<blockquote>
<p>How is it possible for a country to have both deflation and a weak currency?</p>
</blockquote>
<p>It is possible because strength of a currency is relative to other countries whereas deflation is not.</p>
<ul>
<li><p>Deflation is negative change in price level. If price level index in China  was 150 in 2023 and now it's 120, country experienced deflation.</p>
</li>
<li><p>When people talk about how strong currency is it is almost exclusively in relation to other currencies. That is usually people call currency strong(er) when it is worth more than some other currency. For example, if 1 USD exchanges for 2 GBP then USD would be the strong currency and GBP the weak currency.</p>
</li>
</ul>
<p>As a result country can both experience deflation and have weak currency. Under law of one price the exchange rate (S) between two countries US and UK would be given as:</p>
<p><span class="math-container">$$S_{USD/GBP} = \frac{P_{USD}}{P_{GBP}}$$</span></p>
<p>where <span class="math-container">$P_{USD}$</span> is price level in USA and <span class="math-container">$P_{GBP}$</span> price level in UK. Suppose the price level in US is 100 and in UK it was 200 then the exchange rate under the law of one price would be 1USD = 2GBP. Hence US currency would be strong and UK currency weak.</p>
<p>Now suppose that UK had deflation and its price level was reduced to 150. Now the exchange rate would be 1USD = 1.5GBP. UK had deflation, yet its currency is still the weaker currency. Hence both of these are possible at the same time.</p>
<p>Moreover, this was just simple example assuming law of one price holds. In real life exchange rate depends on various other factors such as interest rates, economic performance, expectations etc.</p>
<p>For example, in the flexible price monetary model of exchange rates the exchange rate is given as:</p>
<p><span class="math-container">$$S = \alpha_0(m_{US}-m_{UK})  + \alpha_1 (y_{US}- y_{UK}) + \alpha_2 (E[\delta p_{US}] - E[\delta p_{UK}) + \alpha_3(i_{US} - i_{UK})$$</span></p>
<p>where <span class="math-container">$m$</span> is money supply, <span class="math-container">$y$</span> real output, <span class="math-container">$\delta p$</span> inflation or deflation (if negative) and <span class="math-container">$i$</span> interest rate.</p>
<p>In this model even if there is deflation in UK (<span class="math-container">$\delta p_{UK} &lt;0$</span>), GBP can get even more weaker if in US economic performance gets stronger. More complex models will include more important factors still. Point of showing this model is that currency can depreciate even if country experiences deflation.</p>
<blockquote>
<p>Also, why don't people arbitrage this away?</p>
</blockquote>
<ol>
<li><p>From your premises its not clear that there is any arbitrage opportunity. As shown in the previous section, currency can be weak while there is deflation. Exchange rate would still adjust to prevent arbitrage as explained previously.</p>
</li>
<li><p>It is possible that there is real life arbitrage opportunity. Real life arbitrage opportunities occasionally exist because markets are not adjusting instantaneously (e.g. see discussion in Mark (2001) International Macroeconomics and Finance: Theory and Econometric Methods).</p>
<p>However, no information in your question implies there is an arbitrage opportunity. The phenomenon you describe can occur even when there is no arbitrage as discussed above.</p>
</li>
</ol>

CC BY-SA 4.0
2024-05-16T00:00:57.127Z
"Now the exchange rate would be 1USD = 1.5GBP. UK had deflation, yet its currency is still the weaker currency." But in this example, GBP did gain against USD. Meanwhile, in 2024, the Chinese yuan is weakening. So the law of one price is not holding right now, it seems?
Betterthan Kwora
CC BY-SA 4.0
2024-05-16T00:15:59.240Z
@BetterthanKwora that could be explained by the more complex monetary model explained afterwards. Also IRL law of one price indeed does not hold because of transportation costs, but it can be thought of as crude approximation.
1muflon1
CC BY-SA 4.0
2024-05-15T08:42:40.943Z
2024-05-15T08:42:40.943Z
1muflon1
<p>As of early 2024, China has lower inflation than America, if not deflation. But the Chinese yuan is also weak right now, requiring Chinese central bank intervention in favor of the yuan to maintain its US dollar peg. Normally, I think of inflation and weak currency as going together. This is most apparent during hyperinflation scenarios, where Weimar Germany and Zimbabwe also had weak currencies relative to the rest of the world, but can also be observed in the case of &quot;regular&quot; inflation scenarios, such as Turkey and Argentina. How is the opposite possible in China right now?</p>
<p>Also, why don't people arbitrage this away? Presumably, the cost of a widget in Beijing just went down, as measured in yuan. And, relative to the US dollar, it went down even further due to the currency shift. Why don't people just ship widgets to America, until the rising Chinese widget price leads to Chinese inflation?</p>

CC BY-SA 4.0
2024-05-15T02:31:38.457Z
Where is the arbitrage in your example. Shipping something isn't risk free. Also, there are hundreds of thousands of products. Many not even tradable at all (haircuts, restaurants, ...). The Yuan isn't even traded freely and there exists an onshore and offshore marker. You are also nowhere near hyper inflation, so these examples don't apply. You can find lots of FX rate determination theory in [this answer](https://quant.stackexchange.com/a/67940/54838).
AKdemy
CC BY-SA 4.0
2024-05-16T00:03:31.640Z
I was speaking of the arbitrage opportunities that arise when the law of one price does not hold. But I suppose China's capital control system makes it hard to take advantage of this.
Betterthan Kwora
<inflation><currency><currency-exchange>
How is it possible for a country to have both deflation and a weak currency?
Betterthan Kwora
# How is it possible for a country to have both deflation and a weak currency?

