For the assignment I will examine whether or not a linear regression model is suitable for estimating the relationship between Human development index (HDI) and its components. Linear Regression is a statistical technique that correlates the change in a variable to other variable/s, the representation of the relationship is called the linear regression model.
Variables are measurements of occurrences of a recurring event taken at regular intervals or measurements of different instances of similar events that can take on different possible values. A dependent variable is a variable whose value depends on the value of other variables in a model. Hence, an independent variable is a variable whose value is not dependent on other variables in a model. The dependent variable here is HDI and this will be regressed against the independent variables which include Life expectancy at birth, Mean years of schooling, expected years of schooling and Gross National Income per capita Hence we can model this into Yi = b0 + b1 xi + b2 xi + b3 xi + b4 xi + where Y is HDI, β0 is a constant, β1 β2 β3 β4 are the coefficients and denotes for random/error term.
R2 is how much your response variable (y) is explained by your explanatory variable (x). The value of R2 ranges between 0 and 1, and the value will determine how much of the independent variable impacts on the dependent variable. The R2 value will show how reliable the regression represents the actual data in forecasting population values of Human Development. R2=1(∑e2/∑y2) where ∑y2 is Total sum of squares (TSS) and ∑y2 is Residual sum of squares (RSS)
The closer the R2 value is to the 1 value the more reliable the regression line is as an index, and if it is equal to 1 it represents a perfect fit. For my data, I have regressed my dependent variable against all my independent variables and computed the R2 to be 0.9933 (99.33%), which shows a strong correlation between...
...
ECONOMETRICS



First of all, I would like to apologize for showing the results in Spanish, but I couldn’t find the way to change Gretl’s language. However, all the explanations are in English, so I hope there is no problem to understand the results.
Secondly, I would just inform you that the timeseries data that I have used is “U.S. macro data, 19502000” from Greene Sample folder in Gretl.
Before building the model…
I would try to explain the variable “Real GDP” using the variables “Real consumption expenditures”, “Real PrivateSector Investment”, “Real government expenditure”, “Unemployment rate” and “Inflation rate”. To do so, the first thing we should do is to check if there is correlation risk between the independent variables. We will use the Correlation Matrix to figure out this:
Since the coefficient of correlation between the variables Real Consumption, Real PrivateSector Investment and Real Government expenditure is very close to 1, it means that those variables are providing almost the same information, so I would delete some of them, and check the coefficient of correlation again.
Once Real PrivateSector investment and Real Government Expenditure have been deleted from the correlation matrix, the coefficients of correlations between variables are acceptable now, and we can be sure that every variable gives different information about the model.
However, I could have also used another statistic to check is...
...Econometrics is the application of mathematics and statistical methods to economic data and described as the branch of economics that aims to give empirical content to economic relations. [1] More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference."[2] An influential introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships."[3] The first known use of the term "econometrics" (in cognate form) was by Paweł Ciompa in 1910. Ragnar Frisch is credited with coining the term in the sense that it is used today.[4]
Econometrics is the unification of economics, mathematics, and statistics. This unification produces more than the sum of its parts.[5] Econometrics adds empirical content to economic theory allowing theories to be tested and used for forecasting and policy evaluation
Basic econometric models: linear regression
The basic tool for econometrics is the linear regression model. In modern econometrics, other statistical tools are frequently used, but linear regression is still the most frequently used starting point for an analysis.[7] Estimating a linear regression on two variables can be visualized as fitting a line through data points representing...
...ECON 140
Section 13, November 28, 2013
ECON 140  Section 13
1
The IV Estimator with a Single Regressor and a Single Instrument
1.1
The IV Model and Assumptions
Consider the univariate linear regression framework: Yi = β0 + β1 Xi + ui
Until now, it was assumed that E (ui Xi ) = 0, i.e. conditional mean independence.
Let's relax this assumption and allow the covariance between Xi and ui to be dierent from zero.
Our problem here is that ui is not observed.
Doing OLS yields inconsistent estimates (remember the OVB formula).
In this case we refer to Xi as an endogenous variable.
The way to get consistent estimates is to use an instrument, which is a variable that satises the
following two properties:
1. Relevance: Cov (Zi , Xi ) = 0.
2. Exogeneity: Cov (Zi , ui ) = 0.
In words: since the variation of Xi is contaminated (it is correlated with the variation of ui ), it
follows that we need a variable that allows us to get variation in Xi that is clean, i.e. it holds ui
xed.
1.2
The Two Stage Least Squares Estimator
Since the OLS estimator doesn't yield consistent estimates, we need an estimator that uses the
instrument and yields consistent estimates.
This estimator is called Two Stage Least Squares (TSLS).
This is how it works:
1. In the rst stage, regress Xi on a constant term and Zi : Xi = π0 + π1 Zi + vi .
2. In the second stage, regress Yi on a constant term and the predicted values from the...
...7.5 − 0.051 × 9.75 + 8.827 = 14.75 (h) Jim’s expected years of education is 2 × 0.0315 = 0.0630 less than Bob’s. Thus, Jim’s expected years of education is 14.75 − 0.063 = 14.69.
3.
