Fatema Matefa, you have indeed a longitudinal (panel) data by construction: a 2 x 18 panel to be precise. Having only two countries, however, makes the econometric estimation fairly easy as you can "pool" your data and then e.g. run a time series regression using "country" a as control covariate, and hence there is no need to rely on panel-data estimations methods. However, I am not aware of your problem at hand and I am just anticipating that with 18 years of data and 2 countries a time-series approach is more appropriate than a panel-data approach.

Panel data are absolutely not adequate for your data. In panel data, you have between countries variations and within (time) variation. With only two countries there will not be enough between variation, so you cannot use random-effects models. Accordingly, you are obliged to use fixed-effects models. In this case, you might use countries as dummy variables (LSDV models) which is a simple OLS regression with dummies for countries. Even in this case, with too few observations (18 periods) your estimates will not be reliable. Try to use other techniques that also require more data than you have or better, try to expand your data for more countries and a longer time period.

I agree with previous comments that your data is limited for panel regression

I agree with what other scholars have recommended. The problem is 2 folds. An n of 18 observations for each county with only 2 countries. So too few n's and only 2 countries, not enough for a panel. Drop the panel idea and go with the dummy variable suggestion. Even then, could you expand n, otherwise you run into small sample size-related problems?

Fatema Matefa , complementing other answers, that seem to worry about the small sample equal to T = 18 years, the T = 18 is not a problem if you decide to apply Bayesian methods. Bayesian methods do not rely on asymptotics of large-samples as traditional (frequentist) methods do.

Fatema Matefa , to my best of knowledge, there are no rules regarding the size a cross-sectional part of panel data should be or attain.

I would say, the most important thing to do is to ensure your data satisfy the available assumptions underlying all the various models (Random, Fixed, or Ordinary Least Square), and even beyond are other diagnostic tests to run in order to make a choice.

Even with time series for more than two countries, I would first do separate time series regressions for every country (for many countries, I recommend to do that for some - say 10 - of them), because a comparison of the estimated coefficients contain considerable information concerning the model specification. If coefficients are quite different, one would have to think over, why this is the case. In a pooled estimation, this information is likely to be hidden. For annual data, 18 seem sufficient, unless your model specification is too complex (i.e. many explaining variables, lags, transformations etc.), which reduces the degrees of freedom.