<p>Transformed coefficients of a vector autoregressive model (VAR) with up to p lags or VAR(p) yield impulse responses that can be used to produce forecast error variance decompositions, or spillovers, in the framework of Diebold and Yilmaz's (DY) 2012 paper &quot;<a href="https://doi.org/10.1016/j.ijforecast.2011.02.006" rel="nofollow noreferrer">Better to Give than to Receive</a>&quot;.</p>
<p>In his paper entitled &quot;<a href="https://doi.org/10.1016/j.intfin.2021.101287" rel="nofollow noreferrer">Causal and Frequency Analyses of Purchasing Power Parity</a>&quot;, Nagayasu uses DY spillovers to test the hypothesis of causality between exchange rates and inflation rates.</p>
<p>To that end, Nagayasu first fits a stationary bivariate VAR(p), which is composed of two endogenous variables: a first-differenced logged spot exchange rate (Eq. 1), and the corresponding first-differenced logged inflation differential between the two countries (Eq. 2), in both cases dependent on their respective past values and the past values of the other endogenous variable, up to p lags. Second, spillovers or causal linkages between relative inflation and exchange rates are calculated using generalized impulse response functions to avoid identification problems.</p>
<p>Now imagine you want to interpret the DY spillovers calculated the way described above as a test of relative purchasing power parity. For relative purchasing power parity to hold, relative inflation between two countries should be proportional to shifts in the spot exchange rate, and vice versa, with the constant of proportionality ideally equal to one. Is it possible to prove, from those DY spillovers alone, that relative purchasing power parity holds? If so, how?</p>

CC BY-SA 4.0
2024-03-12T10:04:29.223Z
Judging by the edits, it seems to me that spelling out the details has helped you improve your understanding of the matter (and that is common.) Perhaps you will soon be able to answer your own question.
Richard Hardy
CC BY-SA 4.0
2024-03-12T10:27:02.230Z
I do hope you are right. Any help is still appreciated though. :)
Pavel Filip
<inflation><exchange-rates><var>
Spillovers as test of purchasing power parity
Pavel Filip
# Spillovers as test of purchasing power parity

(Asked by: username_0 on 2024-03-12)

Transformed coefficients of a vector autoregressive model (VAR) with up to p lags or VAR(p) yield impulse responses that can be used to produce forecast error variance decompositions, or spillovers, in the framework of Diebold and Yilmaz's (DY) 2012 paper "[Better to Give than to Receive](https://doi.org/10.1016/j.ijforecast.2011.02.006)".

In his paper entitled "[Causal and Frequency Analyses of Purchasing Power Parity](https://doi.org/10.1016/j.intfin.2021.101287)", Nagayasu uses DY spillovers to test the hypothesis of causality between exchange rates and inflation rates.

To that end, Nagayasu first fits a stationary bivariate VAR(p), which is composed of two endogenous variables: a first-differenced logged spot exchange rate (Eq. 1), and the corresponding first-differenced logged inflation differential between the two countries (Eq. 2), in both cases dependent on their respective past values and the past values of the other endogenous variable, up to p lags. Second, spillovers or causal linkages between relative inflation and exchange rates are calculated using generalized impulse response functions to avoid identification problems.

Now imagine you want to interpret the DY spillovers calculated the way described above as a test of relative purchasing power parity. For relative purchasing power parity to hold, relative inflation between two countries should be proportional to shifts in the spot exchange rate, and vice versa, with the constant of proportionality ideally equal to one. Is it possible to prove, from those DY spillovers alone, that relative purchasing power parity holds? If so, how?

**Tags:** inflation, exchange-rates, var
> **Comments:**
> **username_1**: Judging by the edits, it seems to me that spelling out the details has helped you improve your understanding of the matter (and that is common.) Perhaps you will soon be able to answer your own question.  
> **username_0**: I do hope you are right. Any help is still appreciated though. :)  

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## 0 answers

