3 measurement errors in variables

 assume there exists an exact linear ralationship between true weights and true heigts:

 W_i=B₀+B₁H_i. however ,weights and heights mersured with errors as follows,

Y_i=W_i+w_i   and X_i=H_i+V_i

  when w_i and V_i  are unarrelated with Y_i and X_i respectively . to figure out the relationship between weights and heights,suppose you run the following regression:

    Y_i=B₀+B₁X_i+U_i for i=1,2,3,......,n

a) show that OLS estimator of B₁ is biased toward zero.

b) under which anditions,the OLS estimator of B₁  is unbiased?

1  discuss the five threats to the internal validity of regression studies. to regress beef    demand (B)on the constant(C),the price of beef(p)  and per capital disposable I name (YD),obtain     dependent variable:B            sample:1960    1987

                    method: last squares            included observation:28

                   date: 12/12/07   time   15:34

variable                            coefficient           std.error               t-statistic            prob

c                                      37.53605            10.04020              3.738575          0.0010

p                                     -0.882623              0.164730            -5.357981          0.0000

YD                                  11.89115                1.762162             6.748045         0.0000

r-squared                      0.658030              mean dependent var    106.6500

adjusted r-squared        0.630672             S.D.dependent    var      10.00561

S.E of regression           6.080646            A kaike info criterion    6.549056

sum squared resid       924.3564              schhuerz    criterion       6.691792

log likelihood                -88.68678                      F-statistic           24.05287

durbin-watsm stat      0.292597                    prob( F-statistic)            0.000001

a) omitted variable bias

b) wray funtional form

c) sample selection bias

d)errors-in-variables bias

e) simultaneous bias

2 time series analusis of us inflation rates

  define DINF=INF(-1).which is the first difference of inflation rate .before you run autoregession models,you did on ADF tests on .inflation rate.

ADF test  statistic -2.546901     1%     critical  value*    -3.4725

                                                  5%     critial  value     -2.8797

                                                  10%     critial  value     -2.5763

*mackinnon critical values for rejection of hypothesis of a unit not.

augmented   dick-fuller    test   equation         date:12/15/07 time: 18:50

dependent  variable: D(INF)                               sample(adjusted):   1960:2    1999:4

method: least  squares                                     included   observiations: 159 after adjusting end points

variable                 coefficient                std.error               t-statistic            prob

INF(-1)                    -0.105769               0.041568              -2.546901       0.0118

D(INF(-1))            -0.189017                    0.082751         -2.284149          0.0237

D(INF(-2))              -0.236062                0.079496           -2.969496       0.0035

D(INF(-3))             -0.207285                0.078366              2.651488        0.0035

C                           0.480850              0.217344               2.212351          0.0089

                                                                                                                    0.0284

r-squared                      0.231259             mean dependent       var     0.017695

adjusted r-squared       0.2211291                S.D.dependent           var     1.698389

S.E of regression           1.508327           A kaike info criterion    3.690821

sum squared resid       350.3579              schhuerz    criterion       3.787327

log likelihood                -298.4203                     F-statistic         11.58186

durbin-watsm stat      1.994166                  prob( F-statistic)         0.000000