke, Boivin, and Eliasz (2005), and use the standard normalization implicit in the principal components and take *C*′*C*/*T*=*I*, where *C*(·) represents the common space spanned by the factors of *X _{t}* in each block.

#### 1.2 Data

We use quarterly data from 1974*Q*1 to 2005*Q*1. The data set spans 17 OECD countries and 600 series. We refer to UK as the “domestic” economy. The “foreign” countries are Canada, United States, Germany, France, Italy, Belgium, Netherlands, Portugal, Spain, Finland, Luxembourg, Sweden, Finland, Norway, Australia, New Zealand, and Japan. The foreign block includes most of the UK main trading partners and the major industrialized economies across the world.

For each “foreign” country, we collect data on real activity, inflation, money and interest rates. For real activity, we consider data on output growth, employment, consumption, and investment. Inflation is measured on the basis of a variety of domestic price indices, wage growth, and import prices. The series on money consist of a range of monetary aggregates from narrow to broad. Short-term interest rates are collected for each country.

The data for the UK are very similar in composition to that of the “foreign block.” We collect many different real activity indicators, inflation series including components of the retail price index, narrow and broad money, and a set of asset prices such as house prices and the effective exchange rate. In addition to these macro variables, we included a large number of disaggregated deflator and volume series for consumers' expenditure. The Office for National Statistics (ONS) publishes over 140 subcategories of consumer expenditure data in value, volume, and deflator terms, going back to the 1960s (see ONS 2007). This gives us a ready-made collection of consistent disaggregated price (and volume) data over a long time period.

As in Bernanke, Boivin, and Eliasz (2005), we first difference variables that are nonstationary. In addition, all variables are standardized prior to estimation. More details are given in Appendix B.

It should be noted that our focus is on the trade channel of the international transmission mechanism, which operates through movements in the exchange rate and the terms of trade, and their impact on domestic prices and activity. In future research, it will be interesting to include other financial variables in the foreign block to investigate, for instance, whether the transmission of international shocks is affected by the net financial asset position of the domestic country.

#### 1.3 Estimation

We estimate the model using a two-step procedure. In the first step, the unobserved factors and loadings are estimated via the principal components estimator employed by Bernanke, Boivin, and Eliasz (2005). In the second step, we use the estimated factors along with the UK 3-month Treasury bill rate to estimate our VAR model via Bayesian methods. We choose this two-step procedure for computational convenience. In particular, the large cross-sectional dimension of our data set implies that a one-step procedure that simultaneously estimates the unobserved factors, the factor loadings, and the VAR coefficients involves prohibitive computational costs.^{2} Moreover, Bernanke, Boivin, and Eliasz show that two-step and one-step procedures produce very similar results for their data.^{3}

Our benchmark model includes four UK factors. We choose *k*= 4 as the impulse responses (reported below) do not change significantly if additional UK factors are added to the model. This choice implies that the second step in our estimation procedure involves the estimation of a VAR with nine endogenous variables. We include four lags in the model in order to adequately capture the dynamics. This choice implies a large number of free parameters in our VAR system to be estimated using around 120 observations. In order to deal with this estimation problem in an efficient manner, we follow Sims and Zha (1998) and employ a Bayesian estimator. In particular we incorporate some prior information into the estimation procedure, resulting in estimates which are more precise than those obtained from a pure maximum likelihood approach. Details of the priors and the estimation procedure are given in Appendix A.

#### 1.4 Identification of Structural Shocks

We are interested in studying the dynamic effect of four shocks: an unanticipated fall in the interest rates in the rest of the world, an unanticipated expansion in international activity, a positive international supply shock, and an expansionary domestic monetary policy shock. We interpret the first shock as an expansionary “monetary policy” shock that occurs simultaneously in the foreign block of the VAR. The recent easing of monetary policy across the world can, arguably, reflect such scenario.^{4}

** Foreign shocks** The foreign shocks are identified using three schemes based on recursive ordering, nonrecursive ordering, and a mixture of sign and zero restrictions. The variables in the FAVAR are ordered as follows: [Δ

*Y**

_{t}, Π*

_{t}, Δ

*M**

_{t},

*R**

_{t},

*F*

^{uk}

_{j,t},

*R*] with

_{t}*j*= 1 … 4.

