What helps forecast U.S. Inflation?- Mind the Gap!

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1 What helps forecast U.S. Inflation?- Mind the Gap! Ayşe Kabukçuoğlu University of Texas at Austin Enrique Martínez-García Federal Reserve Bank of Dallas This Draft: January 9, Abstract In macroeconomic analysis and inflation forecasting, the traditional Phillips curve has been widelyused to exploit the empirical relationship between inflation and domestic economic activity. Atkeson and Ohanian (), among others, cast doubt on the performance of Phillips curve-based forecasts of U.S. inflation relative to naïve forecasts. This indicates a difficulty for policy-making and private sector s longterm nominal commitments which depend on inflation expectations. The literature suggests globalization may be one reason for this phenomenon. To test this, we evaluate the forecasting ability of global slack measures under an open economy Phillips curve. The results are very sensitive to measures of inflation, forecast horizons and estimation samples. We find however, terms of trade gap, measured as HP-filtered terms of trade, is a good and robust variable to forecast U.S. inflation. Moreover, our forecasts based on the simulated data from a workhorse new open economy macro (NOEM) model indicate that better monetary policy and good luck (i.e. a remarkably benign sample of economic shocks) can account for the empirical observations on forecasting accuracy, while globalization plays a secondary role. JEL Classification: F4, F44, F47, C53, F6 KEY WORDS: Global Slack, New Open Economy Phillips Curve, Forecasting. We would like to thank XXXXX and many seminar and conference participants at XXXXX for helpful suggestions. This research was completed while Ayşe Kabukçuoğlu was a summer intern at the Federal Reserve Bank of Dallas, whose support is greatly appreciated. We acknowledge the excellent research assistance provided by XXXXX. All remaining errors are ours alone. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Dallas, or the Federal Reserve System. Ayşe Kabukçuoğlu, Department of Economics, The University of Texas at Austin, 5 Speedway Stop C3, Bernard & Audre Rapoport Building.6, Austin, TX ayse@utexas.edu. (Contacting author) Enrique Martínez-García, Federal Reserve Bank of Dallas. Correspondence: N. Pearl Street, Dallas, TX 75. Phone: + (4) Fax: + (4) enrique.martinez-garcia@dal.frb.org. Webpage:

2 Introduction Forecasting inflation accurately and reliably- plays a critical role for policy-making and for the decisions of the private sector in making long-term nominal commitments. In macroeconomic analysis and inflation forecasting, the traditional Phillips curve has been a widely used model that captures broadly the empirical relationship between inflation and unemployment rate, capacity utilization or output gap. As documented by Atkeson and Ohanian (), the Phillips curve has flattened since 984. Their finding was that the Phillips curve-based models did not yield more accurate forecasts than the naïve, 4 quarter random walk benchmark. Stock and Watson (7) emphasized the role of lower volatility in inflation in the U.S. and in the world in this period. Hence the risk of naive forecasts, computed as the mean square forecast error, declined. Forecasts under a Phillips curve specification have become less accurate. A survey by Stock and Watson (8) suggest recent forecasts based on univariate specifications including the Phillips curve performed well only occasionally. A prominent explanation to the break in the Phillips curve suggested in the literature is globalization - the integration of global markets in goods, labor and capital. The recent literature postulated the global slack hypothesis, i.e. foreign slack as well as domestic slack drives inflation in the short-run. Hence, a more relevant specification, the open economy Phillips curve that ties inflation to global measures of economic activity has become a focus of investigation. However, the evidence on the role of global slack is mixed. Binyamini and Razin (7) and Martinez-Garcia and Wynne () made theoretical explanations and Borio and Filardo (7) provided empirical evidence for the global slack hypothesis. On the other hand, Milani (, ) among others, argue that the foreign economic activity has a role on domestic supply and demand, but its effect on domestic inflation is negligible, finding weak evidence for the global slack hypothesis. Even when the theoretical validity of an open economy Phillips curve is assured, forecasting inflation under the open economy framework is a challenging task. It is in general difficult to find sufficiently long, reliable and robust time series of global slack -global output gap or capacity utilization. This has been documented in the current paper as well as in previous studies. Therefore, it gains particular importance to evaluate forecast accuracy with various global slack measures and to compare their performances to those from alternative measures. In this paper, we test whether global slack measures have predictive power for U.S. inflation. These measures are constructed by mostly theoretically-consistent output gap or capacity utilization series of the U.S. and several different groups of countries combined. In addition, following a recent theoretical finding in Martinez-Garcia and Wynne (), we test the performance of a global slack measure defined as a combination of two variables: domestic slack and terms of trade gap. The measure of terms of trade gap is HP-filtered terms of trade, while the domestic slack series are the U.S. measures of output gap, capacity utilization and HP-filtered GDP. Our first finding is that, perhaps in agreement with the existing literature, these global slack variables yield mixed results in predicting different inflation measures. However, a striking result in this paper is that the terms of trade gap, alone, is a good forecasting variable for U.S. inflation. It yields more accurate forecasts relative to the naive autoregressive process of inflation and it is also robust to various forecast horizons, inflation measures and estimation samples, including the late 98s the period of break in the Phillips curve pointed out by Atkeson and Ohanian (). On the other hand, we document that most

3 global slack measures yield relatively more accurate forecasts for core inflation while the forecast with terms of trade gap and domestic slack perform well at short horizons for headline inflation measures. Overall, the forecasting performances are not very robust to forecast horizons and estimation samples. We conduct pseudo out-of-sample forecasts for six measures of U.S. inflation at horizons varying between -quarter to -quarter ahead. Our benchmark estimation and sample periods are 98:-99:4 and 99:-:4, respectively. For robustness analyses we go back as far as to 949: and perform rolling forecasts, to the extent that data series are available. Our metric for forecast accuracy is the mean square forecast error (MSFE) of a reduced form new open economy Phillips curve with distributed lags of inflation and slack, relative to the MSFE of the restricted forecast described as a univariate, autoregressive process of inflation. We compute bootstrap standard errors for the MSFEs following Clark and McCracken (6). Another major contribution of this paper is our extensive robustness analyses where we compare the performance of a selected measures of slack to a set of widely used variables in the forecasting literature. We test the predictive performances of a domestic slack series (CBO U.S. slack), a global slack series (OECD Total), a measure of domestic liquidity growth (U.S. M growth) and global liquidity growth (G7 average of monetary aggregates) and two variables of terms of trade gap (HP filtered U.S. terms of trade, and HP filtered U.S. terms of trade ex. oil). We report the following stylized facts: Forecasts with the domestic slack perform significantly better than the simple AR process inflation until late 96s and particularly at short horizons. The global slack measure outperforms the simple AR process significantly only in late 98s and at short horizons. In episodes where domestic liquidity growth perform well in forecasting U.S. inflation, global liquidity growth does not; and vice versa. This result is robust to several inflation measures and horizons for the rolling forecasts starting in 963 through early 98s. After that period, the relative MSFEs of the forecasts are insignificant for both variables. Forecasts with HP filtered terms of trade perform significantly better relative to the naïve forecast with the estimation samples starting in 95s till late 98s (with the exception in , where the performance deteriorates). At the episodes where terms of trade performs relatively weak, terms of trade ex. oil does significantly better. Therefore, we show that many conventional alternatives do not improve upon the naïve forecast especially in recent years, while HP-filtered terms of trade stands out as a relatively successful variable. In the remainder of the paper, we try to understand these patterns in the light of a workhorse New Open Economy Macroeconomics (NOEM) model. Our strategy is to use a model that can capture the effects of two other competing (or complementary) hypotheses in addition to globalization good luck and good monetary policy - that are commonly discussed in the literature as plausible explanations for the observed strengths and weaknesses in the forecasting performances. To this end, we simulate data based on the model and use the data to conduct forecasts similar to those in the empirical section. We estimate MSFEs for many plausible parameter values that capture changes in trade openness, volatility in TFP or monetary shocks (which we call good luck ) and effectiveness of monetary policy (i.e. Taylor rule parameters). For most of these patterns of forecast accuracy, we find that globalization seems to be a relatively weak channel, while anti-inflationary monetary policy and good luck seem to be the plausible reasons.

