Econometrics Study Material

This document provides study material for econometrics, including discussions on regression models, estimation and inference in uniform distribution models, and unbiased estimators. It also includes a bibliography of recommended books on econometrics.

ECONOMETRICS
Student’s Name
Subject
Date

QUESTION 1
Yes I do agree that the regression model; yi = xi
, β +ei is homoskedastic if the observations ( yi, xi)
are independent and identically distributed (i.i.d). For i.i.id sample ( yi, xi), yi, and xi are not
independent of each other but it implies that the sample ( yi,xi) is independent from ( y j, x j) for i
is not equal to j. By definition, E( ei| Xi) =0 for ( yi, xi) is i.i.d an implication that the independent
variable ( Xi),does not have any information on the dependent variable (Y i) from its conditional
probabilit1. Again, using the law of iterated expectation (LIE), the mean of error terms E( ei) =
0 .It can be concluded that if ( yi, xi) are i.i.d, then the error terms ei are i.i.d too thus Y i = Xi
, β +ei
is homoskedastic.
QUESTION 2
If we need to show issues regarding estimation and inference in a uniform distribution model, we
must show by examples how to deduce unbiased estimator and show consistency estimators of θ
by the calculation of maximum MLE of two estimators and comparing the results and using it to
infer and make a viable conclusion.
For U(0,2):
Let θ =1
For sample {2} , the Maximum likelihood estimator , MLE for Xi = 2 thus θ = MLE ( Xi) = 2
Similarly, For U(1,3):
θ1 = 2 An = 3*1=3
Comparing θ1 and, a difference in the MLE is noted thus the MLE for θ is tighter than the MLE
for θ1 .
1 Johnston, John, and John E. DiNardo. Econometric Methods. (New York, NY,
2009),134-159

From the above illustration, one of the issues that arise from the estimation and inferences
regarding different consistent estimators of uniform distribution is the mean and variance
parameters used. A uniformly distributed random variable with a mean of 0 will yield a different
result from and uniformly distributed random variable with a mean of 1and vice versa.
Therefore, correct prior information on the parameters of uniform distribution has a likelihood of
yielding correct results hence correct interpretation.
QUESTION 3
Since E(v) = 0 and E[xi ei ¿, then the error terms are independent and identically distributed then
the regressor constants ^β1 and ^β2 are also independent and identically distributed. By definition,
the constants ^β1 and ^β2are unbiased estimators of β1 and β2 respectively2. Thus the values of ^β1
and ^β2 are estimate the population parameters β1 and β2 with accuracy and can be used to
interchangeably. If the value of ^β1 is b, then the estimated value of β1 is b and a one unit increase
in ^β1 increases the value of independent value by b units and vice versa. Similarly, If the value of
^β2 is z, then the estimated value of β2 is z and a one unit increase in ^β2 increases the value of
independent value by z units and vice versa
2 Enders, Walter.Applied Econometric Time Series.(New York,2015), 98-115

Bibliography
Johnston, John, and John E. DiNardo. Econometric Methods. New York, NY: McGraw-Hill, 2009.
Enders, Walter.Applied Econometric Time Series. New York: John Wiley & Sons Inc, 2015.