Silviase/jgov_v1.4_full_ann huggingface dataset:
shock. Therefore, the shape of the IRs suggests that the risk of a second-round effect would be low at least in terms of the cross-country average.

To assess the shape of IRs, we introduce a simple measure. As long as inflation is stationary, the slope of the IR becomes zero in the long run. Hence, we measure the extent to which the slope of the IR deviates from zero during a year by the mean absolute deviations of $ IR(k)-IR(k-1) $ . We call this measure the variability of inflation responses (VIR). More specifically, the VIRs for the first and second year after commodity price shocks are defined by

$$ V I R_{1}\ =\ \hat{\sigma}_{c}\frac{1}{12}\sum_{k=1}^{12}\left|\hat{\gamma}_{k}-\hat{\gamma}_{k-1}\right|, $$

$$ V I R_{2}\ =\ \hat{\sigma}_{c}\frac{1}{12}\sum_{k=13}^{24}\left|\hat{\gamma}_{k}-\hat{\gamma}_{k-1}\right|, $$

respectively. Here, $ VIR_{1} $ quantifies the mean deviation of inflation responses for the first year after a one-standard-deviation commodity price shock. Similarly, $ VIR_{2} $ quantifies that for the second year after the same shock. We multiply the mean absolute deviations by the standard deviation of commodity price shock to allow for comparisons of the VIRs across different commodity price shocks. In the benchmark estimations, $ VIR_{1} $ is 0.53 percent but $ VIR_{2} $ is only 0.13. The substantial reduction between VIRs reflects the transitory effect of commodity price shocks on inflation.

Apart from the transitory effect on inflation, a few remarks should be made on the benchmark estimation. First, even though the effects on inflation are transitory, the impact on the price level is not negligible. As shown in Figure 1, our estimates of the commodity price shock $ \hat{\varepsilon}_{c,t} $ are substantially volatile. In fact, at an annual rate, the standard deviation of $ \hat{\varepsilon}_{c,t} $ is estimated at 33.8 percent from February 2001 to December 2008. Hence, if a one-standard-deviation commodity price shock hits an economy, the CPI increases by 7.20 percent in period 24. $ ^{12} $ This magnitude of price responses is not negligible when we allow for the volatility of commodity price shocks.

Second, the estimated IR function in panel (a) of Figure 2 is broadly consistent with the estimated pass-through of commodity prices to the CPI that previous studies have discovered. Recall that IRs are defined as the price responses (i.e., the cumulative IRs of inflation). If we approximate the long-run price responses using the estimate of $ IR(24) $ , the estimate of 0.213
suggests a pass-through of 21.3 percent. Looking at the previous studies, Rigobon (2010) estimates the maximum pass-through of wheat prices to the CPIs in 50 countries. If we take the average of the maximum pass-through estimates over 50 countries, the results are 18.2 percent (See Table A.6 in Rigobon (2010)). Using 27 countries, Cecchetti and Moessner (2008) find that the commodity price pass-through to the one-year-ahead CPI ranges from 0 to 25 percent.

Third, our choice of sample periods does not affect our main result. In estimation, the transitory effect may result from the commodity price shock that became volatile in the 2000s. However, even if we use data from the 1990s, the estimated IRs are basically unaffected at least in point estimates. Panel (b) of Figure 2 plots the estimated IRs of the CPI. $ ^{13} $ In this case, $ VIR_{1} $ and $ VIR_{2} $ are 0.39 and 0.09, respectively, implying a substantial reduction within two years after the shock. $ ^{14} $

### 3.2 Comparisons to the standard approach

In this subsection, we compare our benchmark results to those from the standard approach.

To address this issue, we determine which standard approach is directly comparable to ours. Note that our approach identifies shocks from (4) and then estimates IRs from (2), rather than identifying shocks via the multivariate system of equations as in VAR. In VAR, the estimated commodity price shocks vary, depending on numerous factors such as identifying assumptions, the number of variables, and countries included in the system. Hence, the IRs estimated from VARs are not directly comparable to those from our approach. Further, it would not be easy to disentangle the factors that contribute to different results in comparing between local projections and VAR.