In the recursive scheme, the impact matrix *A*_{0} is lower triangular, implying that the rest of the world does not react to UK domestic conditions within the period. We will maintain the latter assumption across all identification schemes. On average, the short-term interest rates in the foreign economies react contemporaneously to world activity, inflation, and liquidity but these international factors react to *R**_{t} with at least one lag.

As for the nonrecursive scheme, we impose the contemporaneous restrictions:

- (3)

where, following Sims and Zha (2006), the third and fourth rows identify money demand and money supply shocks in the rest of the world. The marks “×” represent freely estimated parameters.

The identifying assumption in the nonrecursive scheme is that, on average, foreign interest rates do not respond to pressures stemming from world activity and inflation within the period, possibly reflecting the fact that these data are less timely. Information about monetary aggregates, in contrast, is available more quickly and fluctuations in these have an impact on *R**. It is worth anticipating that the estimates based on the recursive scheme, in which the *R** is allowed to respond contemporaneously to innovations in Δ*Y** and Π*, are very similar to the estimates based on the nonrecursive identification.

In the third scheme, we impose a mixture of sign and zero restrictions:

- (4)

where the sign restrictions are imposed as described in Appendix A. In the foreign block, a shock to aggregate demand is associated, on impact, with an increase in world activity, inflation, liquidity, and interest rates; a positive supply shock implies a fall in inflation and a rise in real activity; an increase in money demand brings about a decline in output and inflation and a rise in money growth and interest rates; and a positive shock to the short-term interest rates comes with a decline in the other international factors. Notice that unlike in the recursive and nonrecursive schemes, world demand and supply shocks are now identified via the sign restrictions.^{5}

** Domestic monetary policy shock** A vast literature on closed and open economies has identified the monetary policy shock by ordering last a short-term interest rate in recursive structural VARs. The recursive identification in

*small-scale*models is typically associated with a number of anomalies such as the price and liquidity puzzles, and the exchange rate and forward discount puzzles. These empirical facts are anomalies because they are inconsistent with the predictions of a number of, though not all, theories. A possible interpretation of the anomalies is that the recursive scheme is unsuited for recovering correctly a policy shock.

In an effort to improve the identification of the monetary shock, several authors have proposed alternative schemes ranging from nonrecursive to sign restrictions. While the success of the alternative schemes in ameliorating the anomalies has been mixed so far, it is worth emphasizing that virtually all contributions to the empirical literature on the international transmission have used small scale models.

In a closed economy, Bernanke, Boivin, and Eliasz (2005) show that using a wide information set, of the kind available to central banks when formulating their decisions, improves the identification of the policy shock such as to eliminate virtually the price puzzle. Interestingly, they solve the price puzzle using the same recursive identification that in small-scale structural VARs delivers a large and significant positive response of prices to a contractionary policy shock.

We take a FAVAR approach to the international transmission of monetary policy shocks and ask whether the limited information set, rather than the use of the recursive identification, is responsible for the open-economy anomalies found in earlier studies. To this end, we identify a domestic monetary policy shock in 1 as the only shock that does not affect contemporaneously the other factors in the system.

Two points are worth noting on the recursive identification. First, the fact that the domestic factors do not have an economic interpretation is not problematic here. Each UK series is a linear combination of the domestic factors, and the restriction that the domestic factors do not respond to policy innovations within the period implies that the underlying UK series do not react contemporaneously to the domestic monetary shock. Second, a few domestic series, such as those associated with the financial markets, are likely to respond contemporaneously to movements in the policy rate. Our ability of correctly identifying a monetary policy shock hinges, then, upon removing the contemporaneous relationship between the short-term interest rate and the financial variables before extracting the domestic factors.

Following Bernanke, Boivin, and Eliasz (2005), we estimate a regression of the form where represents the common space spanned by the first *k* principal components of the panel of domestic variables while is an estimate of all the common components other than *R _{t}*. In practice, the estimates of are obtained extracting principal components from the subset of slow-moving UK variables, which by assumption are not affected contemporaneously by

*R*. Then, the identification of the domestic policy shock, and only that, is achieved by recursively ordering and

_{t}*R*, with

_{t}*R*last.

