University Econometrics Assignment: Question Solutions and Analysis

This document provides a detailed solution to an econometrics assignment, addressing questions on Hume's definition of causation, unbiased estimators, and regression analysis. The assignment includes explanations of key concepts such as causal relationships, the interpretation of regression coefficients, and the use of Stata output to support findings. The document analyzes the concept of causation, exploring its limitations and the role of mathematical models. It then delves into unbiased estimators in regression models, outlining specific scenarios where the coefficient term remains unbiased. The assignment further examines a regression model, providing a statistical analysis of educational attainment based on parental education, incorporating Stata outputs and detailed interpretations of the coefficients and R-squared values. The analysis includes the impact of additional variables such as ability on educational attainment, as well as the inclusion of squared terms to assess non-linear relationships.

Running head: ECONOMETRICS 1
Econometrics
Student Name
Institution

ECONOMETRICS 2
Question 1
Part (a)
Hume defined causation as the universal relationship between object or variable X and Y if and
only if:
i) A universal relationship exist between X and Y variables or events
ii) There exist time precedence of variable Y by X variables or events
iii) A spatiotemporal connection exist between X and Y variables or events
Hume’s definition of causation is problematic. Understanding the idea of “necessary
connection” in Hume’s definition of causation is a problem because the statement “necessary
connection” is subjective. According to (James, 2012), the idea of necessary connection is
derived from the act of inspecting objects or experiences that a conjoined and that are
consecutive rather than from the observable characteristics in the actual object or event.
Moreover, Hume’s definition of “causation” implied that causation cannot be determined
mathematically but through experience. This statement is ambiguous the interpretation of the
statement may differ from one expert to another hence problematic. Experts in mathematical
field have proven that causal relationship can be determined by developing models (either
multivariate or linear models). Such models are important in estimating the degree of
relationship between response variable and explanatory variable, significance of explanatory
variables, and variation of the response value by explanatory value.
Part (b)
The estimation is not credible
Explanation: Lewi’s counterfactual theory of causation asserts that if event A did not occur, the
event C would not have occurred. In this case, the researchers’ conclusion is not credible because

ECONOMETRICS 3
the conclusion insinuates if there were not antibiotic intake, then rate of cancer contraction
would not be on increase.
Evidence: the causes of breast cancer are many whereby some of the causes are avoidable while
others are genetic-related hence unavoidable. Risk factors such as alcohol drinking for women
are avoidable while risk factors such family history are unavoidable (Kail, 2008).
Question 2
Part (a)
There are three circumstances where the coefficient term in your model (without the intercept
term) be an unbiased estimator. Such circumstances include:
i) In the ANOVA-style model for categorical values. In ANOVA model where binary
values are used to encode variables the resultant regression model is parameterized as
k-1dummy variables
ii) In cases where modelling is done for standardized data and the resultant intercept
value of very close to zero by design.
iii) In special cases where the multivariate model analysis is carried with hidden
intercepts
The coefficient term in a regression model without the intercept term is an unbiased estimator if
and only if ANOV A-style model for categorical where binary codes are used, where data is
standardized, and multivariate model analysis is conducted with hidden intercepts (Karakaplan,
2017).
Part (b)
Var (X|Y=y) = E[X- μX ∨Y (( y ))2∨Y = y]
= ∑
x∈ Rx
n
( xi−μX ∨Y (( y))2 PX ∨Y = y(xi) )

ECONOMETRICS 4
= E[ X2 ∨Y = y ]-μX ∨Y (( y ))2 thus conditional variance is a function of y
Since my model is linear and an unbiased estimator, then the data employed in model
construction is standardized therefore, the coefficient of intercept is very close to zero if not zero
thus omitted. In situations where the coefficient of intercept is omitted, intercept value is close
to zero, then the value of the conditional variance tends to zero. Therefore, the regression line
passes strictly trough the origin.
Question 3