4 Methodology. Data Figure plots the series employed throughout the paper. The US inflation rate is calculated as annualized log-differences of quarterly series of six price indices: consumer price index (CPI), core CPI (CPI ex. food and energy), personal consumption expenditure deflator (PCE), trimmed-mean PCE, GDP deflator and producer price index (PPI). We perform inflation forecasts using a wide range of domestic and global slack measures. Our domestic measures consist of CBO US slack, FRBD US slack, OECD US slack, IMF US slack and HP filtered US real GDP. For global slack measures, we use FRBD G7, FRBD G39, OECD G7, OECD Total and IMF Advanced series. All series are available quarterly, except for the IMF measures of domestic and global slack, which is available in annual frequency. We therefore disaggregate these series into quarterly frequency using quadratic match average. Terms of trade series is calculated as the ratio of US export price index of goods and services and US import price of goods and services. For terms of trade ex. oil, however, we use the price indices for exported goods and nonpetroleum imported goods due to limited data availability. We HP filter these two series in order to obtain a measure of the terms of trade gap. We define global money growth as the average of the percentage growth rates of broad money stock in G7 countries. While we pick the series for monetary aggregates that are most similar in definition, we are constrained by quarterly data availability for Canada, France, Germany, Italy and Japan particularly for late 96s or early 97s. Since we would like to extend the robustness analysis of forecasting experiments to a large estimation sample, we make our primary decision on selection based on data availability. Therefore our series start in the second quarter of 963 and we use M for US, M4 for UK. We splice two short series of M3 for Canada, M for Germany, Italy and Japan. For France, we also use a spliced series, which combines MR up to the first quarter of 97 and M3 afterwards. (A more detailed explanation is available in the appendix.). Models We specify three models to test the predictive power of various regressors. The first two of these models are univariate forecasting models while the third is a bivariate model. Consider first the traditional backwardlooking Phillips curve relating inflation to aggregate real economic activity as typically specified by the previous literature π h t+hjt = a + λ (L)π t + λ (L)x t + ɛ ur,t+h () Denoting the quarterly forecast horizon by h, it is possible to forecast h-quarter ahead inflation, π h t+hjt with the distributed lag of earlier inflation rates, π t as a proxy for expected inflation, and the distributed lag of the domestic slack measure, x t. We start with assessing the predictive performance of domestic slack in order to compare our results with those of the earlier studies using this specification in the literature. We define h-quarter ahead (annualized) inflation π h t+hjt = 4 h [log(p t+h/p t )] and forecast inflation for horizons ranging from quarter-ahead to -quarters ahead. The number of lags for each variable is se- 3

5 lected based on SIC. To keep the model parsimonious and since the frequency of the variables is defined as quarterly, the maximum possible lags allowed for each variable is set as four. Our second specification relies on an open-economy interpretation of the Phillips-curve. As the global financial integration substantially increased in the past 3 years, its consequences on inflation, and the consequences of foreign economic activity in particular, has become a focus of attention in inflation forecasting. This stream of literature utilizes an augmented Phillips curve adding another regressor in the above specification, hence testing the predictive performances of domestic slack and foreign slack together as a global slack measure. We follow a similar approach by testing the performance of a single variable, the global slack measure which incorporates both domestic and foreign slack, in the following specification π h t+hjt = a + λ (L)π t + λ (L)y t + ɛ ur,t+h () where y t is now defined as the global slack measure. We further evaluate the performances of other variables such as domestic and global liquidity growth or terms of trade gap measures under the same framework. While the long-run relationship between the growth rate of monetary aggregates and the rate of inflation is established by the quantity theory of money and therefore testing the forecasting performance of liquidity growth has analytical content, we do not have a similar rationale in forecasting inflation with terms of trade. However, we perform these forecasting exercises here to readdress the role of these measures in order to provide with a comparison with our main forecasting strategy and also to make an extensive robustness analysis of the earlier work. The issue of how to measure the output gap -both domestic and foreign has been known as a major challenge. For purely statistical approaches, which in most cases derive potential output using actual (real) output series through a filtering technique (most commonly the HP filter), the choice of the filter is usually an arbitrary decision. In addition, applying these techniques are known to create end-point problems. For structural estimates of the output gap, relying on a production function (such as Cobb-Douglas) and quantifying the total factor productivity, the capital stock or labor employed tend to pose measurement problems (Gerlach, P. ). Measuring the foreign output gap, however is an even more challenging task since for the emerging market economies that are believed to potentially affect the US inflation, the data series to measure unemployment rates or capacity utilization in manufacturing are usually either too short or they are not available. Furthermore, there is also not a clear idea on how the dynamics of foreign output gap affects the domestic inflation. Therefore, estimating the open-economy Phillips curve based on the combination of domestic and foreign slack as a measure of the global slack becomes a difficulty. To circumvent the problem of measuring the foreign slack, we follow the theoretical approach taken in a previous work by Martinez-Garcia and Wynne (a). It is shown that using a two-country version of the New Open Economy Macro model of Clarida, Gali, and Gertler () and under the producer currency pricing (PCP) assumption, the dynamics of the domestic (cyclical) inflation, ˆπ t can be expressed in terms of D Agostino and Surico (9a) evaluate the forecasting performance of the average growth rate of broad money in G7 economies and find that the results are significantly more accurate compared to forecasts with US money growth. Stock and Watson (999) in their widely cited paper, forecast U.S. inflation with a large set of variables, including economic indicators other than the variables of real economic activity. These include U.S. effective exchange rate and a number of foreign exchange rates. They report that exchange rates do not yield better inflation forecasting performance than a Phillips curve specification. 4

6 the domestic output gap, ˆx t and the terms of trade gap, ẑ t (in log deviations): ˆπ t = βe t ˆπ t+ + Φ[(ϕ + γ) ˆx t + Ψ π,z ẑ t ] (3) where ϕ and γ are two structural parameters of the model, Φ and Ψ π,z are deep parameters composed of the structural parameters. Hence, it is possible to define global slack in reduced form as a combination of domestic slack and terms of trade. To estimate this new formulation of the open-economy Phillips-curve we follow the literature, and take a backward-looking approach for the reduced-form estimate of the curve. The regression equation in this case can be described as an autoregressive distributed lag model which is our first model to forecast inflation: π h t+hjt = a 3 + λ 3 (L)π t + λ 3 (L)x t + λ 33 (L)z t + ɛ ur3,t+h (4) Under this specification, x t denotes one of the domestic output gap measures and z t denotes one of the terms of trade gap measures (all variables in levels) as described in the previous section. Having suggested three different unrestricted reduced-form models, we finally introduce the restricted model. Under this specification, we estimate a univariate autoregressive process: π h t+hjt = a r + λ r (L)π t + ɛ r,t+h (5) We perform forecasts based on the pseudo out-of-sample forecasting method and particularly focus on recursive samples. Therefore, at any given date t, we forecast inflation using all available data up to date t. For our benchmark experiments, the estimation sample begins in the second quarter of 98 and ends in the fourth quarter of 99 and the pseudo out-of-sample forecasting period begins in the first quarter of 99 and ends in the fourth quarter of. To evaluate the forecasting accuracy of any given variable under each of the unrestricted models above, we compute the relative mean-squared forecasting error (MSFE), which is defined as MSFE of the unrestricted model relative to that of the restricted model. In order to gain insight about our findings and our potential explanations for them, we also run forecasts with the simulated data consistent with the model in Martinez-Garcia and Wynne (a). Under various parameterization of the model, we try to understand how factors such as trade openness, the stance of monetary policy towards inflation and the relative size of the monetary and productivity shocks to the economy affect the predictive ability of these variables. 3 Findings The results of the pseudo out-of-sample forecast with one variable over the benchmark sample are reported in Tables and ; while the results with two variables are summarized in Tables 3 and 4. Our findings can be listed as follows:. Based on the one-variable forecast results, it is not possible to say that global slack measures outperform the domestic slack measures. In general, both measures almost equally yield more accurate predictions compared to an AR process when the inflation measure is core CPI and trimmed mean PCE. For other measures of inflation however, we conclude that the AR process of inflation performs 5

7 better.. Global money growth (measured as G7 average) exhibits a better forecasting performance relative to US money growth, at all horizons for CPI, core CPI and PCE deflator. Both variables have a significantly poor performance compared to the AR process in all other inflation measures. Under the forecasts of CPI and PCE inflation, G7 money growth does also better compared to domestic or global slack measures. However, this is not true for the other measures of inflation. 3. Forecasting performance of terms of trade (HP-filtered) is comparable to those of domestic and global slack measures. Terms of trade ex. oil has no significant improvement over the AR specification across any of the inflation measures and at any horizon. 4. Our results of the two-variable forecasts are rather mixed. Forecasts with domestic slack and terms of trade provide higher accuracy at short horizons for CPI and PCE compared to the forecasts with domestic or global slack alone. For GDP deflator and core CPI, one-variable forecasts do better. When domestic slack and terms of trade ex. oil are evaluated, it can be concluded that the two variables combined improve forecasting performance for GDP deflator especially at short horizons and for PPI at long horizons. Results with two-variable forecasts using domestic or global money growth measures in addition to terms of trade or terms of trade ex. oil, do not improve the predictions. In addition to our benchmark forecasting experiment, we conduct a series of other experiments going back in time to the extent that the series are available. More specifically, starting with the initial observation in the sample, we shift the estimation sample by one quarter and obtain the MSFEs of the forecasts for each rolling window. Each window spans 48 quarters of an estimation sample and 48 quarters of a forecasting sample. We perform these experiments for three groups of variables: a domestic slack measure vs. global slack measure; terms of trade vs. terms of trade ex. oil and finally domestic vs. global liquidity growth. Among several alternatives, we choose CBO measure as the domestic slack variable and OECD Total as our global slack measure. Our selection of the two measures is based mainly on the length of the series and relatively better performance compared to other slack measures. In Figures a-4b, we show how forecasting performance of these pairs of variables evolves over time. In these figures, several interesting points emerge. 5. The predictive ability of money growth measures vary significantly over time. In particular, we observe a pattern such that whenever domestic money growth has a poor performance, global money growth performs well and vice versa. During late 97s, there is a remarkable deterioration in the forecasting power of global money growth, which is outperformed by domestic money growth especially in long-horizon forecasts. After this period, forecasting ability of global money growth recovers rapidly although its performance compared to the AR process is not necessarily superior. 6. Terms of trade and terms of trade ex. oil produce a similar -albeit slightly weaker- crossing pattern in terms of forecasting performance over time. Except for core measures of inflation (Core CPI and trimmed mean PCE, which are also relatively short series), terms of trade yields significantly more accurate forecasts starting in late 95s through mid 97s and its performance deteriorates in general during late 97s. The MSFEs of the forecasts with terms of trade ex. oil follow a not so uniform pattern and shows a great variability in performance across horizons or inflation measures while 6