_{t}### 2. RESULTS

- Top of page
- Abstract
- 1. AN OPEN-ECONOMY FAVAR
- 2. RESULTS
- 3. THE EXCHANGE RATE AND FORWARD DISCOUNT PUZZLES REVISITED
- 4. SUBSAMPLE ANALYSIS
- 5. CONCLUSIONS
- Appendices
- LITERATURE CITED

This section describes the empirical results of the open economy FAVAR developed in Section 1. We report estimates of the principal components and compute the dynamic effects of an unanticipated fall in the interest rates in the rest of the world, an unanticipated expansion of international activity, and a positive international supply shock.

We report results based on the recursive identification and sign restrictions in the main text. Impulse responses based on the nonrecursive identification are given in Appendix C.

#### 2.1 International Comovements

We extract four common components from the foreign block of the panel using the identification described in Section 1.2. Figure 1 plots the principal components of real activity, inflation, money growth, and nominal interest rates.

A few patterns are apparent. The industrialized world experienced, on average, four severe recessions: in the mid-1970s, at the beginning of the 1980s, in 1991, and between 2001 and 2002. These dates match roughly the evidence in Kose, Otrok, and Whiteman (2003) on the existence of an international business cycle, in Artis et al. (2003) for the Euro area, and the slowdown associated with the burst of the dot.com bubble.

The decline in the measure of international inflation is consistent with the notion of global disinflation put forward by Rogoff (2003). The world factor for money growth in the left-bottom corner exhibits a steadily declining pattern. The years 2002 and 2003, which many commentators have referred to as a period of global excess liquidity, have been characterized by unprecedented volatility (see D'Agostino and Surico Forthcoming). The panel in the right-bottom corner displays the international comovements in the short-term interest rates. The peak in the early 1980s follows the peak in the measure of global inflation during the late 1970s. Since then, the international common component of interest rates has declined significantly reaching its lowest historical values in the very recent past.

#### 2.2 A Decrease in Foreign Interest Rates

In this section, we consider the impact of a shock that reduces interest rates by 1% (on average) in the foreign block of the model. A generalized fall in interest rates may represent a situation in which special circumstances, possibly triggered by a common shock, require central banks across the world to deviate from the path implied by the systematic component of their monetary policy. Under these circumstances, which seem to fit the experience of low policy rates in 2004 as well as the response to the financial market turbulence in 2007–2008, an unanticipated fall in interest rates across the world can be thought of as a monetary policy shock that occurs, on average, in the foreign block.

Figure 2 plots the dynamic effects of an expansionary monetary shock in the foreign countries based on the recursive identification scheme.^{6} Only selected variables are displayed. The decline in international interest rates generates a significant expansion in world real activity, with an increase, on average, by 0.2% in quarterly growth.^{7} The shock increases the international inflation factor by around 0.1% at the 3-year horizon. The magnitude of these responses are very similar to those obtained in studies that focus on the monetary policy shocks in the United States (see, e.g., Christiano, Eichenbaum, and Evans 1996). The impact of the shock on international liquidity is relatively short-lived, with the response becoming insignificant in about 1 year.

Moving to the UK effects, the nominal effective exchange rate (NEER) appreciates as a consequence of the capital inflows generated by the relatively high domestic interest rates. The terms of trade improve significantly and as a result the UK experiences a trade deficit. UK inflation displays a delayed response to this shock. Quarterly GDP deflator and CPI inflation responds significantly at around the 2-year horizon, increasing by 0.2%. There is an increase in quarterly GDP growth, quarterly consumption growth, and investment in response to this shock, with each variable rising by 0.2% at the 1-year horizon. The UK experiences, therefore, a prosper-thy-neighbor situation.

Real house price inflation increases significantly for 2 years after the shock. Equity returns, as measured by the growth rate of the Financial Times Stock Exchange (FTSE) are higher in the quarters immediately following the shock. These effects are consistent with the increase in domestic real activity.

In Figure 3, we present the dynamic effects of a negative interest rate innovation in the foreign block based on the mixture of sign and zero restrictions reported in 4. It is worth emphasizing that the sign restrictions are imposed on the foreign block only, whereas we leave unconstrained the signs of the responses of the domestic variables.

