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This is a replication file for the oil price-GDP bivariate VAR-GARCH-M model from Elder and Serletis(2010), "Oil Price Uncertainty", Journal of Money, Credit and Banking, Vol. 42, No. 6, 1137-1159. This uses a diagonal GARCH-M model on two structural shocks with the square root of the current oil shock variance entering the VAR as a shift variable. There's a Choleski factorization to map the structural shocks to the variables themselves.
Unlike many types of non-linear models, the impulse responses in this model aren't dependent upon the lagged values of the dependent variables. However, they aren't linear in the shock size because of the GARCH variance depends upon the square and that propagates through. Positive and negative shocks have different effects. The "IRF" program computes the responses of GDP to shocks (with either sign) of a "typical" size in oil prices. It also computes the responses on a model estimated without the "M" effect. Error bands are computed by Random Walk Metropolis.
Note that there are a number of features of this model which are specific to this being a combination of an (very flexible) oil price and a sluggishly moving macro aggregate like GDP. The constraint garchp(1)(3)=0.0 eliminates the GARCH lag term on the first structural shock. However, that's not a requirement of the model; it's there because, when the model is estimating without that constraint, that coefficient goes negative. The "M" effect is only on the oil price variance, and is only included in the GDP equation.
This requires version 8.0 or later, and for version 8.0, you also need the function on the MODELLAGMATRIX.SRC file. (That's built-in with 8.1 or later). Because that's a function (not a procedure), you need to do a
SOURCE MODELLAGMATRIX.SRC
instruction in order to make it usable. (Again, this isn't necessary with RATS 8.1 or later)
This example is covered in detail in the RATS ARCH/GARCH and Volatility Models e-course.
oilgdpgarch.rpfEstimation of model(4.62 KiB) Downloaded 215 times oilgdpgarchirf.rpfCalculation of IRF's with confidence bands (requires oilgdpgarch.rpf)(7 KiB) Downloaded 187 times Elder_Serletis_oil_prices_Real_GDP.txtData file(4.78 KiB) Downloaded 539 times modellagmatrix.srcGlue routine for %MODELLAGMATRIX (required with RATS v8.0 or earlier)(888 Bytes) Downloaded 488 times
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