Annex: Methodological approach to panel estimations of exchange rate pass-through
The analysis uses panel data to assess whether exchange rate pass-through is dependent on the specific inflation environment in a given country; panel methods are used due to the small number of high-inflation observations in the 36 OECD countries in the reference period from 2000 to 2024. The analysis presented here focuses on the question of whether exchange rate pass-through is dependent on the prevailing inflation environment in a given country. Due to the fact that for many of the 36 OECD countries under review – especially the advanced economies in the OECD – there are comparatively few observations with high inflation rates during the reference period (January 2000 to June 2024), only panel data analysis methodologies are employed here. Using panel data generally improves the accuracy of the estimation compared with purely country-specific estimations, as this takes account of the variance in the data both over time as well as across the countries under review. In addition, by factoring in country-specific constants (fixed effects), it is possible to control for unobserved time-invariant heterogeneity between the countries, which would not be possible in the case of purely country-specific estimations. One disadvantage is that these panel estimations assume that the slope coefficients are homogenous, at least within each group of countries under analysis. 46
The estimations capture the average impact of exchange rate developments on consumer price inflation without differentiating between the causes of exchange rate movements. All of the estimations are based on single-equation models that do not differentiate between the sources of exchange rate movements. Compared with more complex models, single-equation models have the advantage that model variations, such as possible regime dependence – in this case, dependence of exchange rate pass-through on the inflation environment – can be easily integrated into the model with the results remaining intuitive to interpret. The literature shows that exchange rate pass-through can differ depending on the cause of a change in exchange rates. 47 However, reduced-form estimations also provide valuable insight, as they depict the average impact of exchange rate movements on consumer price inflation during the reference period, regardless of the source of the change in the exchange rate, which cannot always be determined definitively and directly.
The stability of exchange rate pass-through over time is assessed by estimating an empirical model on a rolling basis, i.e. repeatedly for overlapping three-year estimation windows that shift by one month each time. A common method for estimating exchange rate pass-through is the distributed lag (DL) model. The DL model allows the exchange rate to affect prices with a time lag as well. This model is sometimes applied to multiple countries at the same time (cross-section). In this case, it is referred to as a “panel DL model”. 48 This approach is also employed in this analysis. This model does not explicitly take account of the prevailing inflation environment in any given country.
$$ \begin{align} \Delta p_{i,t} &= \alpha_i+ \sum_{k=0}^{6} \beta_k\, \Delta neer_{i,t-k}+ \sum_{k=0}^{6} \phi_k\, \Delta p^*_{i,t-k} \\& + \sum_{k=0}^{6} \eta_k\, og_{i,t-k}+ \sum_{k=0}^{6} \theta_k\, \Delta oil_{t-k}+ \varepsilon_{i,t} \end{align} \tag{1} $$
The model explains domestic consumer price inflation based on nominal effective exchange rate changes, inflation in partner countries, the output gap, and crude oil prices, each including time-lagged effects. In the model, the dependent variable is the monthly rate of change in the consumer price index in country \( i \) \((\Delta p_{i,t}) \), the explanatory variables are the rate of change in the nominal effective exchange rate of country \( i \) \( (\Delta neer_{i,t}) \) as well as a number of control variables that potentially affect consumer prices in country\( i \) and that are possibly correlated with the exchange rate term. 49 These are the inflation rates in partner countries weighted by their shares of trade \( (\Delta p^*_{i,t}) \), the output gap in country \( i \) \((og_{i,t}) \) – i.e. the deviation of current output from potential output 50 – and the rate of change in global crude oil prices (\( \Delta oil_t \)). Alongside the contemporaneous values, lagged values of these three explanatory variables and the rate of change in the exchange rate are also included in the model. 51 In addition, the model contains country-specific fixed effects (\( \alpha_i \)).
The sum of the seven\( \beta_k \) coefficients for each three-year estimation window rises noticeably towards the end of the reference period, which is indicative of increasing exchange rate pass-through over time. The estimated \( \beta_k \) coefficients are of key importance for determining exchange rate pass-through. Their sum reflects the cumulative percentage effect that a present depreciation of the domestic currency by 1 % exerts on the consumer price index over a period from \( k=0 \) to \( K=6 \) months. In order to assess the stability of the correlation, the model is estimated for a panel of 36 OECD countries across overlapping three-year windows. Here, the estimation period is successively shifted along by one month and the model is re-estimated; this is repeated until the end of the reference period, which, in this case, is mid-2024. There is a clearly noticeable rise in the calculated pass-through effect towards the end of the reference period (see also Chart 2.1 in the main text). 52
Panel local projections are suitable for examining whether the strength of exchange rate pass-through is non-linearly dependent on the inflation environment. In order to examine whether exchange rate pass-through is dependent on the prevailing inflation environment in a given country, state-dependent panel local projections are used. 53 These enable the dynamic adjustment path of domestic consumer prices in relation to exchange rate changes to be estimated in a simple and robust way. Unlike the panel DL model used previously, panel local projections allow non-linear (i.e. regime-dependent) and other asymmetric effects to be integrated flexibly without the need to specify a fixed structure for their dynamics. 54 For this reason, all other estimations are based on this methodology.