The signs of the impact and, to a lesser extent, the shapes of the responses are broadly in line with the results in Figure 2. The NEER, terms of trade and trade balance, for which no sign restrictions is imposed, move in directions consistent with the theory. Domestic prices and wages as well as money growth increase significantly. In the first year after the shock, the mass probability that output and consumption growth are positive in the UK is about 60%.

To the extent that the structural innovation to the international component of national interest rates can be interpreted as a foreign monetary shock, our results for CPI inflation, money, and GDP growth, which are variables typically employed in small-scale VARs, are in line with the estimates available in the literature (see Kim and Roubini 2000, Faust and Rogers 2003, and the references therein).

For all other variables referring to diverse and more disaggregated series, the results presented in this section are, to the best of our knowledge, new.

#### 2.3 An Unanticipated Increase in Foreign Real Activity

This section describes the dynamic effects of an unanticipated expansion in international real activity. Figure 4 is based on the recursive identification scheme.^{8} The unexpected increase in the world component of real activity causes a significant, prolonged increase in international inflation and international interest rates.

The impact on the NEER, the terms of trade, and the trade balance is not statistically different from zero. There is little evidence of a significant impact on domestic activity, real house price inflation, and equity returns. UK inflation increases by around 0.2% at the 2-year horizon. These features could be consistent, for instance, with an expansion in global demand that puts upward pressure on the prices of inputs and intermediate goods, which are then passed on to the prices of final goods. But it should be emphasized that these are reduced-form correlations.

The estimates based on sign and zero restrictions are displayed in Figure 5. The sign imposed on the foreign block of the FAVAR implies that the expansion in international real activity can now be interpreted as a world demand shock. The responses are broadly in line with the dynamic effects obtained via the recursive scheme. In particular, there is evidence of a positive impact on measures of UK inflation, while real activity measures do not change significantly.

#### 2.4 International Supply Shocks and the Distribution of Domestic Prices

Recent studies have investigated how prices at the sectoral level respond to (domestic) *monetary policy* shocks. Key contributions include Boivin, Giannoni, and Mihov (Forthcoming) and Balke and Wynne (2007). In analogy to previous studies, we can also analyze the dynamics of the components of the UK consumption deflator and the associated quantities, as those variables (from the ONS) enter our FAVAR model. In contrast to previous studies, we investigate how these sectoral prices (and quantities) respond to an international common *supply* shock.

In the top left panel of Figure 6, we report the (nonstandardized) responses of the (level of) the components of the UK consumption deflator to a positive international supply shock.^{9} The panels show the standard deviation and the skewness of the responses (across the sectors) at each forecast horizon. Most prices fall in response to a supply shock. However, there is some evidence of heterogeneity with some prices falling by a substantially smaller amount (or even increasing) in response to the shock. The increase in the standard deviation of the responses suggests that the *dispersion* of prices and quantities increases with the horizon, indicating that some components become permanently cheaper.

In the last row of Figure 6, we show that the distribution of price responses is negatively skewed, especially in the first 15 quarters. The distribution of quantity responses is positively skewed, especially in the first 5 quarters. The increase in skewness suggests that an international supply shock transmits to the UK economy as a shock to relative prices.^{10} The positive relationship between skewness and aggregate price level suggest that such a shock to relative prices can be inflationary.

Following Boivin, Giannoni, and Mihov (Forthcoming), we consider if this change in relative prices is statistically significant. For each sector, we calculate the relative price response where *p _{i}* is the response of the

*i*th sector's price level to the supply shock, denotes the average response across sectors, and

*J*indexes the Gibbs sampling iterations. For each sector, we compute λ, the fraction of relative price responses (across

*J*) that are positive. Figure 7 plots the proportion of sectors, for which λ > 0.95 or λ < 0.05.

The figure shows that around 40% of the prices in our sample are significantly different from the average 5–10 quarters after the shock.^{11} At the 3-year horizon, this percentage falls to around 20, while it takes more than 20 quarters for all relative price effects to dissipate completely. Our results are, therefore, in line with Boivin, Giannoni, and Mihov (Forthcoming)—i.e., they display relative price movements in the short–medium run with the responses converging to the average in the long run.