8 outperforming terms of trade at certain intervals. Particularly for the 98s however, terms of trade and terms of trade ex. oil appear to be doing better in forecasting inflation compared to monetary aggregates or output gap measures. 7. For slack measures however, and with limited data availability, the patterns mentioned above can no longer be pronounced. Our comparison of domestic and global slack measures show that the predictive power of the two measures move almost together through time, and with rare occasions they become significantly more powerful than the AR process in forecasting inflation. Starting from 949 through 97s (where global slack measures are not available) the CBO measure of US slack has a significantly better performance than the AR specification, especially at short horizons. In a nutshell, and as a summary of our findings, we report three puzzles in the light of our findings. First, theory does not provide with an explanation for why domestic and global slack measures do not perform well and global money growth comes out as a superior measure to forecast U.S. inflation. Second, and related to the previous puzzle, we are not clear as to why domestic slack measures along with terms of trade (or terms of trade ex. oil) do not improve forecasting accuracy as much as expected. Third, in theory, we would expect the HP-filtered slack measures to perform not as great as the slack measures that are calculated with a production function approach. Hence, this is the third puzzle we document in the results. 4 Interpreting the results In order to understand the empirical results more clearly, we simulate a slight variant of the workhorse log-linearized New Open-Economy Macro model by Martinez-Garcia, Vilan and Wynne () under the PCP assumption. Accordingly, the model consists of four basic structural equations for each country and two exogenous shocks with the additional expression for money growth. Aggregate demand is described by an equation that links the output gap, ˆx t to domestic and foreign interest rates, î t and î t, natural rates în t and în t, and inflation gaps ˆπ t and ˆπ t γ( )(E t ˆx t+ ˆx t ) [(( )+Γ)[(î t î n t ) E t ˆπ t+ ] Γ[(î t î n t ) E t ˆπ t+ ] (6) Aggregate supply is defined as a Phillips curve relating inflation gap to domestic and foreign output gaps ( α)( βα) ˆπ t βe t ˆπ t+ + [( + Θγ) ˆx t + (( )ϕ + ( Θ)γ) ˆx t ] (7) α Monetary policy rule is expressed à la Taylor (993) î t ρ i î t + ( ρ i )[Ψ π ˆπ t + Ψ x ˆx t ] + ˆε m t (8) Domestic money growth is derived by first differencing the ad-hoc log-linear money demand equation ˆm t = ŷ t η î t + ˆπ t. (9) We also define the natural interest rate as the weighted average of expected domestic and foreign productivity growth, 7

9 î n t + ϕ Θi,aE t [ â γ + ϕ t+] + Θ i,a E t[ â t+ ] () the potential output as the weighted average of domestic and foreign productivity gap, ŷ n t and finally terms of trade and terms of trade gap, ctot t + ϕ [ λ a â t + λ γ + a â t ] () ϕ γ(ŷ t ŷ t ) γ (γ )( ) and ctot g t γ( ˆx t ˆx t ) γ (γ )( ) () respectively. For Foreign, the equations of the model can be described symmetrically. Finally, the law of motion for productivity shocks and monetary shocks is governed by ât â t ˆε a t ˆε t a N ˆmt ˆm t ˆε m t ˆε m N t δa δ a,a δ a,a δ a ât â t a, ρ a,a δm ˆmt δ m where the composite parameters are given by ˆm t m, ρ m,m ˆε a + t ˆε t a ρ a,a a ˆε m + t ˆε m t ρ m,m m (3)! (4) (5)! (6) Θ i,a γ Γ ( ) [γ + (γ )( )] h i Θ γ (γ )( ) γ (γ )( ) γ ( γ )( )( η) ( ) ( γ )( )( η) ( γ )( )( η η ) λ a + ( γ )( )( η η ) λ a Θ i,a γ " γ ( γ )(! )( η) ( γ )( )( η η ) λ a + ( ) ( γ )(! # )( η) λ ( γ )( )( η η a ) 8

10 " # λ a + ( γ ) γ(( ) + ( )( η)) ϕ( ( γ )( )( η η )) + " # λ a ( γ ) γ(( ) + ( )( η)) ϕ( ( γ )( )( η η )) + " # λ a ( γ ) γ( + ( )( η )) ϕ( ( γ )( )( η η )) + " # λ a + ( γ ) γ( + ( )( η ) ϕ( ( γ )( )( η η )) + η η n n + ( n) n( ) n( ) + ( n)( ) The model parameters are summarized in the table below. Model parameters Structural parameters Intertemporal discount factor < β < Inverse of the intertemporal elasticity of substitution γ > Inverse of the Frisch elasticity of labor supply ϕ > Interest semi-elasticity of money demand η > Elasticity of substitution across varieties within a country θ > Elasticity of substitution between Home and Foreign bundles > Share of Home goods in the Home basket < < Share of Home goods in the Foreign basket < < Home population size, Mass of Home varieties < n < Foreign population size, Mass of Foreign varieties < n < Calvo price stickiness parameter < α < Monetary policy parameters Monetary policy inertia < ρ i < Sensitivity to deviations from the inflation target Ψ π > Sensitivity to deviations from the potential output target Ψ x > Shock parameters Persistence of the productivity shock < δ a < Volatility of the productivity shock > Correl. between Home and Foreign productivity innovations < ρ ε a,ε a < Persistence of the monetary policy shock < δ m < Volatility of the monetary policy shock > Correl. between Home and Foreign monetary innovations < ρ ε m,ε m < 9

11 Under the benchmark parameterization, the structural parameters of the model are chosen as β =.99, γ = ϕ = 5, =.5, =.94, and α =.75, in the light of Chari, Kehoe and McGrattan (). This is also similar to the closed economy model of Neiss and Nelson (3) and Neiss and Nelson (5). We assume that countries are equal in population, n =.5 and the allocation of home and foreign goods in the consumption basket of each country is symmetric, =. We set η = 4 as described in Gali (8). We assume that the Taylor rule is inertial and the policy rule is identical in both countries. Following Rudebusch (6), we set monetary policy parameters estimated to match the U.S. data such that ρ i =.78, Ψ π =.4 and Ψ x =.33, and the AR() monetary shock process parameters of persistence and volatility such that δ m =.9 and =.36, respectively. For the productivity shock process, these parameters are chosen as δ a =.97, and =.73, as in Heathcote and Perri (). Based on their estimates, the crosscountry spillover parameter δ a,a is set at.5.the correlations of domestic and foreign productivity and monetary innovations are ρ a,a =.9 and ρ m,m =.5, following Chari, Kehoe and McGrattan (). We assume further that the monetary and productivity innovations are uncorrelated with each other. We run a Monte Carlo simulation of the model with trials and with 6 periods for each trial. Using the simulated data, we forecast inflation using one-variable recursive forecasts with domestic and global money growth, terms of trade gap and HP filtered terms of trade; domestic and global output gap and HP filtered domestic and global output. In particular, we calculate the (relative) MSFEs at several different parameter combinations, while keeping all other parameters at their benchmark values. The analyses conducted here can be grouped under three experiments. The first experiment is on monetary policy which pays attention to forecasting performance under changes in the monetary policy parameters Ψ π and ρ i. The second experiment is on trade openness, which involves a grid search over parameters and. The third experiment is called good luck 3, and it focuses on how forecasting performance of the regressors listed above is altered when the parameters of innovations, specifically the volatility of shocks, and take on different values. We run two versions of this experiment. In the first one, we change the parameterization of U.S. only, keeping the ROW parameters constant. In the second version, we conduct the experiment symmetrically for both countries. We produce the simulated data with a grid search for these three pairs of parameters as follows. For Ψ π, we try values of grid points in the interval (, 4] and for ρ i in the interval (, ). For openness parameters and, we try the values in the intervals (.5, ] and (, ], respectively. Finally for and, we set values both varying within (, ]. We obtain several results based on these experiments:. As the volatility of the monetary shock, falls in the U.S., forecasting performance using any of the explanatory variables (domestic and global output gap, domestic and global money growth and terms of trade gap tends to increase monotonically holding volatility of productivity shock, constant. (Figures 5a-5c). As the volatility of the productivity shock in the U.S. move from its benchmark value towards a lower value, forecasting performance using domestic output gap, domestic and global money growth and terms of trade (HP filtered) tends to increase monotonically holding volatility of monetary shock, constant. (Figures 5a-5c) 3 In the current terminology, good luck is used in order to explore the possibility of exogenous changes in the distribution of the shock process. These changes might cause a draw of unusually beneign sample of good shocks to the economy. Hence the term is employed on a more broad sense; and our computational exercise here aims to shed light on the effects of phenomena including but not limited to the Great Moderation.

