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Postby tom_1993_ » Sun May 27, 2018 8:18 am

Assume I want to regress the labor tax rate on the inherited public net debt-to-GDP ratio (i.e. the public net debt-to-GDP of last year) and total government spending (in % of GDP) of country X.

Put another way
LAB_t = β_0 + β_1*GOVSPEND_GDP_t + β_2*INHDEBT_GDP_t + ε_t

INHDEBT_GDP_t is assumed to be exogenous.
However, government spending is clearly endogenous: revenues influence spending and vice versa. To address tis endogeneity problem, I need to find an instrument that is highly correlated with government spending, but not directly affected by the labor tax rate. One possible instrument for the government expenditures (in % of GDP) is the old-age dependency rate. It is quite high correlated with government spending (61%) and is rather exogenous.

To address the endogeneity problem, I need to use the 2SLS-estimation procedure.

Stage 1) GOVSPEND_GDP_t = δ_0 + δ_1*INHDEBT_GDP_t + δ_2*OLD_DEPENDENCY_t + μ_t

Stage 2) LAB_t = β_0 + β_1*((GOVSPEND_GDP_t )^ + (μ_t )^) + β_2*INHDEBT_GDP_t + ε_t
LAB_t = β_0 + β_1*(GOVSPEND_GDP_t)^ + β_2*INHDEBT_GDP_t + ε_t^*
with ε_t^* = ε_t + β_1*(μ_t)^

EViews estimates both stages simultaneously using instrumental variables techniques.
In "Equation specification" I give as input: lab c inhdebt_gdp govspend_gdp
In the "Instrument list" I give as input: inhdebt_gdp old_dependency (include a constant)

When running this regression I have a R² of -1.663298 and adjusted R² of -1.815487, meaning the model is worse than drawing a horizontal line (right?).

When I try other instruments (e.g. total population and real GDP per capita) for government spending, the fit becomes better. However, each of the two instruments is weakly correlated with government spending (each has a correlation of barely 30%).

Using total population and real GDP per capita as instruments, the R² becomes 0.200782 and the adjusted R² increases to 0.155112. How is it possible that the fit is better despite the fact that the instruments are weaker?

When I use them seperately (only total population or only real GDP per capita) the (adjusted) R² is again negative.

When I use all 3 instruments (old dependency rate, population and real GDP per capita) the fit is again worse: R² of -0.146550 and adjusted R² of -0.212067.

How is it possible that the weakest instruments (being real GDP per capita and population) generate the best results?

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