lagged variables as instruments and interaction terms

[farbrorlumpen]

Im working on my bachelor-thesis and the topic is the political business cycle over a sample of data in sweden from 1982 up to 2019, so covering 11 elections. In the spirit of primarliy Schultz(1995) but also Alessina etc I have devised two hypotheses I want to test in Eviews and they are as follows:

H1: When the incumbent government is rightwing and trails low in the polls before an election it lowers taxes to sway voters.
H2: When the incumbent government is leftwing and trails low in the polls before an election it increases transfers to sway voters.

Now to answer these hypotheses I have made two regressions for table01 is
TRANS= (transfers to households) in procentual change annualized
BNP1= (gdp) in procentual change annualized
NX = (net exports) in procentual change annualized
OFN = (Public expd) in procentual change annualized
Un= (unemployment) in procentual change annualized
Disp= (disposable income of households) in procentual change annualized
The transformations to procentual change is to render the series stationary.

Soss = dummie for a leftwing government
fval = the quarter when the government presents its budget for the year with an election.
ledningpart= the standing of the incumbent party compared to its result in the most recent election

At first I thought of including a lagged depended variable so trans(-1), this however lead to serious autocorrelation as shown by the LM test, and I gave up on that idea. Now its pretty apparent to me that i have simultaneity as both NX and OFn are part of the gdp identity, same for the rest of the variables. Now what my supervisor suggested was to lag all independent variables at some appropriate lag length. Now the problem here is that using lagged values as instruments is not really supported in the literature and as it stands I have not really found any solid support for this circumnavigate any endogenity problems. So how do I handle this given that im limited to using least squares in eviews?

Secondly I have alot of interaction terms meaning collinearity problems. However the recommendation from the literature here is to include cross terms of all these variables and all the sources point out that collinerarity is to be expected. So what is the recommendation do I keep them in? If so is there any output of conditional varaiances or standard errors reported in eviews? As I need to calculate the estimated standard erros for different values of my interaction terms to do any meaningfull inference?