MONETARY POLICY REPORT | WINTER 2025 (appendix 1)
(authors: František Brázdik, Stanislav Tvrz)
One year on, we present here the next in a series of modifications and minor extensions of the g3+ core forecasting model[1] reflecting economic developments and experience with the use of g3+. The current extended version of g3+ has been used to prepare a shadow forecast, presented in this appendix. The shadow forecast is intended to introduce the extended version of g3+ and describe its benefits and specific features, not to capture specific risks of the baseline scenario of the Winter 2025 MPR. This extended model will be the CNB’s main forecasting tool starting with the Spring 2025 MPR.
Extension of the foreign block of the g3+ model to include US interest rates
The foreign block of g3+ mainly captures economic relationships within the effective euro area but now also includes a link between the euro area and Fed monetary policy. The main change in this block is that observed US interest rates have been added to the model (see Chart 1). The model now includes the three-month Secured Overnight Financing Rate (3M US SOFR), defined in roughly the same way as its European counterpart, the 3M EURIBOR. We consider the difference between these two rates to be the main fundamental explaining the evolution of the USD/EUR cross rate. It is also a determining element of the uncovered interest parity (UIP) equation in the foreign block. The part of the USD/EUR rate that cannot be explained by the interest rate differential is interpreted as a risk premium. This premium can be divided according to degree of persistence. For the USD/EUR rate, we interpret the persistent part of the dollar risk premium as a structural premium. This enters the domestic part of the g3+ model as one of the factors driving the CZK/EUR rate. According to empirical tests, the USD/EUR and CZK/EUR cross rates are correlated, even after adjusting for interest rate differentials. When the euro strengthens (weakens) against the dollar, the koruna tends to strengthen (weaken) against the euro, usually reflecting improving (worsening) sentiment in foreign exchange markets. This relationship is modelled in g3+ using the persistent part of the risk premium derived from the UIP condition in the foreign block of the model.
Chart 1 – Selected foreign variables
comparison of baseline scenario of forecast with shadow forecast produced by extended g3+ model
3M EURIBOR
%
3M US SOFR
%
USD/EUR exchange rate
USD/EUR
Interest rate differential
percentage points; differential between 3M rates in USD and EUR
Modification of the LIRE schemes
Following the structural changes made to the foreign block of g3+ a year ago, we have now modified the limited information rational expectations (LIRE) schemes[2] for foreign variables, which enter the model as external assumptions. Based on practical experience with the updated g3+ model over the past year, we have shortened the LIRE schemes from nine to seven quarters (see Table 1). Agents in the model thus now look only seven quarters into the future at any given moment in time and the outlook more than one year ahead is anticipated only partially. This modification primarily reflects the experience of the recent period of turbulence, which saw large shifts in external assumptions over the entire forecast horizon. Owing to the increased uncertainty in the economic environment, however, the true impacts of the changes in the outlooks for foreign variables tended to be smaller than the model predicted. Shortening the expectations schemes leads to a modest improvement in the model’s predictive power, i.e. a reduction in the mean forecast error on the historical data.
Table 1 – Comparison of LIRE schemes for the external outlook
(measure of anticipation in %)
| t+1 | t+2 | t+3 | t+4 | t+5 | t+6 | t+7 | t+8 | t+9 | |
| Original LIRE scheme | 100 | 100 | 100 | 100 | 100 | 80 | 60 | 40 | 20 |
| New (shortened) scheme | 100 | 100 | 100 | 100 | 75 | 50 | 25 | - | - |
Inclusion of the asymmetric impacts of the ECB’s unconventional monetary policy
The 3M EURIBOR shadow rate concept captures the effects of the ECB’s unconventional monetary policy in the foreign block of g3+, i.e. the increases and decreases in the ECB’s balance sheet due to asset purchases and sales. During the stepwise discontinuation of the ECB’s asset purchase programmes, an asymmetry can be seen between the effects of increases and decreases in the central bank’s balance sheet. In the present phase, therefore, the impacts of asset sales on interest rates are expected to be roughly half the magnitude of those observed when the assets were purchased. This asymmetry is taken into account in the shadow forecast via an updated estimate of the unconventional component of foreign monetary policy (the shadow rate), which is around 0.4 pp lower than in the baseline scenario.
Extension of the domestic block of the model to include interest rates with longer maturities
Another modification is that interest rates with maturities longer than three months have been added to the domestic block.[3] Specifically, the three-year Czech government bond yield was chosen (see Chart 2). This maturity broadly corresponds to the end of the CNB’s forecasting horizon and is much longer than the previously used three-month interest rate (3M PRIBOR).[4] This introduces into the model a two-point yield curve that has a moderately positive slope in the steady state. The longer interest rate is modelled as a partially endogenous variable that reflects the expected 3M PRIBOR, which, however, it can deviate from due to an exogenous time premium. The longer interest rate passes through to the other parts of the domestic block via effective interest rates for households and firms. Longer rates have low weight in households’ consumption decisions; short-term interest rates, from which rates on deposit accounts and short-term time deposits are derived, play a greater role. By contrast, rates with longer maturities have larger weight in investment decisions because of the multi-year planning horizons of firms (and households in the case of investment in housing).