12 3. As the volatility of the monetary shock, falls in both countries, forecasting performance using any of the explanatory variables (domestic and global output gap, domestic and global money growth and terms of trade gap tends to increases monotonically holding volatility of productivity shock, constant. (Figures 5d-5f) 4. As the volatility of the productivity shock in both countries move symmetrically from its benchmark value towards a lower value, forecasting performance using domestic output gap, domestic and global money growth and terms of trade (HP filtered) tends to increase monotonically holding volatility of monetary shock, constant. (Figures 5d-5f) 5. As the monetary policy inertia, ρ i increases, forecasting performance falls regardless of how aggressive the stance of the monetary policy towards inflation is, i.e. for any Ψ π, when we forecast with domestic output gap, global output gap, terms of trade (HP filtered) or global money growth. With domestic money growth, no significant relationship between the monetary policy parameters and the relative MSFEs are observed. (Figures 6a-6c) 6. For a given value of ρ i, varying the value for Ψ π creates different implications across the variables used for forecasting inflation. In particular, there is a positive and monotonic relationship between relative MSFEs and Ψ π when we forecast inflation with domestic and global output gap. In contrast, when forecast is done with terms of trade (HP filtered) or global money growth, higher Ψ π improves forecasting performance. Moreover, the highest forecasting performance is obtained especially when the monetary policy is very aggressive and the monetary policy is not very persistent. (Figures 6a-6c) 7. Higher trade openness, (or lower ) affects forecasting performance negatively with domestic output gap, positively for global output gap. (Figures 7a-7c) 8. For any value of,and for any of the explanatory variables, varying in general does not have any significant impact on forecasting performance. (Figures 7a-7c) Figures a-4b could be analyzed under three periods. We will start with analyzing the most recent period, the post-979 period, which is characterized by three major events: Volcker disinflation, increased trade openness and the Great Moderation starting in the second half of 98s. The literature has provided with some very useful quantitative and empirical findings on how some of the parameters of the model have changed through time. Among these, Benati and Surico (8), based on a time-varying VAR, suggest that inflation s predictability fell as the persistence of inflation and as the Taylor rule coefficient on the inflation gap rose during the Volcker era. The model we utilize suggests similar results (see Figures 6a-6c) for all explanatory variables except for HP filtered terms of trade and global money growth and hence the deterioration in the forecasting performances of these variables in particular can in part be attributed to the aggressive stance of the monetary policy towards inflation. Next, we turn to how openness might have played a role in the predictive ability of the variables. The model suggests that (see Figures 7a-7c) the impact of higher openness, if any, must have been considerably small given that moving from the most extreme value for of (autarky) to.94 implies a small deterioration in forecasting accuracy. Hence we rule out openness as a major channel in affecting the forecasting performance.

13 The literature suggests that one explanation for the Great Moderation is that the standard deviation of the productivity shocks declined. Accordingly, the estimated standard deviation of the TFP innovations modeled as an AR() process (under varying utilization) declined from.78 to.6 while the persistence of the shocks increased from.74 to.94. These two changes in the parameters, when the volatility of monetary shock, is held constant, creates a decline in the relative MSFEs of forecasts with all variables (5a-5c). While it is important to quantify the relative magnitudes of the volatility of these shocks, Great Moderation still appears likely to be an important episode that accounts for the declining ability to forecast inflation in our simulation exercise as also pointed out in the literature (See for example, D Agostino, Giannone and Surico (5)). Under an anti-inflationary regime and macroeconomic stability, HP filtered terms of trade might be suggested as a useful variable in forecasting inflation which exhibits considerable success both empirically and theoretically; while the remaining variables we test here do not provide us with a satisfactory performance under the given environment. The second subperiod in Figures a-4b we are interested to explain is the period characterized with macroeconomic instability, weak monetary policy both in the US and in the ROW. When we interpret the period after the collapse of Bretton Woods as a period of high monetary volatility starting in 97, then we are able to understand through the lens of the model why G7 money growth performs poorly in forecasting inflation (while it still remains as a puzzle for why US money growth performs very well.) Again, in this period, this seems like a very plausible explanation for the sudden deterioration of forecasting performances of domestic and global slack measures. However, we have to keep in mind that a more indepth quantitative assessment of the relative volatility of shocks needs to be made in order to make a strong case for this channel. But the model does not tell us why terms of trade gap performs well for most measures of inflation until mid 97s even though the economic environment points towards weak performance in theory. For the pre-97s, in a relatively more stable macroeconomic environment and with a relatively strong monetary policy, the model suggests high forecasting performances for all variables which is seen to be valid to a great extent when Figures a-4b are investigated. One puzzle that we are unable to explain with the current model is that why the US money growth does not perform well; which is reminiscent of and most likely to have a common root with the puzzle regarding the US and G7 money growth during the era. 4. Interpreting the results (new experiments) We run a Monte Carlo simulation of the model with trials and with 6 periods for each trial. Using the simulated data, we forecast inflation using one-variable recursive forecasts with domestic and global money growth, terms of trade gap and HP filtered terms of trade; domestic and global output gap. In particular, we calculate the (relative) MSFEs at several different parameter combinations, while keeping all other parameters at their benchmark values. In these trials, we evaluate forecasting performances based on the median (relative) MSFE, median p-value of the hypothesis that the relative MSFE is less than, and the fraction of statistically significant trials with p-values less than or equal to %. The analyses conducted

14 here can be grouped under three main experiments. The first set of experiments is called good luck 4, and it focuses on how forecasting performance of the regressors listed above is altered when the parameters of innovations, specifically the volatility of shocks, and take on different values. We run two versions of this experiment. In the first version, we conduct the experiment symmetrically for both countries. Hence for and, and and, we set values both varying within (, ]. In the second one, we change the parameterization of U.S. only, keeping the ROW parameters constant. The second group of experiments is on monetary policy which pays attention to forecasting performance under changes in the monetary policy parameters Ψ π and Ψ x, one with high inertia, ρ i =.78 and one with low inertia, ρ i =. We produce the simulated data with a grid search for these three pairs of parameters as follows. For Ψ π, we try values of grid points in the interval (, 3] and Ψ x, in the interval (, ]. The final experiment is on trade openness, which involves a grid search over parameters and. Hence for and, we try the values in the intervals (.5, ] and (, ], respectively. We obtain several results based on the first good luck experiment and demonstrate them in Figures 9a-9f and a-c: a. Output gap measures tend to generate a higher fraction of statistically significant draws than domestic money and terms of trade. b. The regions for domestic output and foreign output that are more statistically significant tend to overlap. The same happens with money growth to some extent. However, the overlap is small between terms of trade gap and HP-filtered terms of trade. The HP-filtered terms of trade has more overlap with money and the terms of trade gap with the output gaps. c. Money and HP-filtered terms of trade have a limited overlap with the output gap measures (or the terms of trade gap measure), so it is possible to think that if the volatility driving the productivity and monetary shocks has changed over time then the forecasting of these different variables may have changed as well. What our evidence suggests is that relative to the benchmark, changes in the volatility of monetary and productivity shocks are more likely to have a major impact on HP-filtered terms of trade, but not so much on output gaps unless the departures in volatility from the benchmark are very large. Therefore, given that the benchmark values for and are.73 and.36, respectively, the Great Moderation does not seem very likely to have caused a deterioration in forecasting performances of domestic and global slack measures which can also be seen in the pattern in mid-98s in Figures A-B. An interesting point is on the differences between the forecasting power of HP-filtered terms of trade and the terms of trade gap even though there is a strong correlation between these two variables for the benchmark variables (Figure 5a). We do not have actual measures of terms of trade gap, so in the empirical analysis we use the HP-filtered terms of trade. Another interesting point is that the model shows that forecasting power is actually similar between money and HP-filtered terms of trade than with the terms of trade gap or the output gaps. Moreover, at the benchmark parameterization the statistically significant draws appear to be larger in the case that we use terms of trade HP-filtered than when we use the actual terms of trade gap. This could also contribute to explain why in environments where the monetary shocks are small relative to the productivity shocks, then HP-filtered terms of trade can be a good forecasting 4 In the current terminology, good luck is used in order to explore the possibility of exogenous changes in the distribution of the shock process. These changes might cause a draw of unusually beneign sample of good shocks to the economy. Hence the term is employed on a more broad sense; and our computational exercise here aims to shed light on the effects of phenomena including but not limited to the Great Moderation. 3

15 variable. Our results from the monetary policy experiments suggest the following: a. With high inertia more aggressive monetary policy on inflation (for a given Ψ x ) reduces the percentage of instances in which the forecasting power is statistically significant. Global and domestic slack are stronger forecasting variables if inertia is low than if it is high. If inertia is low, then increases in Ψ π result in higher percentages of statistically significant samples. However, Ψ x does not seem to have much of an effect. In turn, the pattern is somewhat reserved when we look at the high inertia case: whenever Ψ x increases, then the share of statistically significant samples tends to increase now for a given Ψ π. Moreover, for a given Ψ x increases in the anti-inflation bias of policy (Ψ π ) tend to reduce the share of statistically significant samples. b. Under low inertia, the results with global and domestic slack and with global and domestic money are very similar. In the case with high inertia, though, the results are very different. Global and domestic money do not have that much value as forecasting variables and they are often dominated by global and domestic slack although slack is not that great as a predictor, either. Two issues to consider here are:. If we have an explanation that is symmetric but accounts for the reversals between domestic and foreign variables, then we can reasonably well-document those with the evidence we have on US inflation. The effect would be symmetric anyway. The forecasting power of foreign money on US inflation, therefore, should be the same that US money would have on foreign inflation in this two country model. If we depend on an experiment that is asymmetric to make our case, then the symmetry of the effects cannot be presumed and it becomes all the more relevant to see empirically what happens with the "foreign inflation." That can serve as a cross-validation tool, but it also complicates the empirical analysis for us. However, the question is: can any of these variables forecast US and foreign inflation at the same time? This is an issue always, but with a symmetric explanation we are trying to explain one particular pattern of the inflation dynamics but with an asymmetric model we are trying to replicate two different patterns of those dynamics across countries. So in that case it becomes really relevant to document those patterns.. Unlike Benati and Surico, where they estimated the model before running their experiments, we have calibrated the model. One possible argument in favor of calibration is that the model is too simplified so we are concerned that estimating it would lead to misspecification bias and, therefore, would complicate the interpretation of our estimates and our subsequent experiments even more. However, we need to keep this very much in mind and make a comment about it in the paper. 4