The method of Romer and Romer (2004, 2010) to estimate IRs is directly comparable to ours. Their narrative approach first identifies shocks and then estimates IRs from a separate equation with identified shocks. In our context, their approach is to run the following regression:

$$ \pi_{j,t}=\alpha_{j}+\sum_{i=1}^{q}\beta_{i}\pi_{j,t-i}+\sum_{i=0}^{r}\gamma_{i}\hat{u}_{c,t-i}+\xi_{j,t}. $$

With a slight abuse of notations, $ \alpha_{j}, \beta_{i} $ , and $ \gamma_{i} $ are parameters to be estimated. Unlike the local
projection, (7) requires $ \beta_{i} $ and $ \gamma_{i} $ to compute IRs. However, the estimated IRs can vary, depending on specifications. For this reason, we set q at 12 but r = 6, 12, or 18. $ ^{15} $

Table 2 presents VIRs under three specifications for r in (7) along with the results from local projections. Note that VIRs from the Romer and Romer's method are not very robust across specifications. But the table also shows substantial reductions in VIR in all specifications, reconfirming the robustness of our benchmark results. Also note that $ VIR_{2} $ in local projections is large relative to the standard approach. Hence, our local projections give us conservative estimates in evaluating the long-lasting effect of commodity price shocks on inflation.

### 3.3 Allowing for cross-country differences in IRs

#### 3.3.1 Economic factors affecting IRs

Equation (2) assumes that the IRs of the CPIs to a commodity price shock are the same across all countries. We relax this assumption and introduce economic factors that may affect IRs. Following the literature, we consider (a) whether the currency is pegged to the U.S. dollar, (b) the adoption of inflation targeting (IT), (c) the degree of economic development, and (d) the degree of trade openness. We then divide the sample countries into country groups to characterize IRs.

To this end, we augment (2) with interaction terms. Our estimation equation is

$$ p_{j,t+k}-p_{j,t-1}=\tilde{\alpha}_{j,k}+\sum_{i=1}^{q}\beta_{i,k}(p_{j,t-i}-p_{j,t-i-1})+\gamma_{j,k}u_{c,t}+u_{j,t+k}^{k}, $$

for $ k = 0, 1, \ldots, K $ . Here, $ \gamma_{j,k} $ is the IR for country j and is specified as

$$ I R(k,j)=\gamma_{j,k}=\gamma_{k}+\gamma_{U S D,k}D_{j}^{U S D}+\gamma_{I T,k}D_{j}^{I T}+\gamma_{L D C,k}D_{j}^{L D C}+\gamma_{T O,k}D_{j}^{T O}, $$

where $ D_{j}^{g} $ for g = USD, IT, LDC, TO denotes the dummy variable and its coefficient measures the difference across country groups g. The dummy variable takes one or zero under the following conditions. For g = USD, $ D_{j}^{USD} = 1 $ if country j pegs its currency to the U.S. dollar. Likewise, $ D_{j}^{IT} = 1 $ for IT countries, $ D_{j}^{LDC} = 1 $ if a country is grouped with the less developed countries.
(LDCs), and $ D_{j}^{TO}=1 $ if country j is categorized as a country with a high degree of trade openness. Note that, although we express these four dummy variables as being independent of t for notational simplicity, these new dummy variables are in practice time-dependent. $ ^{16} $ We also replace $ \alpha_{j,k} $ by $ \tilde{\alpha}_{j,k} $ defined by $ \tilde{\alpha}_{j,k}=\alpha_{j,k}+\alpha_{USD,k}D_{j}^{USD}+\alpha_{IT,k}D_{j}^{IT}+\alpha_{LDC,k}D_{j}^{LDC}+\alpha_{TO,k}D_{j}^{TO} $ to control for the direct effect of these dummy variables on inflation.

The interpretations of introducing the dummy variables are as follows:

Exchange rate flexibility De Gregorio, Landerretche, and Neilson (2007) and Rigobon (2010) find a stabilizing role of the exchange rate on consumer prices in response to commodity price shocks. Because commodity prices are denominated in U.S. dollars, the pass-through of commodity prices to the CPIs would be affected by variations in the flexible nominal exchange rate. If appreciations of a country’s currency take place with increases in commodity prices, ceteris paribus, the CPI’s response in this country would be smaller in response to a commodity price shock than in countries with currencies pegged to the U.S. dollar. If $ \gamma_{USD,k} > (<)0 $ , we interpret this to mean that the flexibility of the exchange rate vis-à-vis the U.S. is stabilizing (destabilizing) consumer prices.

Inflation targeting Monetary policy may play an important role in stabilizing inflation and inflation expectations in response to commodity price shocks. For example, Blanchard and Galí (2010) argue that an improvement in monetary policy has contributed to the decline in the oil price pass-through since the 1980s. Cross-country differences in monetary policies may also matter for price responses. If inflation expectations are well anchored by IT, IT may dampen price responses to commodity price shocks. $ ^{17} $ In this case, $ \gamma_{IT,k} $ would be estimated as negative.

