Econometrics Assignment

Jigjiga University
College of Business and Economics
Department of Project Management and Planning
Assignment I for the course of Advanced Econometrics: Theory and Applications

Prepared By:

Natnael Fisseha Redehey

09 June 2023

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 Econometrics Assignment

Question 1

A. t-statistic for Xt1 = 0.104/0.005 = 20.8 t-statistic for Xt2 = -3.48/2.2 = -1.58 t-
statistic for Xt3 = 0.34/0.15 = 2.27

The critical value for a two-tailed t-test at the 5% significance level with 92 degrees of
freedom (95 observations - 3 parameters estimated) is approximately +/- 1.98. Since
the absolute value of all three t-statistics are greater than the critical value, we can
reject the null hypothesis that the corresponding coefficients are equal to zero.
Therefore, all three parameters are statistically significant at the 5% level.

B. The coefficient of determination, also known as R-squared, is a measure of how

much of the variation in the dependent variable (Yt) is explained by the
independent variables (Xt1, Xt2, and Xt3). It is calculated as the explained sum
of squares (ESS) divided by the total sum of squares (TSS).

R-squared = ESS/TSS = (109.6-18.48)/109.6 = 0.831

Therefore, 83.1% of the variation in Yt is explained by the independent variables in

the model.

Question 2

a. Based on economic theory, we can expect the following signs for the coefficients of
the independent variables in the equation:

 The coefficient of Pt is expected to have a negative sign, indicating an inverse

relationship between the price of meat and per capita consumption of meat. As
the price of meat increases, people tend to consume less meat, ceteris paribus.
 The coefficient of Ydt is expected to have a positive sign, indicating a direct
relationship between disposable income and per capita consumption of meat.
As disposable income increases, people tend to consume more meat, ceteris
paribus.

b. The theoretical model for the equation is as follows: Per capita consumption of meat (Yt) is a
function of the price of meat (Pt) and per capita disposable income (Ydt). Mathematically, this
can be expressed as:

Yt = β0 + β1Pt + β2Ydt + ε

Where:

 β0 is the intercept term

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 Econometrics Assignment

 β1 is the coefficient of Pt, representing the change in Yt for a unit change in Pt, holding
Ydt constant
 β2 is the coefficient of Ydt, representing the change in Yt for a unit change in Ydt,
holding Pt constant
 ε is the error term, representing the random variation in Yt that is not explained by the
independent variables.

Question 3

a. R-squared (R2) is a statistical measure that represents the proportion of the variance
in the dependent variable that can be explained by the independent variables in the
model. In this case, the R-squared value is 0.33, which means that only 33% of the
variation in the dependent variable (t) is explained by the independent variables (Pt
and Ydt) in the model [1].

b. If other variables were to be added to this model, they would need to be relevant to
the dependent variable (t) and have a significant influence on it. Possible variables
that could be added to this model may include factors such as inflation rates, interest
rates, or consumer confidence levels, depending on the context of the data being
analyzed [2].

Question 4

a. The estimated equation shows the relationship between the salary of a lecturer and
the independent variables such as the number of books published, number of articles
published, number of excellent books published, number of dissertations supervised,
and years of teaching experience. The coefficients represent the impact of each
independent variable on the lecturer's salary. For example, for every book published,
the salary increases by 230 Birr per year, and for every year of teaching experience,
the salary increases by 189 Birr per year.

b. The signs of the coefficients may or may not meet prior expectations depending on
what the expectations were. However, it can be said that the positive signs of the
coefficients indicate a positive relationship between the independent variables and the
lecturer's salary.

c. The relative sizes of the coefficients seem reasonable as they are in line with what
is expected in academia. For instance, published books and articles, as well as
excellent books, have a positive impact on the lecturer's salary, while the number of
dissertations supervised has a relatively smaller impact.

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 Econometrics Assignment

d. Based on the estimated equation, writing an excellent book would have the most
significant impact on a lecturer's salary, followed by supervising three dissertations
and writing two excellent articles. However, it is important to note that these
recommendations are solely based on the estimated equation, and other factors such as
the relevance of the topics and quality of work should also be considered before
making a decision.

Question 5

To test the significance of the level of GNP in explaining the value of imports, we
need to conduct a t-test for the coefficient of X1. The null hypothesis is that the
coefficient of X1 is equal to zero, which means that GNP does not have a significant
impact on imports. The alternative hypothesis is that the coefficient of X1 is not equal
to zero, which means that GNP has a significant impact on imports.