16 Predictive performances of variables Domestic Global ToT ToT gap Domestic Global output output HP-filtered money money Good luck # (symmetric) # gap gap growth growth Good luck # + (asymmetric) # / + Monetary policy Ψ π " (low inertia) Ψ x " Monetary policy Ψ π " (high inertia) Ψ x " + Openness " + + " 5 Conclusion In progress... 6 Appendix. Data Description Abbreviations BEA = US Bureau of Economic Analysis; BLS = US Bureau of Labor Statistics; BBK =German Federal Bank; BIS = Bank for International Settlements; CAO = Cabinet Office (Japan) CBO = Congressional Budget Office; FRB = Federal Reserve Board; FRBD = Federal Reserve Bank of Dallas; FRED = Federal Reserve Economic Data (St. Louis Fed); IMF = International Monetary Fund; INSEE = National Institute of Statistics and Economic Studies (France); ISTAT = Istituto Nazionale Di Statistica (Italy); OECD= Organisation for Economic Cooperation and Development; OECDMEI= OECD Main Economic Indicators; ONS = Office for National Statistics (UK); SAAR = Seasonally adjusted at an annual rate; SA=Seasonally adjusted; SCAN = Statistics Canada All series are quarterly unless indicated otherwise and obtained from Haver Analytics. In general, we indicate the original source if the series is available outside Haver Analytics. While we try to be consistent in terms of the definitions across countries, under cases in which data availability is limited, we use the series with the closest definition.. Price indices 5

17 Series used for US inflation: All series are seasonally adjusted. Start dates of the series vary across different measures and they all end in :4. Base years and start dates of each series are indicated in parentheses. We take CPI (all items) (8-8=, 947:) from the BLS, core CPI (all items ex. food and energy) (8-84=, 957:) from the BLS, GDP implicit price deflator (8-84=, 947:) from the BEA; PCE chain price index (5=, 959:) from the BEA, trimmed mean PCE chain price index (4-5=, 977:) from FRBD and PPI (finished goods) (98=, 947:) from the BLS. Series used for terms of trade gaps: We use exports and imports under the heading price indexes for GDP in National Income and Product Accounts in BEA to calculate US terms of trade. Both series are seasonally adjusted, with the base year 5= and cover periods 947:-:4. Terms of trade series is calculated as export price index/import price index. Terms of trade gap is the HP filtered (λ = 6) terms of trade series. Terms of trade gap ex. oil is calculated similarly (with the same base year and seasonally adjusted), using imports of non-petroleum goods (chain price index) and exports of goods (chain price index) from BEA (967:-:4).. Monetary aggregates All series are seasonally adjusted and quarterly (end-of-period aggregates of monthly series). For UK and US, we have M4 and M data available from OECD and FRB (963:-:4), respectively. For other countries, data become limited for certain periods and sources and therefore we splice two series. Therefore we obtain M3 for Canada from BIS (96:-98:4) and OECD (98:- :4); M for Germany from BIS (963:-99:4) and BBK (98:-:4); M for Italy from Bank of Italy (963:-997:/997:-:4); M for Japan from Bank of Japan (963:-966:4) and FRED (967:-:4). For France, we splice MR and M3 from BIS (963:-969:4 and 97:-:4, respectively). For France, Germany and Italy, the first part of the series is converted from the national currency to Euros using the European Currency Unit (999). 3. Slack measures All measures used cover the period 98:-:4 unless stated otherwise. CBO US slack: Defined as Output Gap in Percentage of Real GDP, and is calculated as (RPGDPt RGDPt) RGDPt where RPGDPt and RGDPt are real potential GDP and real GDP at quarter t, respectively (SAAR, Billions of Chained 5 Dollars). We take our real GDP series from BEA and real potential GDP series from CBO. US HP-filtered series is simply quarterly US real GDP series with HP filter (λ = 6) applied. Then the logs of the cyclical component is taken and multiplied by. FRBD US slack: The series is constructed by the FRBD, and the methodology can be described as follows. First, the Phillips Curve is estimated with annualized quarterly inflation (specifically, core CPI) and unemployment rate/capacity utilization rate. The regression equation for this is specified as is constructed as follows. We first estimate the Phillips Curve with annualized quarterly inflation (specifically, core CPI) and unemployment rate/capacity utilization rate. The regression is specified as π t = α + α π t + α 3 π t + α 4 π t 3 + ( α α 3 α 4 )π t 4 + α 5 ur t + ɛ t 6

18 where π t = 4 log(p t /p t ), p t is the price index, ur t is unemployment rate where we define the potential unemployment rate as ur = ˆα /ˆα 5. We run a similar regression with capacity utilization rate, capu t and define the potential rate of capacity utilization, capu = ˆα /ˆα 5, similarly. Then the slack measure is computed as follows by running the following regression π t+4 π t = β (ur t ur ) + ( β )(capu t capu ) + ɛ t and the slack measure is calculated as slack t = ˆβ (ur t ur ) + ( ˆβ )(capu t capu ). FRBD G7 slack: Produced by the FRBD and calculated by applying the procedure described above for each member of the G7 economies. After obtaining the domestic slack measure for a given country, the GDP shares of each country is calculated so that for country i at quarter t, share i,t =GDP i,t / i GDP i,t. The G7 slack is the GDP-weighted average of the slack measures of individual countries. The data series we use here are as follows: GDP series to construct the GDP shares of each country (sources indicated in parentheses): Canada (SCAN), France (INSEE), Germany (BBK), Italy (ISTAT), Japan (CAO), UK (ONS), US (BEA). All series are in billions of US Dollars, seasonally adjusted (978:-:4). For France, Germany and Italy, the series are working day adjusted. Manufacturing capacity utilization rates (%) come from manufacturing surveys, covering the period 978:-:4 and are seasonally adjusted for the following countries: France, Germany and US For Italy, the data come from OECDMEI; for Japan, we use manufacturing operation rate; for Canada, we do splicing for capacity utilization rate from OECDMEI (978:-986:4) and the manufacturing survey from SCAN (987:-:4); while we apply a similar procedure for UK with capacity utilization rate series from Datastream (978:-985:) and the manufacturing survey from OECDMEI (985:- :4). As a measure of inflation, we use core CPI. All series are seasonally adjusted, come from OECDMEI and the base year is 5= for all countries with the exception that the base year is = for Japan and 8-84= for the US. FRBD G39 Slack: This measure is calculated by HP filtering (λ = 6) of FRBD G39 index which uses constant 5 (PPP adjusted) weights to aggregate GDP series of the 39 countries: Argentina, Australia, Austria, Belgium, Brazil, Canada, China, Czech Republic, Denmark, Finland, France, Germany, Greece, Hong Kong, Hungary, India, Indonesia, Italy, Ireland, Japan, Korea, Luxembourg, Malaysia, Mexico, Netherlands, New Zealand, Norway, Peru, Poland, Singapore, South Africa, Spain, Sweden, Switzerland, Taiwan, Thailand, Turkey, UK and US. GDP series used are quarterly; and for some countries for which only disaggregated (annual) data are available, we apply quadratic match average method to interpolate these series. We use 5 PPP data from the IMF. IMF US and IMF Advanced Slack: Both slack measures are defined as Output Gap in Percentage of Real GDP (%) for the US and for a group of advanced countries (Australia, Austria, Belgium, Canada, Cyprus, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, UK and US). These measures are published by IMF WEO, annually and 7

19 available between 98-. Therefore we interpolate the series by quadratic match average method to disaggregate into quarterly frequency. OECD US, OECD G7 and OECD Total Slack: All three measures are defined as the Output Gap of the Total Economy (%), published by OECD Economic Outlook. OECD Total consists of 3 OECD countries: Australia, Austria, Belgium, Canada, Cyprus, Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, Korea, Luxembourg, Mexico, Netherlands, New Zealand, Norway, Portugal, Slovakia, Spain, Sweden, Switzerland, Turkey, UK and US and the series go back to 97:4. US HP-filtered GDP: Calculated using quarterly US real GDP series from BEA. First, the logs of the series is taken and multiplied by and then Hodrick-Prescott filter (λ = 6) is applied. A Tables and Figures 8

20 Table. Relative MSFEs 99Q:Q4 Horizon Consumer Price Index Consumer Price Index (ex. Food & Energy) Autoregressive CBO US Slack FRBD US Slack IMF US Slack OECD US Slack US HP- Filtered US Money Growth PCE Price Index Trimmed Mean PCE Price Index Autoregressive CBO US Slack FRBD US Slack IMF US Slack OECD US Slack US HP- Filtered US Money Growth GDP Deflator Producer Price Index Autoregressive CBO US Slack FRBD US Slack IMF US Slack OECD US Slack US HP- Filtered US Money Growth This table reports the forecasting performances with an estimation sample covering 98Q:99Q4 and a pseudo out-of-sample forecasting sample over 99Q:Q4. The first row of each panel shows the MSFEs of forecasts with the simple univariate AR process of inflation (restricted model) and are therefore in absolute terms. The remaining entries are the MSFEs of the forecasts under the unrestricted model relative to the MSFEs of the restricted model. Asterisks denote that the relative MSFEs are statistically different and (more accurate) than the MSFEs of the benchmark (restricted) model at (***), 5 (**), and (*) percent significance levels. 9

21 Table. Relative MSFEs 99Q:Q4 Horizon Consumer Price Index Consumer Price Index (ex. Food & Energy) Autoregressive FRBD G FRBD G IMF Adv OECD G OECD Total G7 Money Growth PCE Price Index Trimmed Mean PCE Price Index Autoregressive FRBD G FRBD G IMF Adv OECD G OECD Total G7 Money Growth GDP Deflator Producer Price Index Autoregressive FRBD G FRBD G IMF Adv OECD G OECD Total G7 Money Growth This table reports the forecasting performances with an estimation sample covering 98Q:99Q4 and a pseudo out-of-sample forecasting sample over 99Q:Q4. The first row of each panel shows the MSFEs of forecasts with the simple univariate AR process of inflation (restricted model) and are therefore in absolute terms. The remaining entries are the MSFEs of the forecasts under the unrestricted model relative to the MSFEs of the restricted model. Asterisks denote that the relative MSFEs are statistically different and (more accurate) than the MSFEs of the benchmark (restricted) model at (***), 5 (**), and (*) percent significance levels.