The degree of economic development The literature on commodity price pass-through states that a higher oil intensity and/or higher share of food in the CPI basket would lead to a higher pass-through coefficient. $ ^{18} $ Unfortunately, if we use these data for regressions, a number of countries need to be dropped from the sample. In this regard, IMF (2008, 2011) notes that energy intensity and
food share of the CPI are substantially higher in LDCs than in DCs and finds that the pass-through of commodity price shocks to CPIs is negatively related to the degree of economic development. If $ D_{j}^{LDC} $ captures well the difference in the commodity share in the CPI, we expect that price responses to a commodity price shock would be larger in LDCs than in DCs.

The degree of trade openness Our regressions also take trade openness into account. Chen (2009) and Gelos and Ustyugova (2012) empirically discuss whether trade openness reduces the commodity price pass-through. Chen (2009) finds that the short-run oil price pass-through is lower in countries with a higher degree of trade openness and argues that increasing the flow of inexpensive imports may offset increases in oil prices. On the other hand, Gelos and Ustyugova (2012) find no negative relationship between trade openness and the commodity price pass-through. We could also argue that the CPI in countries which import more commodities is more affected by commodity prices. Likewise, increases in commodity prices may have more influence on the CPIs in countries that export more commodities. This is because the improved terms of trade generated by higher commodity prices may lead to higher incomes in countries and this in turn may boost aggregate demand, leading to an increase in consumer prices. Hence, while trade patterns may matter for price responses, the sign of $ \gamma_{TO,k} $ would be ambiguous.

Data availability While other economic factors may affect IRs, we limit our attention to the four factors described in the previous pages to avoid dropping a number of countries from the samples. For the exchange rate regime, we rely on the de facto classification constructed by Ilzetzki, Reinhart, and Rogoff (2010). $ ^{19} $ The use of these data drops 15 countries from the sample. $ ^{20} $ We choose IT countries based on the definition of Roger (2009) and Hammond (2012). For $ D_{j}^{LDC} $ , we define the low- and middle-income economies in the WB’s classification as LDCs. These data are missing only in Anguilla, so we dropped Anguilla. Finally, we construct $ D_{j}^{TO} $ from the World Development Indicators (WDIs) of the WB. We take the data of the sum of exports and imports divided by
GDP and split countries into country groups with a high or low degree of trade openness, based on the median of the data. $ ^{21} $ When incorporating trade openness data into the dataset, we drop eight countries from the sample. $ ^{22} $ After all, the process of constructing the panel data with these control variables reduces the number of countries to 120. See panel (e) of Table 1 for countries dropped from the sample.

#### 3.3.2 Results using the dummy variables

In this subsection, we discuss whether the effect of commodity price shocks remains transitory even after controlling for country-specific economic factors.

Before discussing the IRs, we mention how the IRs are related to economic factors. Table 3 reports coefficients on the four dummy variables for each forecast horizon k, along with the Newey-West standard errors below the estimates. First, as shown in panel (a) of the table, $ \hat{\gamma}_{USD,k} $ are all positive and statistically significant for $ k = 1, 2, ..., 14, 21, 23 $ , and 24 at the five percent significance level. This suggests a stabilizing role for the exchange rate, consistent with the literature. The stabilizing role is confirmed particularly in the first year after a commodity price shock.

Second, $ \hat{\gamma}_{IT,k} $ are shown in panel (b) of the same table and are negative for all forecast horizons. This suggests that IT may contribute to dampening price responses to a commodity price shock. However, they do not statistically differ from zero for all forecast horizons.

Third, $ \hat{\gamma}_{LDC,k} $ are overall positive and strengthen as k increases. Panel (c) indicates that some $ \hat{\gamma}_{LDC,k} $ statistically differ from zero when forecast horizons are relatively long (for k = 18, 19, and 21–24). This is consistent with the interpretation that price responses in LDCs tend to be large because the LDCs have high food shares in the CPI consumption basket.

Finally, as indicated in panel (d) of Table 3, we do not find a significantly negative relationship between price responses and the degree of trade openness. When $ \hat{\gamma}_{TO,k} $ is negative, it is neither statistically nor economically significant (see $ \hat{\gamma}_{TO,k} $ for k = 0, 1, and 2). This is consistent with Gelos and Ustyugova (2012), who do not find a statistically significant relationship between the
commodity price pass-through and the degree of trade openness.

