# Effect of positive inflation shock on the exchange rate

How does a positive inflation shock affect the exchange rate? Does the exchange rate appreciate or depreciate? I am looking for an intuitive explanation.

Before intuition. let's determine the outcome. By the Uncovered Interest Rate Parity

$$i_t = i^*_t - [s^e_{t+1 | t} - s_t] \tag{1}$$

where $i_t$ is domestic nominal interest rate, $i^*_t$ is "foreign" nominal interest rate, and $[s^e_{t+1} - s_t]$ is expected appreciation of domestic currency in percentage terms ($s$ is the natural logarithm of "foreign currency per unit of domestic currency" exchange rate).

The "Fisher equation" for the relation between real and nominal interest rate in expected inflation is

$$i_t = r_t + \pi^e_{t+1|t} \tag{2}$$

where $r_t$ is domestic real interest rate, and $\pi^e_{t+1}$ is expected domestic inflation. Putting $(1)$ and $(2)$ side-by side we have

$$r_t + \pi^e_{t+1|t} = i^*_t - [s^e_{t+1|t} - s_t]$$

Assuming that there are no real effects by an inflation shock, and that the international economy couldn't care less (so also $i^*_t$ remains unaffected), using the change operator we have

$$\Delta \pi^e_{t+1|t} = \Delta (s_t-s^e_{t+1|t}) \tag{3}$$

where now the right-hand side represents "change in expected depreciation" of the domestic currency (note that the right hand side may be algebraically negative in which case it is "negative depreciation" = appreciation).

Now, it is reasonable to argue that expectations for tomorrow will take into account what happens today. Moreover, usually current inflation shocks either affect in the same direction expectations about future inflation, or not at all.

So an inflation shock happens in period $t$ which increases the left-hand side of $(3)$. Then so must also increase its right-hand: a domestic positive inflation shock increases expected depreciation of the domestic currency. In other words it creates expectation of currency devaluation. The currency may still be expected to appreciate, but less than before the inflation shock.

Mathematically this can come about in different ways but realistically one should expect that what will happen is that $s^e_{t+1|t}$ will go down, i.e. that the domestic currency will be expected to devalue.

The main intuition behind this comes if one realizes that, for the people abroad, domestic currency is just another product, that has a price. If due to inflation this "product" is worth less (because now it can buy less of utility-enhancing or productive goods), this should be reflected in its price, which is the domestic exchange rate $s$ (price of domestic currency measured in units of foreign currency), which should get lower.

This is the rationale also behind the closely linked "purchasing power parity". Of course, this is a highly stylized analysis and all sorts of real-world imperfections and rigidities will affect what will actually happen. But the tendency is the one described above.