[Joro Kolev]

You write the constraint so that you express on of the parameters in terms of the others: b1=b3+b4 - b2, then you substitute in the original regression to reparametrise:
y=b0+b1*x1+b2*x2+b3*x3+b4*x4 =
b0+(b3+b4 - b2)*x1+b2*x2+b3*x3+b4*x4=
b0+b3*(x1+x3)+b4(x1+x4)+b2*(x2 - x1)
you construct manually z1 = (x1+x3), z1 = (x1+x4), and z3=(x2 - x1)

and you estimate

y = b0+b3*(z1)+b4(z2)+b2*(z3), either using -newey- or -ivregress-. This is your restricted regression.

y=b0+b1*x1+b2*x2+b3*x3+b4*x4, with the restriction b1+b2=b3+b4.

Could it be done in Stata?

[Petar Soric]

You write the constraint so that you express on of the parameters in terms of the others: b1=b3+b4 - b2, then you substitute in the original regression to reparametrise:
y=b0+b1*x1+b2*x2+b3*x3+b4*x4 =
b0+(b3+b4 - b2)*x1+b2*x2+b3*x3+b4*x4=
b0+b3*(x1+x3)+b4(x1+x4)+b2*(x2 - x1)
you construct manually z1 = (x1+x3), z1 = (x1+x4), and z3=(x2 - x1)

and you estimate

y = b0+b3*(z1)+b4(z2)+b2*(z3), either using -newey- or -ivregress-. This is your restricted regression.

Great advice, thanks a lot. It works!