### 3. THE EXCHANGE RATE AND FORWARD DISCOUNT PUZZLES REVISITED

- Top of page
- Abstract
- 1. AN OPEN-ECONOMY FAVAR
- 2. RESULTS
- 3. THE EXCHANGE RATE AND FORWARD DISCOUNT PUZZLES REVISITED
- 4. SUBSAMPLE ANALYSIS
- 5. CONCLUSIONS
- Appendices
- LITERATURE CITED

The exchange rate and forward discount puzzles are among the long-lasting anomalies in the empirical literature on open economies. In contrast to the prediction of the theory, Grilli and Roubini (1995) find that a negative innovation in domestic rates is often associated with an appreciation of the domestic currency on impact. Along similar lines, Eichenbaum and Evans (1995) report that a domestic monetary policy easing is associated with persistent depreciations of the domestic currency rather than persistent appreciations after the initial depreciation, as in Dornbusch's overshooting model.

We are interested in assessing the extent to which the limited information set used in small-scale VARs is responsible for the exchange rate and forward discount puzzles. To make our results transparent, we compare the impulse responses implied by the estimates of the FAVAR with the impulses responses implied a small scale VAR, using recursive restrictions to identify the monetary policy shock in both models.

In the small-scale VAR, we use the 11-variable specification in Cushman and Zha (1997), namely, the growth rates of GDP, GDP deflator, the commodity price index, and the federal funds rate for the United States, and the growth rates of import and export prices, GDP, CPI, M4, the 3-month Treasury bill, and the NEER for the UK.^{12}

Any difference between the impulse responses of the small-scale VAR and the FAVAR can be attributed to the difference in the dimension of the information set.^{13} The intuition is that central banks monitor and respond to a far wider information set than incorporated in small-scale VARs. For the purpose of identifying a monetary policy shock, the use of a narrow information set is likely to introduce severe omitted variable problems and therefore contaminate the policy innovations.

In Figure 8, we show the responses of selected variables to a domestic monetary expansion in the UK. The NEER depreciates after the shock and then it appreciates persistently. Therefore, there is little evidence of an exchange rate puzzle. Note also that the response of the level of NEER is relatively fast and occurs in the first two quarters. This is in contrast to the evidence presented in Eichenbaum and Evans (1995) for the United States, where the response of the exchange rate is characterized by delayed overshooting.

In the left panel of the second row, we report the forward discount premium computed as 0.25(*R*−*R**) − (NEER^{f}− NEER), where the superscript *f* stands for the forecast one quarter ahead.^{14} With the exception of the very first three periods, the forward discount premium is not statistically different from zero in the solid lines of the FAVAR. Our findings are in sharp contrast with the persistent deviations from UIP found by Eichenbaum and Evans (1995) and subsequent studies, and confirmed by the dotted lines of the small-scale VAR.

In reaction to an expansionary domestic policy shock, money growth increases and therefore a liquidity puzzle is not evident. In analogy to the closed-economy result of Bernanke, Boivin, and Eliasz (2005), the price puzzle is small, and zero lies always inside the posterior bands of the CPI inflation response, though the impact is estimated quite imprecisely. The response of GDP growth is positive and statistically significant.

The contrast between the impulse responses implied by the small-scale VAR (dotted lines) and the FAVAR (solid lines) is sharp. The VAR estimates are associated with a very large delayed overshooting anomaly (middle panel in the first row) and forward discount puzzle (first panel in the second row).^{15} There is no liquidity effect for M4, and the price puzzle for CPI is large. In summary, using large information (as embodied in our FAVAR) solves the open-economy anomalies that are apparent in empirical models based on small information set.

### 4. SUBSAMPLE ANALYSIS

- Top of page
- Abstract
- 1. AN OPEN-ECONOMY FAVAR
- 2. RESULTS
- 3. THE EXCHANGE RATE AND FORWARD DISCOUNT PUZZLES REVISITED
- 4. SUBSAMPLE ANALYSIS
- 5. CONCLUSIONS
- Appendices
- LITERATURE CITED

The number of available observations at quarterly frequency limits the extent to which reliable inferences can be drawn from subsample analyses. On the other hand, the UK has experienced an important statutory change in the conduct of monetary policy with the introduction of an explicit target for inflation in December 1992 and the granting of operational independence to the Bank of England and the establishment of the Monetary Policy Committee in May 1997.

