Regressions using panel data, is there a way to account for countries that have opposite reactions towards a change in the same explanatory variable?

Question

For example, if the United States savings ratio is increased with a decline in interest rate, but Canada's savings ratio decreases with a decline in interest rate (savings rates and interest rates are time series data), is there some econometric model that can tell me this even when using panel data? Or am I better off doing two normal OLS-regressions, one for each country?

Answer 1

You could interact the country dummies with your interest rate variable if your panel is long enough.

Remember: the least square dummy variable estimator is equivalent to the fixed-effects approach (e.g. here)

$\text{Saving Ratio}_{it} = \beta_0 + \delta_1 \text{USA}_i + \psi_1 \text{USA}_i \times \text{Interest Rate}_{it} + \delta_2 \text{Canada}_i + \psi_2 \text{Canada}_i \times \text{Interest Rate}_{it} + \gamma \cdot X_{it} + ... + \epsilon_{it}$

This gives you the average country-specific reaction of saving rates to changes in interest rates (if you are willing to adopt a causal interpretation). You can look at the distribution of the interaction between the country dummies and the interest rate variable ($\psi_1,\psi_2,...$) to see how many countries show a positive, zero or negative reaction.