22 Table 3. Relative MSFEs 99Q:Q4 Horizon Consumer Price Index Consumer Price Index (ex. Food & Energy) Autoregressive Terms of Trade CBO US & ToT FRBD US & ToT IMF US & ToT OECD US & ToT US HP-filt. & ToT US Money Growth & ToT G7 Money Growth & ToT PCE Price Index Trimmed Mean PCE Price Index Autoregressive Terms of Trade CBO US & ToT FRBD US & ToT IMF US & ToT OECD US & ToT US HP-filt. & ToT US Money Growth & ToT G7 Money Growth & ToT GDP Deflator Producer Price Index Autoregressive Terms of Trade CBO US & ToT FRBD US & ToT IMF US & ToT OECD US & ToT US HP-filt. & ToT US Money Growth & ToT G7 Money Growth & ToT This table reports the forecasting performances with an estimation sample covering 98Q:99Q4 and a pseudo out-of-sample forecasting sample over 99Q:Q4. The first row of each panel shows the MSFEs of forecasts with the simple univariate AR process of inflation (restricted model) and are therefore in absolute terms. The second entry in each panel reports the relative MSFEs of the univariate forecasts with terms of trade. The remaining entries are the MSFEs of the bivariate forecasts relative to the MSFEs of the restricted model. Asterisks denote that the relative MSFEs are statistically different and (more accurate) than the MSFEs of the restricted model at (***), 5 (**), and (*) percent significance levels.

23 Table 4. Relative MSFEs 99Q:Q4 Horizon Consumer Price Index Consumer Price Index (ex. Food & Energy) Autoregressive ToT ex.oil CBO US & ToT ex. oil FRBD US & ToT ex. oil IMF US & ToT ex. oil OECD US & ToT ex. oil US HP-filt. & ToT ex. oil US Money Gr. & ToT ex. oil G7 Money Gr. &ToT ex. oil PCE Chain Price Index Trimmed Mean PCE Price Index Autoregressive ToT ex.oil CBO US & ToT ex. oil FRBD US & ToT ex. oil IMF US & ToT ex. oil OECD US & ToT ex. oil US HP-filt. & ToT ex. oil US Money Gr. & ToT ex. oil G7 Money Gr. &ToT ex. oil GDP Deflator Producer Price Index Autoregressive ToT ex. oil CBO US & ToT ex. oil FRBD US & ToT ex. oil IMF US & ToT ex. oil OECD US & ToT ex. oil US HP-filt. & ToT ex. oil US Money Gr. & ToT ex. oil G7 Money Gr. &ToT ex. oil This table reports the forecasting performances with an estimation sample covering 98Q:99Q4 and a pseudo out-of-sample forecasting sample over 99Q:Q4. The first row of each panel shows the MSFEs of forecasts with the simple univariate AR process of inflation (restricted model) and are therefore in absolute terms. The second entry in each panel reports the relative MSFEs of the univariate forecasts with terms of trade ex. oil. The remaining entries are the MSFEs of the bivariate forecasts relative to the MSFEs of the restricted model. Asterisks denote that the relative MSFEs are statistically different and (more accurate) than the MSFEs of the restricted model at (***), 5 (**), and (*) percent significance levels.

24 3 5 5 US Inflation (first differences of the price level) US Terms of trade (HP filtered) 5 CPI Core CPI GDP def. PPI PCE TMPCE Q 6 Q 8 Q Domestic slack measures US HP filt. OECD IMF CBO FRBD TOT TOT ex. oil Q 6 Q 8 Q OECD Total OECD G7 IMF Adv. FRBD G7 FRBD G39 Global slack measures Q 6 Q 8 Q 6 Q 6 Q 8 Q 8 US and G7 liquidity growth (%) 6 4 US G7 Q 6 Q 8 Q FIGURE. Time series plots of the data 3

25 4 FIGURE A. Evolution of the relative MSFEs of the forecasts with the US vs. G7 money growth

26 5 FIGURE B. Evolution of the relative MSFEs of the forecasts with the US vs. G7 money growth

27 6 FIGURE 3A. Evolution of the relative MSFEs of the forecasts with the CBO US slack vs. OECD Total slack

28 7 FIGURE 3B. Evolution of the relative MSFEs of the forecasts with the CBO US slack vs. OECD Total slack

29 8 FIGURE 4A. Evolution of the relative MSFEs of the forecasts with terms of trade vs. terms of trade ex. oil

30 9 FIGURE 4B. Evolution of the relative MSFEs of the forecasts with terms of trade vs. terms of trade ex. oil

31 Domestic output gap h= (Median MSFE) Domestic output gap h= (Median p value) Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Median MSFE) Domestic output gap h=4 (Median p value) Domestic output gap h=4 (Fraction with p<%) Domestic output gap h= (Median MSFE) Domestic output gap h= (Median p value) Domestic output gap h= (Fraction with p<%) FIGURE 5A. Model s prediction of the relative MSFEs of forecasts with domestic slack as a function of the parameters of good luck Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 3

32 Global output gap h= (Median MSFE) Global output gap h= (Median p value) Global output gap h= (Fraction with p<%) Global output gap h=4 (Median MSFE) Global output gap h=4 (Median p value) Global output gap h=4 (Fraction with p<%) Global output gap h= (Median MSFE) Global output gap h= (Median p value) Global output gap h= (Fraction with p<%) FIGURE 5B. Model s prediction of the relative MSFEs of forecasts with global slack as a function of the parameters of good luck Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 3

33 ToT (HP filtered) h= (Median MSFE) ToT (HP filtered) h= (Median p value) ToT (HP filtered) h= (Fraction with p<%) ToT (HP filtered) h=4 (Median MSFE) ToT (HP filtered) h=4 (Median p value) ToT (HP filtered) h=4 (Fraction with p<%) ToT (HP filtered) h= (Median MSFE) ToT (HP filtered) h= (Median p value) ToT (HP filtered) h= (Fraction with p<%) FIGURE 5C. Model s prediction of the relative MSFEs of forecasts with HP-filtered terms of trade as a function of the parameters of good luck Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 3

34 ToT gap h= (Median MSFE) ToT gap h= (Median p value) ToT gap h= (Fraction with p<%) ToT gap h=4 (Median MSFE) ToT gap h=4 (Median p value) ToT gap h=4 (Fraction with p<%) ToT gap h= (Median MSFE) ToT gap h= (Median p value) ToT gap h= (Fraction with p<%) FIGURE 5D. Model s prediction of the relative MSFEs of forecasts with terms of trade gap as a function of the parameters of good luck Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 33

35 Domestic money growth h= (Median MSFE) Domestic money growth h= (Median p value) Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Median MSFE) Domestic money growth h=4 (Median p value) Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Median MSFE) Domestic money growth h= (Median p value) Domestic money growth h= (Fraction with p<%) FIGURE 5E. Model s prediction of the relative MSFEs of forecasts with domestic money supply growth as a function of the parameters of good luck Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 34

36 Global money growth h= (Median MSFE) Global money growth h= (Median p value) Global money growth h= (Fraction with p<%) Global money growth h=4 (Median MSFE) Global money growth h=4 (Median p value) Global money growth h=4 (Fraction with p<%) Global money growth h= (Median MSFE) Global money growth h= (Median p value) Global money growth h= (Fraction with p<%) FIGURE 5F. Model s prediction of the relative MSFEs of forecasts with global money supply growth as a function of the parameters of good luck Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 35

37 Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Fraction with p<%) Domestic output gap h= (Fraction with p<%) Global output gap h= (Fraction with p<%) Global output gap h=4 (Fraction with p<%) Global output gap h= (Fraction with p<%) FIGURE 6A. Comparison of the forecasting performances of simulated domestic and global output gap as a function of the parameters of good luck Note: Fraction of statistically significant MSFEs in simulations are reported. 36

38 ToT (HP filtered) h= (Fraction with p<%) ToT (HP filtered) h=4 (Fraction with p<%) ToT (HP filtered) h= (Fraction with p<%) ToT gap h= (Fraction with p<%) ToT gap h=4 (Fraction with p<%) ToT gap h= (Fraction with p<%) FIGURE 6B. Comparison of the forecasting performances of simulated HP-filtered ToT and ToT gap as a function of the parameters of good luck Note: Fraction of statistically significant MSFEs in simulations are reported

39 Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Fraction with p<%) Global money growth h= (Fraction with p<%) Global money growth h=4 (Fraction with p<%) Global money growth h= (Fraction with p<%) FIGURE 6C. Comparison of the forecasting performances of simulated domestic and global money supply growth as a function of the parameters of good luck Note: Fraction of statistically significant MSFEs in simulations are reported. 38