To deal with the short time length of the inflation targeting period, we follow Boivin and Giannoni (Forthcoming) and expand our FAVAR with a dummy variable interacting with all the lags of the domestic factors:

- (5)

where *d _{t}* takes the values of zero before the introduction of the inflation targeting framework and one afterward.

^{16}The entries associated with the foreign block in

*C**(

*L*) are zero. The coefficients in

*B**(

*L*) capture the dynamics of the subsample 1974

*Q*1– 1992

*Q*4, whereas the coefficients in

*B**(

*L*) +

*C**(

*L*) refer to the period 1993

*Q*1– 2005

*Q*1. The dummy variable approach consists in estimating as many additional parameters as the number of lags times the number of domestic factors, and therefore, as argued by Boivin and Giannoni (Forthcoming), it is not too costly in terms of degree of freedom.

In the last two columns of Figure 9, we report the subsample analysis for the dynamic responses of selected variables to a foreign money supply shock identified with the recursive identification. For the sake of comparison, the full-sample estimates in Figure 2 are replicated in the first column. The impulse responses appears *qualitatively* similar across subperiods, with the possible exception of CPI. Not surprisingly, the subsample estimates are associated with larger sampling uncertainty, especially over the second period. Similar results are obtained using sign restrictions.^{17}

In Figure 10, we report a similar experiment for the impulse responses to a domestic (expansionary) monetary policy shock. Two findings are worth noting. First, the impact of the shock is typically less persistent over the last part of the sample. Second, the response of CPI inflation moved from a significant positive reaction before 1992 to a response not statistically different from zero afterward. Consistent with the results in Castelnuovo and Surico (2006), the evidence of less persistent effects of structural shocks and the amelioration of the price puzzle (i.e., the comovement of interest rate and prices following a monetary policy shock) is consistent with the notion of improved monetary policy.

### 5. CONCLUSIONS

- Top of page
- Abstract
- 1. AN OPEN-ECONOMY FAVAR
- 2. RESULTS
- 3. THE EXCHANGE RATE AND FORWARD DISCOUNT PUZZLES REVISITED
- 4. SUBSAMPLE ANALYSIS
- 5. CONCLUSIONS
- Appendices
- LITERATURE CITED

This paper has studied the international transmission of structural shocks in an open economy FAVAR applied to the UK. Unlike previous contributions, we use data on 17 countries and 600 variables, covering prices, activities, and monetary indicators to model the interaction between the foreign and domestic blocks of the VAR.

An expansionary shock to monetary policy in the foreign block causes the nominal exchange rate to appreciate. Real house price inflation, investment, and the growth rates of GDP and consumption increase temporarily but significantly, followed by a peak in wages. CPI and GDP deflator inflation reach their maximum values in the third year after the shock. There is some evidence to suggest that an expansionary demand shock in the foreign block has a positive impact on UK inflation and output growth. The sectoral distribution of UK consumption deflators is negatively skewed after a positive international supply shock, implying a significant impact on the aggregate level of the consumption deflator.

The effects of a UK monetary policy shock are associated with little evidence of exchange rate and liquidity puzzles, and limited evidence of forward discount and price anomalies. In sharp contrast to the estimates of the FAVAR model, a small-scale VAR, of the dimension typically used in earlier contributions, delivers most of the open-economy anomalies in our data set. The results in this paper suggest that the exchange rate and forward discount puzzles may largely reflect the use of limited information, which stands in contrast to the central banks' practice of monitoring and processing a wide range of data.

### Appendices

- Top of page
- Abstract
- 1. AN OPEN-ECONOMY FAVAR
- 2. RESULTS
- 3. THE EXCHANGE RATE AND FORWARD DISCOUNT PUZZLES REVISITED
- 4. SUBSAMPLE ANALYSIS
- 5. CONCLUSIONS
- Appendices
- LITERATURE CITED

