A general and simple way to compare two 2D curve is to see if the corresponding responses are available. Then, according to the correlation coefficient equation, you can use my MATLAB code as below:

close all

clear

clc

%% Input Vectors

% y1=[]; % Manually

% y2=[];

arr = xlsread('Data1.xlsx','Sheet1', 'A:B'); % Excel Data Sheet

y1=arr(:,1);

y2=arr(:,2);

a=size(y1);

mean=mean(y1);

for i=1:a(1)

A(i)=(y1(i,:)-y2(i,:))^2;

B(i)=(y1(i,:)-mean)^2;

end

R=1-sum(A)/sum(B)

In case you do not have the corresponding responses. You can do a regression with an acceptable correlation coefficient for one of the curve and get the responses corresponding to the second curve. Then follow the procedure described above. The final correlation coefficient is equal to

R final=R regression*R MATLAB

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You can do a panel data model using time as a deterministic trend and interact it with country dummies. Then, you can do a test of joint significance for all the coefficients that represent the differences in slope between countries. Notice, that if you include fixed effects they will wipe out the individual invariant variables. Be aware of possible auto correlation in the error term and other issued that you need to address in order to have a valid statistical test.