Regression eqn in first differences. Converting fitted values back to levels

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I have a regression eqn, where all variables(dependent and explanatory) enter in first differences except one explanatory variable,

where I need to show the contribution of each explanatory variable to dependent variable in levels.

There is a solution to interpret the coefficients back in levels like this:

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here he assume y0=0 and x0=0.

If they are not zero, how this solution would change. Also if there is another explanatory variable

in levels, how would this change i.e assume my eqn is

y(t)-y(t-1)=a+b(x(t)-x(t-1))+c*z(t)+e(t)

Econometrics Matematyka Analiza Statystyczna Statystyka

Numer ID Projektu: #17636226

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