The further analysis is based consistently on panel local projections, with the results that do not take account of the specific inflation environment in any given country serving as a reference point for findings that do take account of country-specific inflation environments. As a reference point for the state-dependent regression results, the regressions are first estimated in a state-independent way – i.e. without modelling the effect of country-specific inflation on pass-through – on the basis of panel local projections and an otherwise identical model specification. This ensures that any differences between the results of regime-dependent and regime-independent estimations are not attributable to the use of different methodological approaches, such as panel DL estimations and panel local projections. The state-independent model is specified as follows:
$$ \begin{align} p_{i,t+h} – p_{i,t-1} &= \alpha_{i,h} + \beta_{h} \Delta neer_{i,t} \\ &+ \sum_{j=0}^{J} \left( \delta_{j,h} og_{i,t-j} + \phi_{j,h} \Delta p^{*}_{i,t-j} + \zeta_{j,h} \Delta oil_{t-j} \right) \\ &+ \sum_{j=1}^{J} \left( \gamma_{j,h} \Delta neer_{i,t-j} + \phi_{j,h} \Delta p_{i,t-j} \right) + \varepsilon_{i,t+h} \end{align} \tag{2} $$
Using this model allows the dynamic response of domestic prices to changes in the exchange rate to be calculated in a simple and robust way over various projection periods, with each analysed projection period denoted in months by \( h+1 \) with \( h=\{0,...,H\} \). 55 In addition to the variables included in the previous model, lagged values of the domestic monthly inflation rate are also factored in here.
The panel local projections method estimates pass-through coefficients for each projection period. As separate panel regressions are estimated for each projection period, this approach also produces pass-through coefficients estimated directly for each projection period. 56 The dynamics of the effects are therefore not constrained in the estimation. All else being equal, the parameter \( \beta_h \) thus reflects the percentage effect of a 1 % depreciation in the nominal effective exchange rate on the domestic price level within \( h+1 \) months. The model is estimated for \( h=\{0,...,11\} \), meaning that it covers projection periods of up to one year. 57
The panel local projections model can be expanded to include an indicator variable, which enables pass-through coefficients to be estimated depending on a predefined state, which, in this case, is the inflation environment. The panel local projections model is expanded to include an interaction term between the rate of change in the exchange rate and an indicator variable \( I \). The latter takes a value of one when the annual rate of inflation, \( \pi \), in country \( i \) exceeds a threshold \( q_h \) in the previous month, with the threshold being determined in the model. If annual inflation is below the threshold, the indicator variable takes a value of zero (see Equation 3):
$$ \begin{align} p_{i,t+h} – p_{i,t-1} &= \alpha_{i,h} + \beta_{low,h} \Delta neer_{i,t} \\ &+ \beta_{\Delta high,h} I \left( \pi_{i,t-1} > q_h \right) \Delta neer_{i,t} \\ &+ \sum_{j=0}^{J} \left( \delta_{j,h} og_{i,t-j} + \phi_{j,h} \Delta p^{*}_{i,t-j} + \zeta_{j,h} \Delta oil_{t-j} \right) \\ &+ \sum_{j=1}^{J} \left( \gamma_{j,h} \Delta neer_{i,t-j} + \phi_{j,h} \Delta p_{i,t-j} \right) + \varepsilon_{i,t+h} \end{align} \tag{3} $$
where
$$ I(\pi_{i,t-1}>q_h)=\left\{\begin{array}{@{}l@{\quad}l@{}} 1 & \text{if } \pi_{i,t-1}>q_h,\\ 0 & \text{sonst} \end{array}\right. $$
For each projection period \( h+1 \), the expanded panel local projections model calculates a dedicated threshold value to differentiate between low-inflation and high-inflation regimes. In order to determine such threshold values for the lagged annual rates of inflation, a grid search is carried out for each projection period to calculate the threshold value that maximises the explanatory power of the model across both regimes. 58 Each of the calculated threshold values is then tested for significance. For the entire OECD panel, the threshold values for the inflation rate identified using this method all lie within a fairly narrow range of 3.1 % to 3.9 % and are statistically significant. For the sake of simplicity, it therefore seems reasonable to assume a uniform threshold value of 3 % for all of the projection periods under review instead of the individual endogenously calculated, optimal values. In Charts 2.2 to 2.4 as well as the underlying estimations, the value of 3 % thus always represents the threshold between low-inflation and high-inflation regimes. Subsequently, the dynamic response of prices to exchange rate changes is estimated for various panel compositions (all 36 OECD countries under consideration, OECD advanced economies, OECD emerging market economies, and OECD euro area member countries) conditional on the inflation environment. 59 The coefficients calculated through this approach are shown in Chart 2.3.