#### APPENDIX A: ESTIMATION METHOD

We collect the VAR coefficients of equation (1) into a (*N*× (*N*× 4 + 1)) vector Γ and the right-hand-side (i.e., lags and the intercept terms) of equation (1) into the matrix *X _{t}*. Let denote the OLS estimates of the VAR coefficients, then the conditional posterior distribution of the VAR coefficients is given by (see Uhlig 2005):

where

Γ_{0} and *N*_{0} denote the prior mean and variance of the VAR coefficients. In specifying the prior mean, we loosely follow Sims and Zha (1998). We assume that Γ_{0} implies an AR(1) structure (with the intercept equal to zero) for each endogenous variable. As the variables underlying the factors are already in growth rates (or assumed to be stationary), we center the prior at the OLS estimates of the AR(1) coefficient for each variable (rather than one, i.e., a random walk). As in Sims and Zha, the variance of the prior distribution is specified by a number of hyperparameters that control the variation around the prior. Letting μ denote the hyperparameters we set μ_{0}= 0.6, μ_{1}= 0.1, μ_{2}=μ_{3}=μ_{4}= 1. The diagonal elements of *N*_{0} are given by where *p* denotes the lag length and σ_{j} is the variance of the residuals from an AR(*p*) regression on the *j*th endogenous variable in the VAR. The intercept terms in the VAR are controlled by the term (μ_{0}μ_{4})^{2}.

We use Gibbs sampling to approximate the posterior distribution in the models that employ the recursive identification scheme and in those that use sign restrictions. We use 100,000 Gibbs replications and use the last 10,000 for inference. For the models where the nonrecursive identification is used, importance sampling is used to approximate the posterior distribution of impulse responses from the structural model. An excellent description of the application of importance sampling to structural VARs is given in Doan (2004). Note that we only retain draws of Γ that are stable—i.e., have roots with the unit circle.

** Imposing the sign restrictions** The sign restrictions are imposed as follows. We compute the structural impact matrix,

*A*

_{0}, via a slightly modified version of the algorithm recently introduced by Rubio-Ramírez, Waggoner, and Zha (2005). Specifically, let Ω

_{t}=

*PP*′ be the Cholesky decomposition of the VAR covariance matrix Ω

_{t}(with the foreign variables ordered before the UK variables), and let We draw an

*j*×

*j*matrix

*J*from the

*N*(0, 1) distribution, where

*j*denotes the dimension of “foreign” block in the VAR. We take the

*QR*decomposition of

*J*. That is, we compute

*Q*and

*R*such that

*J*=

*QR*.

We compute, then, a candidate structural impact matrix as where is a *N*×*N* identity matrix with *Q*′ in the top *j*×*j* block. Note that such candidate draw has a lower triangular structure for the UK block and, as in the standard Cholesky decomposition, implies that UK shocks do not have a contemporaneous impact on the “foreign” block. If *A*_{0} satisfies the sign restrictions, we keep it. Otherwise, we move to the next iteration of the Gibbs Sampler.

#### APPENDIX B: DESCRIPTION OF THE DATA

In the interest of brevity, we do not provide an exact list of all 600 series in our panel. However this appendix gives an idea of the type of data used and the underlying sources. The full list is available on request from the authors.

** International data** Our international data set contains data on real activity, inflation, money growth, and interest rates for Canada, United States, Germany, France, Italy, Belgium, Netherlands, Portugal, Spain, Finland, Luxembourg, Sweden, Finland, Norway, Australia, New Zealand, and Japan. All data series are seasonally adjusted. We take log differences of all series apart from interest rates. The data are then standardized.

Where available, our real activity data contain real GDP, industrial production, real household consumption expenditure, investment, exports, gross national income, and unemployment. In terms of coverage, the United States has the most detailed data, with a breakdown of unemployment and production by sector. Most of the data are obtained from Datastream and International Financial Statistics (IFS) database. The unemployment data are taken from the Global financial database and the U.S. series are obtained from Federal Reserve Economic Data (FRED).

Our basic inflation data contain CPI, GDP deflator, measures of wage growth, and import prices. Again, for the United States we are also able to obtain a breakdown of CPI and PPI by sector. The series are obtained from Datastream and IFS.

We attempt to include both narrow and broad money aggregates for each country. Generally, M1 and either M2 or M3 are available for all European countries in our panel. For the United States, we obtain M1, M2, M3, and measures of time and demand deposits. The data are obtained from Datastream, IFS, and FRED.

The international interest rate data primarily contain short-term interest rates. These include discount rates, money market rates, treasury bill rates, and central bank interest rates. The data are obtained from the Global financial database.

