Econometric take home APPS_Part_34

Econometric take home APPS_Part_34 - +-+-+-+-+-+-+ Constant...

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+---------+--------------+----------------+--------+---------+----------+ Constant 6.666079115 8.6211817 .773 .4394 YT -.2932041745E-01 .35260653E-01 -.832 .4057 4577.1882 CT1 1.051478712 .51482187E-01 20.424 .0000 2982.9744 +-----------------------------------------------------------------------+ | Two stage least squares regression Weighting variable = none | | Dep. var. = IT Mean= 654.5295567 , S.D.= 391.3705005 | | Model size: Observations = 203, Parameters = 3, Deg.Fr.= 200 | | Residuals: Sum of squares= 54658669.31 , Std.Dev.= 522.77466 | | Fit: R-squared= -.793071, Adjusted R-squared = -.81100 | | (Note: Not using OLS. R-squared is not bounded in [0,1] | | Diagnostic: Log-L = -1557.1409, Restricted(b=0) Log-L = -1499.3832 | | LogAmemiyaPrCrt.= 12.533, Akaike Info. Crt.= 15.371 | | Autocorrel: Durbin-Watson Statistic = 1.49055, Rho = .25473 | +-----------------------------------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Constant -141.8297176 103.57113 -1.369 .1709 RT 52.04340559 12.971223 4.012 .0001 5.2499007 DY 13.80361384 1.7499250 7.888 .0000 37.898522 Time series identification for EC Box-Pierce Statistic = 40.8498 Box-Ljung Statistic = 41.7842 Degrees of freedom = 10 Degrees of freedom = 10 Significance level = .0000 Significance level = .0000 * => |coefficient| > 2/sqrt(N) or > 95% significant. PACF is computed using Yule-Walker equations. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Lag | Autocorrelation Function |Box/Prc| Partial Autocorrelations X xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 1 | .194*| |** | 7.65*| .194*| |** X 2 | .264*| |*** | 21.82*| .236*| |*** X 3 | .273*| |*** | 36.93*| .207*| |** X 4 | .067 | |* | 37.85*|-.063 | * | X 5 | .054 | |* | 38.44*|-.068 | * | X 6 | .073 | |* | 39.52*| .018 | |* X 7 | .009 | |* | 39.53*| .003 | |* X 8 |-.078 | *| | 40.78*|-.109 | * | X 9 | .019 | |* | 40.85*| .023 | |* X 10 | .002 | |* | 40.85*| .050 | |* X xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Time series identification for EI Box-Pierce Statistic = 27.4753 Box-Ljung Statistic = 28.3566 Degrees of freedom = 10 Degrees of freedom = 10 Significance level = .0022 Significance level = .0016 * => |coefficient| > 2/sqrt(N) or > 95% significant. PACF is computed using Yule-Walker equations. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Lag | Autocorrelation Function |Box/Prc| Partial Autocorrelations X xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 1 | .244*| |*** | 12.13*| .244*| |*** X 2 | .143*| |** | 16.27*| .096 | |* X 3 | .037 | |* | 16.55*|-.019 | * | X 4 |-.001 | *| | 16.55*|-.017 | * | X 5 |-.066 | *| | 17.42*|-.078 | * | X 6 | .003 | |* | 17.43*| .043 | |* X 7 |-.042 | *| | 17.79*|-.033 | * | X 8 |-.107 | *| | 20.10*|-.107 | * | X 9 | .108 | |* | 22.46*| .194*| |** X 10 | .157*| |** | 27.48*| .142*| |** X xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 135
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Chapter 23 Models for Discrete Choice Exercises 1. The log-likelihood is ln L = Σ 0,0 lnProb[ y =0, d =0] + Σ 0,1 lnProb[ y =0, d =1] + Σ 1,0 lnProb[ y =1, d =0] + Σ 1,1 lnProb[ y =1, d =1] where Σ i,j indicates the sum over observations for which y = i and d = j . Since there are no other regressors, this reduces to ln L = 24ln(1 - F ( α )) + 32ln(1 - F ( δ )) + 28ln F ( α ) + 16ln F ( δ ). Although it is straightforward to maximize the log-likelihood directly in terms of α and δ , an alternative, convenient approach is to estimate F ( α ) and F ( δ ). These functions can then be inverted to estimate the original parameters. The invariance of maximum likelihood estimators to transformation will justify this approach. One virtue of this approach is that the same procedure is used for both probit and logit models.
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Econometric take home APPS_Part_34 - +-+-+-+-+-+-+ Constant...

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