I have a question regarding an econometric procedure I would like to apply in order to test if the relationship between economic growth and public debt ratio is nonlinear.
By means of the Hansen methodology (1996, 1999), I would like to test whether the debt-growth relationship is nonlinear. However, I also would like to consider the fact that these two variables might be cointegrated.
For this purpose, I proceeded in two steps:
1. First, I tested whether the two variables, public debt ratio and economic growth, are cointegrated by means of the bounds testing approach (Pesaran et al. (2001)). If this is the case, the growth equation would be represented by an error correction model.
ΔGDPt=c+ Σ aiΔGDPt-i+ Σ bjΔdebtt-j+ϕzt-1+κΔx₃t+...+δΔxmt+utWhere:
Δ: the first difference operator
GDP: real GDP per capita growth (the dependent variable)
debt: public debt GDP ratio
k and m: the autoregressive order of the two variables
zt-1=GDPt-1-c-ρdebt t-1: the error correction term
x₃ to xm: various growth determinants
ut: the error term (independent and identically distributed with mean zero and finite variance)
2. Second, I tested whether the debt-growth relationship is nonlinear by means of the Hansen methodology (1996, 1999). If the results of step 1 have shown that debt and growth are cointegrated, I introduced the error correction term among the various right-hand-side variables.
ΔGDPt=c+ Σ aiΔGDPt-i+ Σ bjΔdebtt-j+ϕzt-1+κΔx₃t+...+δΔxmt+(c+ Σ bj*Δdebtt-j+ϕ*zt-i)1(debtt>d ̅)+etWhere:
debtt is the threshold variable
d ̅∈Γ is the threshold parameter
et :the error term is assumed to be independent and identically distributed with mean zero and finite variance
The function 1() indicates whether or not the threshold variable is above the threshold.
I would like to ask you whether this “two-steps” procedure is correct. I have some doubts about that because, in their paper, Grasso and Manera (2007) mention that “if the adjustment to the long-run equilibrium is asymmetric, that is if it depends on the sign of the shocks, the test for cointegration is misspecified”. Would it mean that the first step of the procedure I would like to apply would not be valid?
Does a methodology allowing to simultaneously test for nonlinearity and also for cointegration between debt and growth exist? If yes, would it be the only available alternative to test the nonlinearity of the debt-growth relationship while in the same time take into account the fact that these two variables might be cointegrated?
I kindly thank you for your consideration and your reply.
Best regards
FYI:
Grasso, M. and Manera, M. (2007) “Asymmetric error correction models for the oil–gasoline price relationship”, Energy Policy, Vol. 35, pp. 156–177
Hansen, B. E. (1996) "Inference when a nuisance parameter is not identified under the null hypothesis" Econometrica, Vol. 64, No. 2, pp. 413-430.
Hansen, B. E. (1999) "Threshold effects in non-dynamic panels Estimation Testing and Inference", Journal of Econometrics, Vol. 93 No. 2, pp. 345-368.
Pesaran, M. H., Shin, Y. and Smith, R. J. (2001) "Bounds Testing Approaches to the Analysis of Level Relationships" Journal of Applied Econometrics, Vol. 16, pp. 289-326.