** UK data** Like the international data, our data set on the UK contains data on real activity, inflation, and money. We also include some key asset prices.

Real activity data include real GDP, industrial production (with a broad sectoral break down), imports and exports, investment, and real household consumption expenditure. The data set includes a very detailed sectoral breakdown of consumption quantities. The data are obtained from the Office of National Statistics (ONS).

Inflation data include the main price indices (GDP deflator, CPI, RPI, and RPIX) and components of the consumption deflator. ONS and the Bank of England are the main sources for the data.

Money data for the UK include M0 and M4, with a sectoral breakdown of the latter. These data are obtained from the Bank of England.

The asset price data include house prices, stock prices, exchange rates (pounds in terms of U.S. dollars, euros, yen, and Canadian and Australian dollars), and the term structure of interest rates. The data are obtained from the Global financial database and the Bank of England.

#### APPENDIX C: IRFs USING THE NONRECURSIVE IDENTIFICATION

This appendix reports the impulse response functions of selected UK variables to a foreign monetary shock and to an increase in foreign real activity using the nonrecursive identification scheme.

Note that this is a research paper format designed for work that may end up as, e.g., a working paper or journal article. It should not normally be used to create a document that is intended to end up as a note for record or memo. It is not always easy to convert a document from research paper to note format.

- 1
Throughout the paper, “rest of the world,”“international,” and “foreign” will be used interchangeably. UK is referred to as the domestic country.

- 2
A full Bayesian estimation of the model would require the use of the Kalman filter to derive the mean and the variance of the conditional distribution of the factors. The computation of the Kalman gain involves the factor loading matrix. The dimension of this matrix is quite large in our model (600 × 36). The fact that the Kalman gain has to be computed for each time period slows down posterior simulation methods considerably. In our attempts, it appears to take around 40 seconds for one draw from the posterior requiring a considerable time to complete a sufficient number of posterior draws.

- 3
Note that their panel includes 120 U.S. series, making one-step estimation feasible.

- 4
An alternative is to focus on a single foreign country. For example one can envisage replacing the international factors in equation (2) with “U.S. factors.” As a sensitivity check, we estimate this alternative model and find that the signs of key impulse responses are unaffected.

- 5
A mixture of sign and zero restrictions are also used by Faust and Rogers (2003).

- 6
Results for the nonrecursive identification are similar, and they are reported in the top panel of Appendix C.

- 7
We rescale the international activity, inflation and liquidity factor responses in the units of (the quarterly growth of) U.S. GDP, CPI, and M2.

- 8
Results for the nonrecursive identification are similar, and they are reported in the bottom panel of Appendix C.

- 9
The use of standardized impulse responses would introduce a spurious wedge between aggregate and average responses. We are grateful to Marc Giannoni for bringing this point to our attention.

- 10
Note that a change in the skewness of the price distribution is a sufficient (but not necessary) condition for the existence of a relative price shock.

- 11
Note that this is significantly higher than the 10% threshold level. Given a 5% significance level one would typically expect 10% or price responses to be significantly different from the average.

- 12
We obtain very similar results estimating the seven-variable specification in Eichenbaum and Evans (1995), which amounts to excluding U.S. commodity prices, and UK CPI, import, and export prices from the 11-variable VAR in the main text.

- 13
Note that we use the same Bayesian estimator for the small-scale VAR with the same priors as in the FAVAR model. See Appendix A.

- 14
The interest rate is divided by 4 because the exchange rate is expressed in quarterly terms.

- 15
Note that the exchange rate and terms of trade response are estimated very imprecisely in the small-scale VAR model.

- 16
We obtain similar results by letting the dummy variable interact with both foreign and domestic factors.

- 17
The dynamic responses to an international supply shock, not reported but available upon request, are also fairly stable across subsamples.

### LITERATURE CITED

- Top of page
- Abstract
- 1. AN OPEN-ECONOMY FAVAR
- 2. RESULTS
- 3. THE EXCHANGE RATE AND FORWARD DISCOUNT PUZZLES REVISITED
- 4. SUBSAMPLE ANALYSIS
- 5. CONCLUSIONS
- Appendices
- LITERATURE CITED

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