We are now ready to discuss the IRs estimated from (8). We divide countries into four country groups, based on exchange rate regimes and the degree of economic development. Given that $ \hat{\gamma}_{j,k}^{IT} $ and $ \hat{\gamma}_{j,k}^{TO} $ do not statistically differ from zero for all k, we consider four country groups: (a) developed countries with flexible exchange rates (DCs with FER); (b) less developed countries with flexible exchange rates (LDCs with FER); (c) developed countries with exchange rates pegged to the U.S. dollar (DCs with USD); and (d) less developed countries with exchange rates pegged to the U.S. dollar (LDCs with USD).

Figure 3 plots the IRs of the CPIs for the above four country groups to a 10 percent increase in commodity price shocks. To represent the IRs for each country group, we take the weighted average of the IRs using the share of IT countries and the share of countries with a high degree of trade openness. For instance, the IRs for LDCs with USD are represented as $ \hat{\gamma}_{j,k} + \hat{\gamma}_{j,k}^{USD} + \omega_{IT} \hat{\gamma}_{j,k}^{IT} + \hat{\gamma}_{j,k}^{LDC} + \omega_{TO} \hat{\gamma}_{j,k}^{TO} $ , where $ \omega_{IT} $ (or $ \omega_{TO} $ ) denotes the share of IT countries (or countries with a high degree of trade openness) in all the sample countries. $ ^{23} $

Comparisons across the four panels reveal that, while the IR functions vary across the country groups, all panels of the figure overall suggest a transitory effect of commodity price shocks. Price increases in DCs with FER in panel (a) of Figure 3 are the smallest among the four country groups due to the stabilizing roles of the exchange rate and economic development. By contrast, the country group of LDCs with USD in panel (d) exhibits the largest price response in its peak response. The peak response in panel (d) is about twice as large as the peak response in panel (a). Nevertheless, the slopes of all IR functions are nearly flat during the second year after the shock, suggesting the low risk of a second-round effect.

### 3.4 Robustness of the transitory effect of commodity price shocks

This subsection performs the robustness analysis to changes in the commodity price indexes and the forecasting equation (4). Our comparisons rely on the VIR. The first row of panel (a) in Table 4 reports the VIRs computed from the average IRs across the four country groups. The resulting VIRs are comparable to the benchmark: $ VIR_{1} = 0.49 $ and $ VIR_{2} = 0.13 $ , respectively.
#### 3.4.1 Alternative commodity price indexes

Panel (a) of Table 4 shows the VIRs when we replace the commodity price shocks with those obtained from alternative commodity price shocks. The second row represents the VIRs based on the WB's energy indexes. Similar to the first row, the VIR reduces from 0.38 to 0.16, suggesting the transitory effect on inflation even in the energy price index. $ ^{24} $ Similar patterns are observed for the IMF's commodity price indexes.

#### 3.4.2 Specifications of forecasting equations

We next consider three alternative specifications for estimating commodity price shocks. First, we introduce the other countries' nominal exchange rates into (4). CRR argue that, in addition to the exchange rates in Australia, Canada, and New Zealand, those in Chile and South Africa have a good forecasting performance. We thus simply add these two countries' exchange rate growth to (4) and reestimate IRs. $ ^{25} $ As indicated in the first row of panel (b) of Table 4, the VIRs in this case are similar in magnitude to those in the first row of panel (a).

Second, we could improve forecasts of $ \pi_{c,t} $ by including the forward premium into (4). Let $ p_{c,t} $ and $ f_{t+1,t} $ be the spot price index of commodities and the one-month-ahead forward price index of the same commodities in period t, respectively. To construct the forward premium, $ p_{c,t} $ and $ f_{t+1,t} $ must be directly comparable in terms of weights of the basket. Unfortunately, however, $ f_{t+1,t} $ is not available for the WB's and the IMF's commodity price indexes. Hence, we rely on the S&P GSCI, where $ f_{t+1,t} $ is available. Given the forward premium calculated from the S&P GSCI and its forward price index, we reestimate the commodity price shock by

$$ \pi_{c,t}=a+b\pi_{c,t-1}+c_{AUS}\Delta s_{t-1}^{AUS}+c_{CAN}\Delta s_{t-1}^{CAN}+c_{NZ}\Delta s_{t-1}^{NZ}+d_{FP}(f_{t,t-1}-p_{c,t-1})+\varepsilon_{c,t}, $$

where $ \pi_{c,t} $ is redefined as the commodity price inflation based on the S&P GSCI and $ d_{FP} $ is the parameter estimated. The second row of panel (b) in Table 4 reports VIRs based on (10). Again,
the results remain essentially unaltered.

