Question 1. Given a population model
a. u has a zero conditional mean. This is actually an assumption of
OLS estimation (the error term should have a zero conditional
mean). Now, why is this necessary? We can see this using graphs
below. In the first graph, the zero conditional mean assumption is
violated, while it is followed in the second graph.
b. This question indicates a violation of another OLS assumption: All independent variables are uncorrelated with the error term. This assumption is called exogenity. If it is correlated, we can use the variable to predict the error term. Violating this assumption biases the coefficient estimate when it is included.
c. OLS assumptions:
1: The population regression model is linear in its parameters
and correctly specified as:
2: The observed data: (yi , xi, wi) for i = 1, ..., n represent an
i.i.d. random sample of size
following the population model.
3: The observed data: xi for i = 1, ..., n are not all the same
value (same for wi for i = 1....n).
4: The expected value of the error term is zero conditional on any
value of the explanatory variable: E[u|X] = 0
Given OLS assumptions:
E[] =
and
E[] =
and
E[] =
The sampling distributions of the estimators ,
and
are
centered about the true population parameter values , and
.
Question 2.
a. Instrumental variables estimator is "biased but consistent". Instrumental variable methods provide consistent estimation when the explanatory variables are correlated with the error terms in a regression model. OLS estimators are biased but inconsistent in such cases. However, if an instrument is available, consistent estimates may still be obtained.
b. 2 Stage Least Squares is numerically similar to Instrument Variable with one instrument. Hence, we can find since X is correlated.
c. Instrument validity is defined as E[Z|u]=0 where Z is the instrumental variable and u is the error term of a univariate regression model.
Requirements for Z to be a valid instrument for X are:
The main idea behind the technique of instrument variable
estimator is that when Z changes, it should also alter X, but not
the part of X that is correlated with the error.
Hope this helped!
Provide comp te explanations with relevant equations and terivo . Questi! 1 (15p): Consider the population...
1. Which of the following conditions will lead to a smaller variance for the intercept estimator for your multiple regression model? (A) X values cluster far from the origin of the X axis (B) X values closely pack around the mean of X in your sample (C) Small sample sizes (D) High correlation among the explanatory variables (E) Small error variance in the population regression function 2. R-squared (A) measures the proportion of variability of the dependent variable that is...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2 3 .14 .25 .01 2 33 .10 .07 3 .03 .05 .02 Find the marginal probability distribution of Y and graph it. Show your calculations. b. Find the conditional probability distribution of Y (given that X = 2) and graph it. Show your calculations. c. Do your results in (a) and (b) satisfy the probability distribution requirements? Explain clearly. d. Find the correlation coefficient...
I need help with research critique summary of this below article in APA format and in text citation and the reference en/poni%20perception%20article.pdf EATING DISORDERS 2018, VOL. 26, NO. 2, 107-126 https://doi.org/10.1080/10640266,2017.1318624 Routledge Taylor & Francis Group PREVENTION SERIES Check to Perceptions of disordered eating and associated help seeking in young women Annamaria J. McAndrew and Rosanne Menna Department of Psychology, University of Windsor, Windsor, Ontario, Canada ABSTRACT Disordered eating is common among young women, but rates of help-seeking are remarkably...
I need Summary of this Paper i dont need long summary i need What methodology they used , what is the purpose of this paper and some conclusions and contributes of this paper. I need this for my Finishing Project so i need this ASAP please ( IN 1-2-3 HOURS PLEASE !!!) Budgetary Policy and Economic Growth Errol D'Souza The share of capital expenditures in government expenditures has been slipping and the tax reforms have not yet improved the income...