Test for the endogeneity of inflation rate in unemployment

Reference no: EM133334708 , Length: 5 pages

Assignment - Simultaneous Equation Models

Question 1). consider the following simultaneous equations model for joint determination of unemployment rate, price inflation and wage inflation:

Π_t = β₁ + β₂ωi_t + β₃ad_t + β₄t + ∈_1t
un_t = α₁ + α₂Π_t + α₃prod_t + ∈_2t
ωi_t = γ₁ + γ₂un_t + γ₃Π_t + ∈3t

where
un_t = unemployment rate (%)
Π_t = inflation rate (%); computed as 100*(ln CPI_t - lnCPI_t-1)
ωi_t = wage inflation (rate of γhange of wages) (%)¡ computed as 100 * (ln wage_t - ln wage_t-1)
pvod_t = rate of change of aggregate demand (GDP growth %)

ad_t = rate of change of aggregate demand (GDP growth %)

t = time trend.

a). Study the identifiability of each equation and of the system.

b). What are the additional restrictions to make the system

i). triangular;
ii). fully reγursive.

Attached herewith please find a dataset for Simultaneous Determination of Priγe Inflation, Wage Inflation and Unemployment Rate: 1995 - 2016, in Stata format with file name (dsem.dta).

c) Estimate the model by 2SLS and 3SLS methods. comment on the results. Use a 5 perγent level of significance throughout.

(d) Test for the endogeneity of inflation rate in the unemployment rate equation.

Question 2). Consider the simultaneous equation model:

y₁ = α₁y₂ + α₂x₁ + u₁

and

y₂ = α₃y₁ + α₄x₁ + α₅x₂ + u₂

• Assume you want to estimate the equation for y₁ using 2SJS. Econometrician A estimates the fist stage equation

y₂ = y₁x₁ + y₂x₂ + u₂

and Econometrician B estimates the relation

y₂ = δ₁x₂ + u₁

They both estimate the second stage equation

y₁ = α₁y^{^}₂ + α₂x₁ + u₁

• Prove that the two econometrician get identical coefficients for α₁ if x₁ and x₂ are orthogonal.

Reference no: EM133334708

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