(Asked by: username_0 on 2024-05-15)

As of early 2024, China has lower inflation than America, if not deflation. But the Chinese yuan is also weak right now, requiring Chinese central bank intervention in favor of the yuan to maintain its US dollar peg. Normally, I think of inflation and weak currency as going together. This is most apparent during hyperinflation scenarios, where Weimar Germany and Zimbabwe also had weak currencies relative to the rest of the world, but can also be observed in the case of "regular" inflation scenarios, such as Turkey and Argentina. How is the opposite possible in China right now?

Also, why don't people arbitrage this away? Presumably, the cost of a widget in Beijing just went down, as measured in yuan. And, relative to the US dollar, it went down even further due to the currency shift. Why don't people just ship widgets to America, until the rising Chinese widget price leads to Chinese inflation?

**Tags:** inflation, currency, currency-exchange
> **Comments:**
> **username_1**: Where is the arbitrage in your example. Shipping something isn't risk free. Also, there are hundreds of thousands of products. Many not even tradable at all (haircuts, restaurants, ...). The Yuan isn't even traded freely and there exists an onshore and offshore marker. You are also nowhere near hyper inflation, so these examples don't apply. You can find lots of FX rate determination theory in [this answer](https://quant.stackexchange.com/a/67940/54838).  
> **username_0**: I was speaking of the arbitrage opportunities that arise when the law of one price does not hold. But I suppose China's capital control system makes it hard to take advantage of this.  

---

## 1 answers

### Answer by username_2 on 2024-05-15. Score: 1 | Accepted answer

> How is it possible for a country to have both deflation and a weak currency?

It is possible because strength of a currency is relative to other countries whereas deflation is not.

* Deflation is negative change in price level. If price level index in China was 150 in 2023 and now it's 120, country experienced deflation.
* When people talk about how strong currency is it is almost exclusively in relation to other currencies. That is usually people call currency strong(er) when it is worth more than some other currency. For example, if 1 USD exchanges for 2 GBP then USD would be the strong currency and GBP the weak currency.

As a result country can both experience deflation and have weak currency. Under law of one price the exchange rate (S) between two countries US and UK would be given as:

$$S\_{USD/GBP} = \frac{P\_{USD}}{P\_{GBP}}$$

where $P\_{USD}$ is price level in USA and $P\_{GBP}$ price level in UK. Suppose the price level in US is 100 and in UK it was 200 then the exchange rate under the law of one price would be 1USD = 2GBP. Hence US currency would be strong and UK currency weak.

Now suppose that UK had deflation and its price level was reduced to 150. Now the exchange rate would be 1USD = 1.5GBP. UK had deflation, yet its currency is still the weaker currency. Hence both of these are possible at the same time.

Moreover, this was just simple example assuming law of one price holds. In real life exchange rate depends on various other factors such as interest rates, economic performance, expectations etc.

For example, in the flexible price monetary model of exchange rates the exchange rate is given as:

$$S = \alpha\_0(m\_{US}-m\_{UK}) + \alpha\_1 (y\_{US}- y\_{UK}) + \alpha\_2 (E[\delta p\_{US}] - E[\delta p\_{UK}) + \alpha\_3(i\_{US} - i\_{UK})$$

where $m$ is money supply, $y$ real output, $\delta p$ inflation or deflation (if negative) and $i$ interest rate.

In this model even if there is deflation in UK ($\delta p\_{UK} <0$), GBP can get even more weaker if in US economic performance gets stronger. More complex models will include more important factors still. Point of showing this model is that currency can depreciate even if country experiences deflation.

> Also, why don't people arbitrage this away?

1. From your premises its not clear that there is any arbitrage opportunity. As shown in the previous section, currency can be weak while there is deflation. Exchange rate would still adjust to prevent arbitrage as explained previously.
2. It is possible that there is real life arbitrage opportunity. Real life arbitrage opportunities occasionally exist because markets are not adjusting instantaneously (e.g. see discussion in Mark (2001) International Macroeconomics and Finance: Theory and Econometric Methods).

   However, no information in your question implies there is an arbitrage opportunity. The phenomenon you describe can occur even when there is no arbitrage as discussed above.

> **Comments:**
> **username_0**: "Now the exchange rate would be 1USD = 1.5GBP. UK had deflation, yet its currency is still the weaker currency." But in this example, GBP did gain against USD. Meanwhile, in 2024, the Chinese yuan is weakening. So the law of one price is not holding right now, it seems?  
> **username_2**: @BetterthanKwora that could be explained by the more complex monetary model explained afterwards. Also IRL law of one price indeed does not hold because of transportation costs, but it can be thought of as crude approximation.  

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