Modelling of time-variable equilibrium values
Starting with the Summer 2024 MPR, the equilibrium rates of economic growth and appreciation of the koruna against the euro were both lowered in the steady state of the model. These are unobserved values describing economic equilibrium in the medium term. This modification was motivated by a gradual reassessment of the equilibrium growth rates in the Czech economy’s convergence process. Relationships for the “shallow” steady states of the macroeconomic variables concerned have therefore been added to the domestic block. Without these changes, the modifications to the equilibrium rates would have involved changes in the model’s view of the historical data. Introducing the shallow steady states as variables and not constants makes it possible to set the historical equilibrium rates differently from the current point steady state, which applies at present and enters the forecast. This addition to the model structure mitigates undesirable effects associated with changes in estimates of long-term economic relationships.
The shadow forecast produced by the extended g3+ model
The shadow forecast is based on the same assumptions and outlooks as the baseline scenario but additionally takes the 3M US SOFR and observed historical three-year Czech government bond yields into account. The assumed 3M EURIBOR shadow rate now reflects the asymmetric approach described above. The forecast produced by the extended g3+ model assesses the current phase of the economic cycle similarly to the baseline scenario and additionally provides a projection for interest rates with longer maturities.
The main change in the structure of the foreign block is the inclusion of the observed 3M US SOFR as the counterpart of the 3M EURIBOR in the USD/EUR exchange rate equation. The implied interest rate differential between dollar and euro rates therefore has a substantially different profile than in the baseline scenario. However, this profile fits the new structure of the foreign block better and thus leads to the identification of generally smaller foreign shocks in the shadow forecast. The higher observed 3M US SOFR (relative to the previously used equilibrium euro area interest rate) now endogenously induces higher ECB interest rates. Given their same outlook, this reduces the need for the identification of restrictive monetary policy shocks in the foreign block. The more accommodative assessment of ECB monetary policy by the updated model therefore affects the domestic economy, fostering a slightly stronger koruna.[5]
The shadow forecast’s view of the domestic economy and its outlook differs little from the baseline scenario. The most important change in the domestic part of the model is the addition of a longer rate (the three-year government bond yield), which is currently slightly below the 3M PRIBOR. Therefore, this change does not currently give rise to any major deviations from the baseline scenario. However, a difference is noticeable in the CZK/EUR rate path, which mostly reflects the changes in the foreign block of the model (primarily the interest rate differential). The koruna is thus roughly 20 hellers stronger at the outlook horizon than in the baseline scenario.
Chart 2 – Shadow forecast of the main domestic variables
comparison of baseline scenario of forecast with shadow forecast produced by extended g3+ model
GDP
y-o-y change in %
Inflation
y-o-y change in CPI in %
Interest rates
%
Nominal exchange rate
CZK/EUR
[1] The extended g3+ core forecasting model was unveiled in an attachment to Inflation Report III/2019. The main features of the model are described in F. Brázdik, T. Hlédik, Z. Humplová, I. Martonosi, K. Musil, J. Ryšánek, T. Šestořád, J. Tonner, S. Tvrz, J. Žáček: The g3+ model: an upgrade of the Czech National Bank’s core forecasting framework, CNB WP 7/2020. The modelling framework for the CNB’s forecasts is described in detail in CNB’s Forecasting and Policy Analyses System: Forecasting Tools in the context of an external review of the CNB’s monetary policy analytical and modelling framework. The previous g3+ update was presented in an appendix to the Winter 2024 Monetary Policy Report.
[2] The properties of the LIRE concept are described in K. Musil, S. Tvrz, J. Vlček: News versus surprise in structural forecasting models: Central bankers’ practical perspective, CNB Research and Policy Notes 2/2021.
[3] The extension of the core forecasting model to include rates with longer maturities builds on the findings and conclusions in F. Brázdik, K. Musil, S. Tvrz: Implementing yield curve control measures into the CNB core forecasting model, CNB WP 8/2023.
[4] Much longer maturities, for example the ten-year government bond yield, were also considered for use as the representative long-term rate. With increasing maturity, however, the relationship between such a long interest rate and the CNB’s policy rates gets looser, because long-term rates tend to reflect the global monetary policy stance and outlook. Although these rates are economically significant (for example, mortgage rates are tied to 5–10-year rates), they play only a minor role in terms of monetary policy.
[5] The effects of introducing US interest rates into g3+ on the forecast for the domestic economy thus cannot be treated as an independent impulse response to a shock to US interest rates. This is because the outlooks for effective euro area variables are the same in the shadow forecast and the baseline scenario only with the addition of US rates to the information set. The change in the structure of the model in the foreign block implies a generally different combination of all foreign shocks explaining both the history to date and the outlook for foreign variables.