There are several reasons:
- Developing countries often pursue loose monetary policy (see Sargent and Wallace, 1981). This should not be surprising, poorer countries often do not large tax bases and borrowing is too expensive for them.
A government intertemporal budget constraint is given by:
$$ G= T + B + \theta$$
So government spending $G$ has to be financed either through taxes (minus interest payments $T$, issuing bonds $B$ or by creating more high powered money $\theta$.
In poor countries people are poor so there aren’t really large tax bases and investors are more hesitant to lend to poor countries that are less likely to pay the debt back.
However, poor countries do not face any constraints on how much high powered money they can create (unless they are part of monetary union, or dollarized). Inflation depends (among other factors) positively on money supply.
- Emerging markets are often export oriented and have higher chances of facing balance of payment crisis (Liviatan and Piterman 1986).
It is beneficial for exporting country to have weak currency so many exporting countries go out of their way (eg China) to try to make their currency cheaper vis-a-vis developed nations by central bank intervention in foreign exchange markets.
Often balance of payment crisis can also force depreciation on currency.