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C9D5 - 1 In the Monte Carlo experiment in the previous...

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Unformatted text preview: 1 In the Monte Carlo experiment in the previous sequence we used the rate of unemployment, U , as an instrument for w in the price inflation equation. SIMULTANEOUS EQUATIONS ESTIMATION: DURBIN–WU–HAUSMAN TEST ( 29 ( 29 ( 29 ( 29 ∑ ∑---- = w w U U p p U U b i i i i IV 2 w u U p w + + + = 3 2 1 α α α p u w p + + = 2 1 β β p u w p + + = 5 . 5 . 1 w u U p w +- + = 4 . 5 . 5 . 2 2 2 2 3 1 2 1 1 β α α α β α α- + + + + = w p u u U w OLS IV b 1 s.e.( b 1 ) b 2 s.e.( b 2 ) b 1 s.e.( b 1 ) b 2 s.e.( b 2 ) 1 0.36 0.49 1.11 0.22 2.33 0.97 0.16 0.45 2 0.45 0.38 1.06 0.17 1.53 0.57 0.53 0.26 3 0.65 0.27 0.94 0.12 1.13 0.32 0.70 0.15 4 0.41 0.39 0.98 0.19 1.55 0.59 0.37 0.30 5 0.92 0.46 0.77 0.22 2.31 0.71 0.06 0.35 6 0.26 0.35 1.09 0.16 1.24 0.52 0.59 0.25 7 0.31 0.39 1.00 0.19 1.52 0.62 0.33 0.32 8 1.06 0.38 0.82 0.16 1.95 0.51 0.41 0.22 9 –0.08 0.36 1.16 0.18 1.11 0.62 0.45 0.33 10 1.12 0.43 0.69 0.20 2.26 0.61 0.13 0.29 w u U p w + + + = 3 2 1 α α α p u w p + + = 2 1 β β p u w p + + = 5 . 5 . 1 w u U p w +- + = 4 . 5 . 5 . 2 2 We ran OLS and IV regressions for 10 samples. As far as we could tell, the IV estimates were distributed around the true value, while the OLS estimates were clearly upwards biased. SIMULTANEOUS EQUATIONS ESTIMATION: DURBIN–WU–HAUSMAN TEST OLS IV b 1 s.e.( b 1 ) b 2 s.e.( b 2 ) b 1 s.e.( b 1 ) b 2 s.e.( b 2 ) 1 0.36 0.49 1.11 0.22 2.33 0.97 0.16 0.45 2 0.45 0.38 1.06 0.17 1.53 0.57 0.53 0.26 3 0.65 0.27 0.94 0.12 1.13 0.32 0.70 0.15 4 0.41 0.39 0.98 0.19 1.55 0.59 0.37 0.30 5 0.92 0.46 0.77 0.22 2.31 0.71 0.06 0.35 6 0.26 0.35 1.09 0.16 1.24 0.52 0.59 0.25 7 0.31 0.39 1.00 0.19 1.52 0.62 0.33 0.32 8 1.06 0.38 0.82 0.16 1.95 0.51 0.41 0.22 9 –0.08 0.36 1.16 0.18 1.11 0.62 0.45 0.33 10 1.12 0.43 0.69 0.20 2.26 0.61 0.13 0.29 w u U p w + + + = 3 2 1 α α α p u w p + + = 2 1 β β p u w p + + = 5 . 5 . 1 w u U p w +- + = 4 . 5 . 5 . 2 3 We will now perform a Durbin–Wu–Hausman test using the first sample. SIMULTANEOUS EQUATIONS ESTIMATION: DURBIN–WU–HAUSMAN TEST 4 . ivreg p (w=U) Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 20---------+------------------------------ F( 1, 18) = 0.13 Model | 5.39052472 1 5.39052472 Prob > F = 0.7207 Residual | 28.1781361 18 1.565452 R-squared = 0.1606---------+------------------------------ Adj R-squared = 0.1139 Total | 33.5686608 19 1.76677162 Root MSE = 1.2512------------------------------------------------------------------------------ p | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- w | .1619431 .4459005 0.363 0.721 -.7748591 1.098745 _cons | 2.328433 .9699764 2.401 0.027 .2905882 4.366278------------------------------------------------------------------------------ Instrumented: w Instruments: U------------------------------------------------------------------------------ . estimates store ivp We begin by running the IV regression. In the command, the instrumented variable(s) and...
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C9D5 - 1 In the Monte Carlo experiment in the previous...

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