I understand that inflation has an impact on the foreign direct investment. But can the opposite be true? The amount of foreign direct investment has an impact on the inflation of the country that receives the investment?
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Yes, FDI and Inflation are correlated.
Think of it this way, if foreigners buy assets, that reduces the supply available for domestic consumption, driving up prices, and if they buy them from citizens, it increases the domestic supply of money.
That being said, the relationship can be complicated because if there's substantial trade of real assets between foreigners, the effect might not trickle down to the domestic populace.
Alice and Bob are citizens of Country X. Charles is a citizen of Country Y. At equilibrium, sans FDI, Alice and Bob price the only pineapple at \$3. If Charles buys that pineapple for \$4 from either of them (assuming symmetric preferences for A & B), he has injected \$1 into the economy of Country X and removed 1 pineapple, consequently the supply of money has increased relative to the supply of assets, and prices should increase.
If Charles had left the pineapple in Country X, and David, a citizen of Country Z then bought it from him for \$5, and Charles did not invest any of that profit into Country X, the supply of capital in X would not be increased by this transaction, nor would the supply of assets, consequently the ratio of money to goods hasn't changed, and country-wide price levels shouldn't fluctuate.
Assuming there was a second pineapple that Alice or Bob held, they could then borrow against it at a higher value (given the new equilibrium price and FMV), leaving more money in the economy and consequently increasing the price of sponges for Bob as the ratio of assets to money would have changed in situ.
Note: This is an off the cuff explanation, not a formal model