International macroe.. - Free

128 CHAPTER 4. THE LUCAS MODELTable 4.3: Possible State ValuesG 1 =[(g θ 1g ∗(1−θ)1 ) 1−γ ]/λ 1 G ∗ 1 =[(g θ 1g ∗(1−θ)1 ) 1−γ ]/λ ∗ 1 d 1 = λ 1 /λ ∗ 1G 2 =[(g θ 1g ∗(1−θ)2 ) 1−γ ]/λ 1 G ∗ 2 =[(g θ 1g ∗(1−θ)2 ) 1−γ ]/λ ∗ 1 d 2 = λ 1 /λ ∗ 1G 3 =[(g θ 2g ∗(1−θ)1 ) 1−γ ]/λ 1 G ∗ 3 =[(g θ 2g ∗(1−θ)1 ) 1−γ ]/λ ∗ 1 d 3 = λ 1 /λ ∗ 1G 4 =[(g θ 2g ∗(1−θ)2 ) 1−γ ]/λ 1 G ∗ 4 =[(g θ 2g ∗(1−θ)2 ) 1−γ ]/λ ∗ 1 d 4 = λ 1 /λ ∗ 1G 5 =[(g θ 1g ∗(1−θ)1 ) 1−γ ]/λ 1 G ∗ 5 =[(g θ 1g ∗(1−θ)1 ) 1−γ ]/λ ∗ 2 d 5 = λ 1 /λ ∗ 2G 6 =[(g θ 1g ∗(1−θ)2 ) 1−γ ]/λ 1 G ∗ 6 =[(g θ 1g ∗(1−θ)2 ) 1−γ ]/λ ∗ 2 d 6 = λ 1 /λ ∗ 2G 7 =[(g θ 2g ∗(1−θ)1 ) 1−γ ]/λ 1 G ∗ 7 =[(g θ 2g ∗(1−θ)1 ) 1−γ ]/λ ∗ 2 d 7 = λ 1 /λ ∗ 2G 8 =[(g θ 2g ∗(1−θ)2 ) 1−γ ]/λ 1 G ∗ 8 =[(g θ 2g ∗(1−θ)2 ) 1−γ ]/λ ∗ 2 d 8 = λ 1 /λ ∗ 2G 9 =[(g θ 1g ∗(1−θ)1 ) 1−γ ]/λ 2 G ∗ 9 =[(g θ 1g ∗(1−θ)1 ) 1−γ ]/λ ∗ 1 d 9 = λ 2 /λ ∗ 1G 10 =[(g θ 1g ∗(1−θ)2 ) 1−γ ]/λ 2 G ∗ 10 =[(g θ 1g ∗(1−θ)2 ) 1−γ ]/λ ∗ 1 d 10 = λ 2 /λ ∗ 1G 11 =[(g θ 2g ∗(1−θ)1 ) 1−γ ]/λ 2 G ∗ 11 =[(g θ 2g ∗(1−θ)1 ) 1−γ ]/λ ∗ 1 d 11 = λ 2 /λ ∗ 1G 12 =[(g θ 2g ∗(1−θ)2 ) 1−γ ]/λ 2 G ∗ 12 =[(g θ 2g ∗(1−θ)2 ) 1−γ ]/λ ∗ 1 d 12 = λ 2 /λ ∗ 1G 13 =[(g θ 1g ∗(1−θ)1 ) 1−γ ]/λ 2 G ∗ 13 =[(g θ 1g ∗(1−θ)1 ) 1−γ ]/λ ∗ 2 d 13 = λ 2 /λ ∗ 2G 14 =[(g θ 1g ∗(1−θ)2 ) 1−γ ]/λ 2 G ∗ 14 =[(g θ 1g ∗(1−θ)2 ) 1−γ ]/λ ∗ 2 d 14 = λ 2 /λ ∗ 2G 15 =[(g θ 2g ∗(1−θ)1 ) 1−γ ]/λ 2 G ∗ 15 =[(g θ 2g ∗(1−θ)1 ) 1−γ ]/λ ∗ 2 d 15 = λ 2 /λ ∗ 2G 16 =[(g θ 2g ∗(1−θ)2 ) 1−γ ]/λ 2 G ∗ 16 =[(g θ 2g ∗(1−θ)2 ) 1−γ ]/λ ∗ 2 d 16 = λ 2 /λ ∗ 2Lucas model, consumption equals GDP so there is no theoretical presumptionas to which series we should use. Since prices depend onutility which depends on consumption. From this perspective, it makessense to use consumption data which is what we do. The consumptionand money data are from the International Financial Statistics and arein per capita terms.The next question is what estimation technique to use? Using generalizedmethod of moments or simulated method of moments (see chapter2.2.2 and chapter 2.2.3) to estimate the transition matrix might begood choices if the dimensionality of the problem were smaller. Sincewe don’t have a very long time span of data, it turns out that estimatingthe transition probability matrix P by GMM or by the SMMdoes not work well. Instead, we ‘estimate’ the transition probabilitiesby counting the relative frequency of the transition events.Let’s classify the growth rate of a variable as being high-growth