40 Domestic output gap h= (Median MSFE) Domestic output gap h= (Median p value) Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Median MSFE) Domestic output gap h=4 (Median p value) Domestic output gap h=4 (Fraction with p<%) Domestic output gap h= (Median MSFE) Domestic output gap h= (Median p value) Domestic output gap h= (Fraction with p<%) FIGURE 7A. Model s prediction of the relative MSFEs of forecasts with domestic slack as a function of the parameters of good luck (asymmetric experiment) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 39

41 Global output gap h= (Median MSFE) Global output gap h= (Median p value) Global output gap h= (Fraction with p<%) Global output gap h=4 (Median MSFE) Global output gap h=4 (Median p value) Global output gap h=4 (Fraction with p<%) Global output gap h= (Median MSFE) Global output gap h= (Median p value) Global output gap h= (Fraction with p<%) FIGURE 7B. Model s prediction of the relative MSFEs of forecasts with global slack as a function of the parameters of good luck (asymmetric experiment) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 4

42 ToT (HP filtered) h= (Median MSFE) ToT (HP filtered) h= (Median p value) ToT (HP filtered) h= (Fraction with p<%) ToT (HP filtered) h=4 (Median MSFE) ToT (HP filtered) h=4 (Median p value) ToT (HP filtered) h=4 (Fraction with p<%) ToT (HP filtered) h= (Median MSFE) ToT (HP filtered) h= (Median p value) ToT (HP filtered) h= (Fraction with p<%) FIGURE 7C. Model s prediction of the relative MSFEs of forecasts with HP-filtered terms of trade as a function of the parameters of good luck (asymmetric experiment) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 4

43 .5.5 ToT gap h= (Median MSFE) ToT gap h= (Median p value) ToT gap h= (Fraction with p<%) ToT gap h=4 (Median MSFE) ToT gap h=4 (Median p value) ToT gap h=4 (Fraction with p<%) ToT gap h= (Median MSFE) ToT gap h= (Median p value) ToT gap h= (Fraction with p<%) FIGURE 7D. Model s prediction of the relative MSFEs of forecasts with terms of trade gap as a function of the parameters of good luck (asymmetric experiment) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 4

44 Domestic money growth h= (Median MSFE) Domestic money growth h= (Median p value) Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Median MSFE) Domestic money growth h=4 (Median p value) Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Median MSFE) Domestic money growth h= (Median p value) Domestic money growth h= (Fraction with p<%) FIGURE 7E. Model s prediction of the relative MSFEs of forecasts with domestic money supply growth as a function of the parameters of good luck (asymmetric experiment) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 43

45 Global money growth h= (Median MSFE) Global money growth h= (Median p value) Global money growth h= (Fraction with p<%) Global money growth h=4 (Median MSFE) Global money growth h=4 (Median p value) Global money growth h=4 (Fraction with p<%) Global money growth h= (Median MSFE) Global money growth h= (Median p value) Global money growth h= (Fraction with p<%) FIGURE 7F. Model s prediction of the relative MSFEs of forecasts with global money supply growth as a function of the parameters of good luck (asymmetric experiment) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 44

46 Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Fraction with p<%) Domestic output gap h= (Fraction with p<%) Global output gap h= (Fraction with p<%) Global output gap h=4 (Fraction with p<%) Global output gap h= (Fraction with p<%) FIGURE 8A. Comparison of the forecasting performances of simulated domestic and global output gap as a function of the parameters of good luck (asymmetric experiment) Note: Fraction of statistically significant MSFEs in simulations are reported

47 ToT (HP filtered) h= (Fraction with p<%) ToT (HP filtered) h=4 (Fraction with p<%) ToT (HP filtered) h= (Fraction with p<%) ToT gap h= (Fraction with p<%) ToT gap h=4 (Fraction with p<%) ToT gap h= (Fraction with p<%) FIGURE 8B. Comparison of the forecasting performances of simulated HP-filtered ToT and ToT gap as a function of the parameters of good luck (asymmetric experiment) Note: Fraction of statistically significant MSFEs in simulations are reported

48 Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Fraction with p<%) Global money growth h= (Fraction with p<%) Global money growth h=4 (Fraction with p<%) Global money growth h= (Fraction with p<%) FIGURE 8C. Comparison of the forecasting performances of simulated domestic and global money supply growth as a function of the parameters of good luck (asymmetric experiment) Note: Fraction of statistically significant MSFEs in simulations are reported

49 Domestic output gap h= (Median MSFE) Domestic output gap h= (Median p value) Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Median MSFE) Domestic output gap h=4 (Median p value) Domestic output gap h=4 (Fraction with p<%) Domestic output gap h= (Median MSFE) Domestic output gap h= (Median p value) Domestic output gap h= (Fraction with p<%) FIGURE 9A. Model s prediction of the relative MSFEs of forecasts with domestic output gap as a function of the parameters of monetary policy (low inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 48

50 Global output gap h= (Median MSFE) Global output gap h= (Median p value) Global output gap h= (Fraction with p<%) Global output gap h=4 (Median MSFE) Global output gap h=4 (Median p value) Global output gap h=4 (Fraction with p<%) Global output gap h= (Median MSFE) Global output gap h= (Median p value) Global output gap h= (Fraction with p<%) FIGURE 9B. Model s prediction of the relative MSFEs of forecasts with global output gap as a function of the parameters of monetary policy (low inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 49

51 HP filtered TOT h= (Median MSFE) HP filtered TOT h= (Median p value) HP filtered TOT h= (Fraction with p<%) HP filtered TOT h=4 (Median MSFE) HP filtered TOT h=4 (Median p value) HP filtered TOT h=4 (Fraction with p<%) HP filtered TOT h= (Median MSFE) HP filtered TOT h= (Median p value) HP filtered TOT h= (Fraction with p<%) FIGURE 9C. Model s prediction of the relative MSFEs of forecasts with HP filtered TOT as a function of the parameters of monetary policy (low inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 5

52 TOT gap h= (Median MSFE) TOT gap h= (Median p value) TOT gap h= (Fraction with p<%) TOT gap h=4 (Median MSFE) TOT gap h=4 (Median p value) TOT gap h= (Median MSFE) TOT gap h= (Median p value) TOT gap h=4 (Fraction with p<%) TOT gap h= (Fraction with p<%) FIGURE 9D. Model s prediction of the relative MSFEs of forecasts with TOT gap as a function of the parameters of monetary policy (low inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 5

53 Domestic money growth h= (Median MSFE) Domestic money growth h= (Median p value) Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Median MSFE) Domestic money growth h=4 (Median p value) Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Median MSFE) Domestic money growth h= (Median p value) Domestic money growth h= (Fraction with p<%) FIGURE 9E. Model s prediction of the relative MSFEs of forecasts with domestic money supply growth as a function of the parameters of monetary policy (low inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 5

54 Global money growth h= (Median MSFE) Global money growth h= (Median p value) Global money growth h= (Fraction with p<%) Global money growth h=4 (Median MSFE) Global money growth h=4 (Median p value) Global money growth h=4 (Fraction with p<%) Global money growth h= (Median MSFE) Global money growth h= (Median p value) Global money growth h= (Fraction with p<%) FIGURE 9F. Model s prediction of the relative MSFEs of forecasts with global money supply growth as a function of the parameters of monetary policy (low inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 53

55 Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Fraction with p<%) Domestic output gap h= (Fraction with p<%) Global output gap h= (Fraction with p<%) Global output gap h=4 (Fraction with p<%) Global output gap h= (Fraction with p<%) FIGURE A. Comparison of the forecasting performances of simulated domestic and global output gap as a function of the parameters of monetary policy (low inertia) Note: Fraction of statistically significant MSFEs in simulations are reported. 54

56 HP filtered TOT h= (Fraction with p<%) HP filtered TOT h=4 (Fraction with p<%) HP filtered TOT h= (Fraction with p<%) TOT gap h= (Fraction with p<%) TOT gap h=4 (Fraction with p<%) TOT gap h= (Fraction with p<%) FIGURE B. Comparison of the forecasting performances of simulated HP filtered TOT and TOT gap as a function of the parameters of monetary policy (low inertia) Note: Fraction of statistically significant MSFEs in simulations are reported

57 Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Fraction with p<%) Global money growth h= (Fraction with p<%) Global money growth h=4 (Fraction with p<%) Global money growth h= (Fraction with p<%) FIGURE C. Comparison of the forecasting performances of simulated domestic and global money supply growth as a function of the parameters of monetary policy (low inertia) Note: Fraction of statistically significant MSFEs in simulations are reported. 56

58 Domestic output gap h= (Median MSFE) Domestic output gap h= (Median p value) Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Median MSFE) Domestic output gap h=4 (Median p value) φ x.5 Domestic output gap h=4 (Fraction with p<%) φ π Domestic output gap h= (Median MSFE) Domestic output gap h= (Median p value) Domestic output gap h= (Fraction with p<%) FIGURE A. Model s prediction of the relative MSFEs of forecasts with domestic output gap as a function of the parameters of monetary policy (high inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 57

59 Global output gap h= (Median MSFE) Global output gap h= (Median p value) Global output gap h= (Fraction with p<%) Global output gap h=4 (Median MSFE) Global output gap h=4 (Median p value) Global output gap h=4 (Fraction with p<%) Global output gap h= (Median MSFE) Global output gap h= (Median p value) Global output gap h= (Fraction with p<%) FIGURE B. Model s prediction of the relative MSFEs of forecasts with global output gap as a function of the parameters of monetary policy (high inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported..5 58