Summarize educ
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
educ | 1,230 13.0374 2.354346 6 20
.
. summarize educ if fatheduc == 12
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
educ | 468 12.63462 1.878835 6 20
.
. summarize educ motheduc fatheduc
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
educ | 1,230 13.0374 2.354346 6 20
motheduc | 1,230 12.17805 2.278067 0 20
fatheduc | 1,230 12.44715 3.263835 0 20
Percentage of men completed twelfth grade but no higher grade = 468
1230*100 = 38.05%

regress educ motheduc fatheduc
Source | SS df MS Number of obs = 1,230

ECONOMETRICS 5
-------------+---------------------------------- F(2, 1227) = 203.68
Model | 1697.9676 2 848.9838 Prob > F = 0.0000
Residual | 5114.31207 1,227 4.1681435 R-squared = 0.2493
-------------+---------------------------------- Adj R-squared = 0.2480
Total | 6812.27967 1,229 5.54294522 Root MSE = 2.0416
------------------------------------------------------------------------------
educ | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
motheduc | .3041971 .0319266 9.53 0.000 .2415603 .366834
fatheduc | .1902858 .0222839 8.54 0.000 .1465669 .2340046
_cons | 6.964355 .3198205 21.78 0.000 6.336899 7.59181
------------------------------------------------------------------------------
Estimated regression model;
Educ = 6.964 + 0.3041motheduc+ 0.1902fatheduc
The value of R^2 explains the sample variation of the dependent variable by independent
variable(s) (Aalabaf-Sabaghi, 2011). Therefore, the sample variation by parent’s education is
24.93%.
Interpretation of the coefficient of the mother education: for every additional unit grade per year
of education completed by mother, the male’s education will increase by 0.34 grades.

regress educ motheduc fatheduc abil
Source | SS df MS Number of obs = 1,230
-------------+---------------------------------- F(3, 1226) = 305.17
Model | 2912.30705 3 970.769018 Prob > F = 0.0000
Residual | 3899.97262 1,226 3.18105434 R-squared = 0.4275
-------------+---------------------------------- Adj R-squared = 0.4261
Total | 6812.27967 1,229 5.54294522 Root MSE = 1.7836
------------------------------------------------------------------------------
educ | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
motheduc | .1891314 .0285062 6.63 0.000 .1332051 .2450578

ECONOMETRICS 6
fatheduc | .1110854 .0198849 5.59 0.000 .0720733 .1500976
abil | .5024829 .025718 19.54 0.000 .4520268 .552939
_cons | 8.44869 .2895407 29.18 0.000 7.88064 9.01674
------------------------------------------------------------------------------
.
. generate abil2 = abil*abil
.
. regress educ motheduc fatheduc abil abil2
Source | SS df MS Number of obs = 1,230
-------------+---------------------------------- F(4, 1225) = 244.91
Model | 3027.03706 4 756.759264 Prob > F = 0.0000
Residual | 3785.24262 1,225 3.08999397 R-squared = 0.4444
-------------+---------------------------------- Adj R-squared = 0.4425
Total | 6812.27967 1,229 5.54294522 Root MSE = 1.7578
------------------------------------------------------------------------------
educ | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
motheduc | .1901261 .0280957 6.77 0.000 .1350051 .2452472
fatheduc | .1089387 .0196014 5.56 0.000 .0704827 .1473946
abil | .4014624 .0302875 13.26 0.000 .3420413 .4608835
abil2 | .050599 .0083039 6.09 0.000 .0343076 .0668905
_cons | 8.240226 .2874099 28.67 0.000 7.676356 8.804097
Estimated regression model;
Educ = 8.240 + 0.1901motheduc+ 0.1089fatheduc + .4014 abil + .050599 abil2
Coefficients in this equation reflect a causal relationship.
Reason: their respective p-values are less than 0.05 hence statistically significant.

ECONOMETRICS 7
References
James Woodward. (2012). Causation: Interactions between Philosophical Theories and
Psychological Research. Philosophy of Science, 79(5), 961.
https://doi.org/10.1086/667850
P. J. E. Kail. (2008). Hume on Causation Helen Beebee. Mind, 117(466), 451.
https://doi.org/10.1093/mind/fzn056
Karakaplan, M. U. (2017). Fitting endogenous stochastic frontier models in Stata. Stata
Journal, 17(1), 39–55. Retrieved from http://search.ebscohost.com/login.aspx?
direct=true&db=aph&AN=124335218&site=ehost-live
Aalabaf-Sabaghi, M. (2011). Applied Statistics for Business and Economics. Journal of the
Royal Statistical Society: Series A (Statistics in Society), 174(3), 848.
https://doi.org/10.1111/j.1467-985X.2011.00709_11.x