Finally, we depart from the forecasting equations of CRR. In the literature on oil price shocks, Kilian (2009) identifies the global demand shock specific to the crude oil market. He argues that the oil price increase after 2003 was driven mainly by the global demand shock. We take the oil demand shocks in Kilian (2009) from February 2001 to December 2007 and reestimate IRs. The VIRs are reported in the last row of panel (b) of Table 4 and can be compared with the case when the energy commodity price shocks are used in the regressions. $ VIR_{1} $ is low in the case of the oil demand shock, compared to $ VIR_{1} $ for the energy commodity price shocks generated from WB's energy price index and tje IMF's fuel price index. However, the magnitude of $ VIR_{2} $ is similar to the cases of CRR's forecasting equation, suggesting the robustness of the main results.

## 4 Evidence from the STAR model

So far, we have controlled for differences across country groups but not for cyclical factors. Recent theoretical and empirical studies on the exchange rate pass-through, however, demonstrate that the pass-through may depend on the state of the economy such as the inflation rate. For example, Taylor (2000) argues that inflation influences the pass-through or pricing power of firms since, as in the model of state-dependent pricing, inflation affects the frequency that firms re-optimize their prices. Empirically, Shintani, Terada-Hagiwara, and Yabu (2013) use a STAR model and find that the exchange rate pass-through depends on the past inflation rate in the U.S. economy.

In this section, we explore the possibility that IRs vary across the states of the economy. In particular, we use the logistic STAR model with the transition variable of each country's lagged inflation to see how IRs vary between high- and low-inflation regimes.

### 4.1 Estimation

We extend the linear model (8) to the STAR model discussed in Teräsvirta (1994). Let superscript L and H on $ \gamma_{j,k} $ and $ \beta_{i,k} $ be the coefficient on the low- and high-inflation regimes, respectively. Our
estimation equation is

$$ \begin{align*}p_{j,t+k}-p_{j,t-1}&=\tilde{\alpha}_{j,k}+F(z_{j,t-d})\left[\sum_{i=1}^{q}\beta_{i,k}^{L}(p_{j,t-i}-p_{j,t-i-1})+\gamma_{j,k}^{L} u_{c,t}\right]\\&+\left[1-F(z_{j,t-d})\right]\left[\sum_{i=1}^{q}\beta_{i,k}^{H}(p_{j,t-i}-p_{j,t-i-1})+\gamma_{j,k}^{H} u_{c,t}\right]+u_{j,t+k}^{k},\end{align*} $$

for each forecast horizon k. Here, $ F(z_{j,t-d}) $ is the transition function, and $ z_{j,t-d} $ is the transition variable where d denotes the delay parameter. The transition function is given by

$$ F(z_{j,t-d})=\frac{\exp(-\delta z_{j,t-d})}{1+\exp(-\delta z_{j,t-d})}, $$

which implies that, as $ z_{j,t-d} \to +\infty $ , $ F(z_{j,t-d}) \to 0 $ , meaning that the coefficients with superscript H dominate the dynamics of the dependent variable. By contrast, as $ z_{j,t-d} \to -\infty $ , $ F(z_{j,t-d}) \to 1 $ , implying that the coefficients with superscript L are dominating. Likewise, if $ \delta \to 0 $ , then $ F(z_{j,t-d}) $ converges to 1/2, which is effectively equivalent to the linear regressions (8), because parameters with superscript H and L can no longer be identified. For the transition variable $ z_{j,t-d} $ , we specify it as the standardized past inflation rate in country j:

$$ z_{j,t-d}=\frac{\pi_{j,t-d}-\bar{\pi}_{j}}{\hat{\sigma}_{j}}, $$

where $ \bar{\pi}_{j} $ and $ \hat{\sigma}_{j} $ are the time-series average and the time-series standard deviations of country j's inflation, respectively.

The IRs for each regime remain easy to compute: $ IR^{L}(k,j) = \gamma_{j,k}^{L} $ and $ IR^{H}(k,j) = \gamma_{j,k}^{H} $ . In general, the IR in country j can be represented by $ IR(k,j,t) = F(z_{j,t-d})\gamma_{j,k}^{L} + [1 - F(z_{j,t-d})]\gamma_{j,k}^{H} $ . In this specification, the past inflation rate affects the IRs to commodity price shocks, suggesting that inflation may affect firms' price setting as in the model of state-dependent pricing. Since an IR for each period and country is the weighted sum of $ IR^{L}(k,j) $ and $ IR^{H}(k,j) $ , we focus on $ IR^{L}(k,j) $ and $ IR^{H}(k,j) $ as extreme cases.

Our estimation strategy basically follows Auerbach and Gorodnichenko (2013), who investigate whether the fiscal multipliers depend on output growth, based on the multi-country panel data. Following them, we standardize the transition variable so that $ z_{j,t-d} $ has zero mean and a unit