leads to a real depreciation, subsequently exacerbating inflation. In this scenario, fiscal policy, rather than monetary policy, becomes the appropriate instrument for curbing inflation.

Mojon and Peersman (2001) claim that the “exchange rate puzzle” may arise in monetary policy responses to foreign monetary policy, advocating for the inclusion of the foreign interest rate as a direct component of the vector of endogenous variables to capture the strong interconnection between domestic and foreign economies. According to this view, the domestic interest rate adjusts to changes in the foreign rate without directly impacting the exchange rate. Consequently, overlooking the foreign interest rate in the model can result in both price and exchange rate puzzles due to the failure to account for increases in the domestic interest rate in response to increases in the foreign rate.

# **AII.4. Indeterminacy: Violation of the Taylor principle**

There is a body of research suggesting that the price puzzle arises due to indeterminacy in monetary policies, specifically the violation of the Taylor principle, in the context of the United States. Woodford (2003) demonstrates that the solution of the system of equations (1)-(3) outlined in Section II is influenced by the level of systematic policy activism adopted by monetary authorities. Notably, the uniqueness of the solution depends on whether the "Taylor principle" is met—in this case ( ∅ >1). If the Taylor principle is satisfied, the dynamics of the economy rely solely on fundamentals, allowing the output, inflation, and interest rate equations to be written as a function of the structural shocks ( ε� ). Conversely, under indeterminacy, the transmission of structural shocks is altered, leading to the augmentation of the system with a latent variable not present in the unique rational expectations equilibrium. Additionally, sunspot shocks may impact expectations and consequently affect the equilibrium of the economic system.

Lubik and Schorfheide (2004) similarly illustrate that the evolution of endogenous variables can be characterized as a combination of structural shocks and a sunspot shock affecting the variables of interest in passive monetary policy scenarios. This sunspot shock may influence inflation expectations, thereby impacting current inflation. Auray and Feve (2008) demonstrate that the price puzzle can arise due to indeterminacy in a model without sticky prices, where monetary policy follows a money supply rule. Castelnuovo and Surico (2010) argue that the price puzzle may result from a spurious correlation induced by the omission of a variable capturing the persistence of expected inflation in VAR models, particularly under a passive monetary policy regime where the nominal interest rate is adjusted less than proportionally in response to inflation movements. They find that the omitted variable problem quantitatively explains the puzzling inflation response to policy shocks observed in data.<sup>42</sup> Outside the United States, Champagne and Sekkel (2018) employ narrative evidence alongside a unique database of real-time data and forecasts from the Bank of Canada's staff economic projections from 1974 to 2015. They show that failing to account for the shift in the conduct of monetary policy that occurred following the announcement of inflation targeting in 1991 resulted in a price puzzle in Canada.

> 42 Clarida et al (1999) also show that the coefficient was less than 1 in the pre-1980 subsample, which is consistent with the results of Castelnuovo and Surico (2010).

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