60 TOT (HP filtered) h= (Median MSFE) TOT (HP filtered) h= (Median p value) TOT (HP filtered) h= (Fraction with p<%) TOT (HP filtered) h=4 (Median MSFE) TOT (HP filtered) h=4 (Median p value) TOT (HP filtered) h=4 (Fraction with p<%) TOT (HP filtered) h= (Median MSFE) TOT (HP filtered) h= (Median p value) TOT (HP filtered) h= (Fraction with p<%) FIGURE C. Model s prediction of the relative MSFEs of forecasts with HP filtered TOT as a function of the parameters of monetary policy (high inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 59

61 ToT gap h= (Median MSFE) ToT gap h= (Median p value) ToT gap h= (Fraction with p<%) ToT gap h=4 (Median MSFE) ToT gap h=4 (Median p value) ToT gap h= (Median MSFE) ToT gap h= (Median p value) ToT gap h=4 (Fraction with p<%) ToT gap h= (Fraction with p<%) FIGURE D. Model s prediction of the relative MSFEs of forecasts with TOT gap as a function of the parameters of monetary policy (high inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 6

62 Domestic money growth h= (Median MSFE) Domestic money growth h= (Median p value) Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Median MSFE) Domestic money growth h=4 (Median p value) Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Median MSFE) Domestic money growth h= (Median p value) Domestic money growth h= (Fraction with p<%) FIGURE E. Model s prediction of the relative MSFEs of forecasts with domestic money supply growth as a function of the parameters of monetary policy (high inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 6

63 Global money growth h= (Median MSFE) Global money growth h= (Median p value) Global money growth h= (Fraction with p<%) Global money growth h=4 (Median MSFE) Global money growth h=4 (Median p value) Global money growth h=4 (Fraction with p<%) Global money growth h= (Median MSFE) Global money growth h= (Median p value) Global money growth h= (Fraction with p<%) FIGURE F. Model s prediction of the relative MSFEs of forecasts with global money supply growth as a function of the parameters of monetary policy (high inertia) Note: MSFEs are relative to the MSFEs of the univariate AR process of inflation (restricted model). Median MSFEs, median p-values and fraction of statistically significant MSFEs in simulations are reported. 6

64 Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Fraction with p<%) Domestic output gap h= (Fraction with p<%) Global output gap h= (Fraction with p<%) Global output gap h=4 (Fraction with p<%) Global output gap h= (Fraction with p<%) FIGURE A. Comparison of the forecasting performances of simulated domestic and global output gap as a function of the parameters of monetary policy (high inertia) Note: Fraction of statistically significant MSFEs in simulations are reported. 63

65 ToT (HP filtered) h= (Fraction with p<%) ToT (HP filtered) h=4 (Fraction with p<%) ToT (HP filtered) h= (Fraction with p<%) ToT gap h= (Fraction with p<%) ToT gap h=4 (Fraction with p<%) ToT gap h= (Fraction with p<%) FIGURE B. Comparison of the forecasting performances of simulated HP filtered TOT and TOT gap as a function of the parameters of monetary policy (high inertia) Note: Fraction of statistically significant MSFEs in simulations are reported

66 Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Fraction with p<%) Global money growth h= (Fraction with p<%) Global money growth h=4 (Fraction with p<%) Global money growth h= (Fraction with p<%) FIGURE C. Comparison of the forecasting performances of simulated domestic and global money supply growth as a function of the parameters of monetary policy (high inertia) Note: Fraction of statistically significant MSFEs in simulations are reported. 65

67 Domestic output gap h= (Median MSFE).4. Domestic output gap h= (Median p value).4 Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Median MSFE).4. Domestic output gap h=4 (Median p value).4 Domestic output gap h=4 (Fraction with p<%) Domestic output gap h= (Median MSFE).4. Domestic output gap h= (Median p value).4 Domestic output gap h= (Fraction with p<%) FIGURE 3A. Comparison of the forecasting performances of simulated domestic output gap as a function of the parameters of openness Note: Fraction of statistically significant MSFEs in simulations are reported. 66

68 Global output gap h= (Median MSFE).4. Global output gap h= (Median p value).4 Global output gap h= (Fraction with p<%) Global output gap h=4 (Median MSFE).4. Global output gap h=4 (Median p value).4 Global output gap h=4 (Fraction with p<%) Global output gap h= (Median MSFE).4. Global output gap h= (Median p value).4 Global output gap h= (Fraction with p<%) FIGURE 3B. Comparison of the forecasting performances of simulated global output gap as a function of the parameters of openness Note: Fraction of statistically significant MSFEs in simulations are reported

69 ToT (HP filtered) h= (Median MSFE).4. ToT (HP filtered) h= (Median p value).4 ToT (HP filtered) h= (Fraction with p<%) ToT (HP filtered) h=4 (Median MSFE).4. ToT (HP filtered) h=4 (Median p value).4 ToT (HP filtered) h=4 (Fraction with p<%) ToT (HP filtered) h= (Median MSFE).4. ToT (HP filtered) h= (Median p value).4 ToT (HP filtered) h= (Fraction with p<%) FIGURE 3C. Comparison of the forecasting performances of simulated HP filtered TOT as a function of the parameters of openness Note: Fraction of statistically significant MSFEs in simulations are reported

70 .4. ToT gap h= (Median MSFE). ToT gap h= (Median p value) ToT gap h= (Fraction with p<%) ToT gap h=4 (Median MSFE). ToT gap h=4 (Median p value) ToT gap h= (Median MSFE) ToT gap h= (Median p value) FIGURE 3D. Comparison of the forecasting performances of simulated TOT gap as a function of the parameters of openness Note: Fraction of statistically significant MSFEs in simulations are reported. ToT gap h=4 (Fraction with p<%) ToT gap h= (Fraction with p<%)

71 Domestic money growth h= (Median MSFE).4. Domestic money growth h= (Median p value).4 Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Median MSFE).4. Domestic money growth h=4 (Median p value).4 Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Median MSFE).4. Domestic money growth h= (Median p value).4 Domestic money growth h= (Fraction with p<%) FIGURE 3E. Comparison of the forecasting performances of simulated domestic money supply growth as a function of the parameters of openness Note: Fraction of statistically significant MSFEs in simulations are reported. 7

72 Global money growth h= (Median MSFE).4. Global money growth h= (Median p value).4 Global money growth h= (Fraction with p<%) Global money growth h=4 (Median MSFE).4. Global money growth h=4 (Median p value).4 Global money growth h=4 (Fraction with p<%) Global money growth h= (Median MSFE).4. Global money growth h= (Median p value).4 Global money growth h= (Fraction with p<%) FIGURE 3F. Comparison of the forecasting performances of simulated global money supply growth as a function of the parameters of openness Note: Fraction of statistically significant MSFEs in simulations are reported

73 Domestic output gap h= (Fraction with p<%) Domestic output gap h=4 (Fraction with p<%) Domestic output gap h= (Fraction with p<%) Global output gap h= (Fraction with p<%) Global output gap h=4 (Fraction with p<%) Global output gap h= (Fraction with p<%) FIGURE 4A. Comparison of the forecasting performances of simulated domestic and global output gap as a function of the parameters of openness Note: Fraction of statistically significant MSFEs in simulations are reported. 7

74 ToT (HP filtered) h= (Fraction with p<%) ToT (HP filtered) h=4 (Fraction with p<%) ToT (HP filtered) h= (Fraction with p<%) ToT gap h= (Fraction with p<%) ToT gap h=4 (Fraction with p<%) ToT gap h= (Fraction with p<%) FIGURE 4B. Comparison of the forecasting performances of simulated HP filtered TOT and TOT gap as a function of the parameters of openness Note: Fraction of statistically significant MSFEs in simulations are reported

75 Domestic money growth h= (Fraction with p<%) Domestic money growth h=4 (Fraction with p<%) Domestic money growth h= (Fraction with p<%) Global money growth h= (Fraction with p<%) Global money growth h=4 (Fraction with p<%) Global money growth h= (Fraction with p<%) FIGURE 4C. Comparison of the forecasting performances of simulated domestic and global money supply growth as a function of the parameters of openness Note: Fraction of statistically significant MSFEs in simulations are reported. 74

76 FIGURE 5A. Correlations of (i) model-consistent domestic output gap and HP filtered domestic output, (ii) model-consistent global output gap and HP filtered global output, (iii) model-consistent ToT gap and HP filtered ToT as a function of the parameters of good luck (symmetric experiment) FIGURE 5B. Correlations of (i) model-consistent domestic output gap and HP filtered domestic output, (ii) model-consistent global output gap and HP filtered global output, (iii) model-consistent ToT gap and HP filtered ToT as a function of the parameters of good luck (with U.S. parameters only) 75

77 Correlation between domestic output gap and HP filtered output Correlation between global output gap and HP filtered output Correlation between TOT gap and HP filtered TOT Correlation between domestic output gap and HP filtered output Correlation between global output gap and HP filtered output Correlation between TOT gap and HP filtered TOT φ x φ π φ x φ π φ x φ π FIGURE 5C. Correlations of (i) model-consistent domestic output gap and HP filtered domestic output, (ii) model-consistent global output gap and HP filtered global output, (iii) model-consistent ToT gap and HP filtered ToT as a function of the parameters of monetary policy (high inertia) φ x.5 φ π φ x.5 φ π φ x.5 φ π FIGURE 5D. Correlations of (i) model-consistent domestic output gap and HP filtered domestic output, (ii) model-consistent global output gap and HP filtered global output, (iii) model-consistent ToT gap and HP filtered ToT as a function of the parameters of monetary policy (low inertia) 76

78 FIGURE 5E. Correlations of (i) model-consistent domestic output gap and HP filtered domestic output, (ii) model-consistent global output gap and HP filtered global output, (iii) model-consistent ToT gap and HP filtered ToT as a function of the parameters of openness 77