Using the formula t = (coefficient of X1 - hypothesized value) / standard error of the

coefficient, we get:

t = (0.03 - 0) / 0.74 = 0.0405

The degrees of freedom for this test are n-2, which is 10 in this case. Using a t-table
with 10 degrees of freedom and a significance level of 0.05, the critical values are -
2.228 and 2.228.

Since our calculated t-value of 0.0405 is less than the critical value of 2.228, we fail to
reject the null hypothesis. Therefore, we can conclude that the level of GNP is not a
significant predictor of the value of imports.

To test the significance of the price index of imported goods in explaining the values
of imports, we need to conduct a t-test for the coefficient of X2. The null hypothesis is
that the coefficient of X2 is equal to zero, which means that the price index does not
have a significant impact on imports. The alternative hypothesis is that the coefficient
of X2 is not equal to zero, which means that the price index has a significant impact
on imports.

Using the formula t = (coefficient of X2 - hypothesized value) / standard error of the

coefficient, we get:

t = (-0.22 - 0) / 0.55 = -0.4

The critical values for this test are the same as the previous test. Since our calculated
t-value of -0.4 is less than the critical value of 2.228, we fail to reject the null
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hypothesis. Therefore, we can conclude that the price index of imported goods is not a
significant predictor of the value of imports.

Question 6

a. To test the significance of the slope parameter, we need to calculate the t-test using
the formula: t = (b - 0) / (SEb), where b is the slope coefficient, 0 is the null
hypothesis value (which is 0 in this case), and SEb is the standard error of the slope
coefficient. From the given data, the slope coefficient (0.81) has a t-statistic of 3.1.
Using this information, we can calculate the standard error of the slope coefficient as
SEb = 3.1 / 0.81 = 3.83. Therefore, the t-test is t = (0.81 - 0) / 3.83 = 0.21. Since this
value is less than the critical t-value (t = 2.101 for a two-tailed test with 17 degrees of
freedom at a 5% significance level), we can conclude that the slope parameter is not
statistically significant.

b. The estimated standard deviation of the slope coefficient can be calculated using
the formula: SEb = sqrt [ (1 - r^2) * SSE / (n - 2) * Var(Yd) ], where SSE is the sum
of squared errors, n is the sample size, and Var(Yd) is the variance of the independent
variable. From the given data, SSE = 13.59 and Var(Yd) = 350.11. Plugging these
values into the formula, we get SEb = sqrt [ (1 - 0.99^2) * 13.59 / (19 - 2) * 350.11 ] =
0.177. Therefore, the estimated standard deviation of the slope coefficient is 0.177.

c. To construct a 95% confidence interval for the intercept term, we use the formula:
CI = b ± t(alpha/2, n-2) * SEb, where b is the intercept coefficient, alpha is the level
of significance (0.05 for a 95% confidence interval), and t(alpha/2, n-2) is the critical
t-value for the given alpha level and degrees of freedom. From the given data, the
intercept coefficient is 15 and the standard error of the slope coefficient is 3.83. The
critical t-value is t(0.025, 17) = 2.110. Plugging these values into the formula, we get
the confidence interval as CI = 15 ± 2.110 * 3.83 = (7.29, 22.71). Since the interval
does not include 0, we can conclude that the intercept term is statistically significant
at a 95% confidence level.

Question 7

The disturbance term or error term is an essential part of any statistical or

mathematical model, particularly in regression analysis. Here are some reasons why
we include the disturbance term in the model:

1. To account for the incomplete relationship between independent and dependent

variables - The error term represents the deviation within the regression line,
indicating the lack of perfect goodness of fit in the model. It accounts for the

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uncertainty or difference between the theoretical value of the model and the
actual observed results.
2. To measure the impact of omitted variables - The disturbance term is a
substitute for all the variables that are omitted from the model but that
collectively affect the dependent variable. There may be several reasons for
leaving out variables, such as incompleteness of theory, unavailability of data,
intrinsic randomness in human behavior, poor proxy variables, principle of
parsimony, and wrong functional form. Thus, the stochastic disturbances play a
critical role in regression analysis.
3. To facilitate statistical inference - The error term helps us make statistical
inferences about the model's parameters. Without the disturbance term, we
would not be able to estimate the model's parameters or conduct hypothesis
tests on them.
4. To ensure the validity of regression assumptions - The error term is
instrumental in validating the assumptions of the linear regression model, such
as normality of error terms, homoscedasticity, and cross-sectional data.
Violation of these assumptions can affect the accuracy of the estimates and
make statistical inference unreliable.

In summary, the disturbance term or error term is an integral part of regression

analysis, accounting for the uncertainty and omissions in the model and facilitating
statistical inference and validation of assumptions.

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