Variable growth rgdp60 tradeshare yearsschool rev_coups assasinations oil Mean 1.86 3131 0.542 3.95 0.170 0.281 0 Standard Deviation 1.82 2523 0.229 2.55 0.225 0.494 0 Units Percentage Points $1960 unit free years coups per year assasinations per year 0–1 indicator variable
(b) Estimated Regression (in table format):
Regressor tradeshare Coefficient 1.34 (0.88) 0.56** (0.13) −2.15* (0.87) 0.32 (0.38) −0.00046** (0.00012) 0.626 (0.869) 1.59 0.29 0.23
yearsschool rev_coups assasinations rgdp60 intercept SER R2 R2
116
Stock/Watson  Introduction to Econometrics  Second Edition
The coefficient on Rev_Coups is −2.15. An additional coup in a five year period, reduces the average year growth rate by (2.15/5) = 0.43% over this 25 year period. This means the GPD in 1995 is expected to be approximately .43×25 = 10.75% lower. This is a large effect. (c) The 95% confidence interval is 1.34 ± 1.96 × 0.88 or −0.42 to 3.10. The coefficient is not statistically significant at the 5% level. (d) The Fstatistic is 8.18 which is larger than 1% critical value of 3.32.
Chapter 7
Hypothesis Tests and Confidence Intervals in Multiple Regression
Solutions to Empirical Exercises
1. Estimated Regressions Model Regressor Age Female Bachelor Intercept 3.32 (0.97)...
...females. Moreover, if they work in social sciences then the wage would go up by 0.124. SEX and SOSCI are dummy variables.
723 data points lie in this model.
Constant
SEX
SOSCI
TENURE
Tratio
8.803/0.127=69.31
0.077/0.029=2.66
0.124/0.039=3.18
0.006/0.002=3.00
Significance Level
Critical (t*)
Constant
SEX
SOSCI
TENURE
10%
1.64697569
Significant
Significant
Significant
Significant
5%
1.96326884
Significant
Significant
Significant
Significant
1%
2.58268445
Significant
Significant
Significant
Significant
The coefficients are all significant at 1%, 5% and 10% levels.
Autocorrelation could be present. Rsquared could be overestimated at 60%, which is quite high. Standard errors are quite low. Econometric data has many factors so standard errors cannot be that low. The DurbinWatson dtest needs to be carried out to confirm the existence of autocorrelation in this example. GLS or NeweyWest method can be used to correct autocorrelation if need be.
References
Travel in London 3 report, Transport for London
Gregory Clark, "What Were the British Earnings and Prices Then? (New Series)" MeasuringWorth, 2013.
...
...UNIVERSITY OF MACAU FACULTY OF BUSINESS ADMINISTRATION BACHELOR'S DEGREE PROGRAMME
ECIF311 ECONOMETRICS II
Second Semester 20102011
Instructor Contacts P. S. Tam Office: L430 (Thursday 4:00 p.m.  7:00 p.m. Or By appointment.) Phone: 83974756 Email: pstam@umac.mo Friday 1:00 p.m.  4:00 p.m. J207 http://webcourse.umac.mo
Class Website
Description:
This course focuses on basic econometric techniques, emphasizing both technical derivations and practical applications. The linear regression model will be reviewed using matrix algebra, and its limitations addressed. Topics on dynamic models, random regressors, simultaneous equations models, and time series econometrics will be covered. If time permits, panel data models and qualitative and limited dependent variable models will also be discussed. Upon completing this course, students are expected to be able to undertake their own econometric analysis.
Prerequisite:
ECIF310 or equivalent. In general, knowledge in basic economic theory, calculus, probability and statistics is required.
Textbook:
Hill, R.C., Griffiths, W.E., and Lim, G.C. Principles of Econometrics, Third Edition. John Wiley & Sons, Inc. 2008. Griffiths, W.E., Hill, R. C., and Lim, G.C. Using EViews for Principles of Econometrics, Third Edition. John Wiley & Sons, Inc. 2008. (They are available from the university bookstore as a bundle with student discount.)...
...Descriptive Statistics
Mean
Variance
Standard Deviation
Sample Covariance
If it is greater than zero, upward sloping. This is scale dependent.
Sample Correlation
This is scale independent: between 1 and 1, close to 1 is upward, 0 is central, 1 is downward sloping.
Finding the regression
Regression formula with one regressor
Slope
Intercept
Finding R2
TSS=ESS+SSR
The Coefficient of Determination = R2
This gives the total fit of , between 0 (chance) and 1 (perfect prediction)
Standard Errors
Standard Error of the Regression
Standard error of
Hypothesis Testing
1.
2. Define H0
3. Define H1
4. Define Tcrit/Pcrit
a. Note, for Tcrit 2 sided test, half
5. Find Tact/Pact
Tact
,
Pact
For one sided, just
Multiple Regression
Omitted Variable Bias
Ommitted variables may increase the apparent importance of another variable, damaging the ability to prove causality.
Effect of OVB on
1. Find the variable outside of the model
2. Find Corr(ZY)
3. Find Corr (ZX)
4. Multiply the signs
5. If positive, there is an upwards bias ()
Adjusted R2
OLS Wonder Equation
A good model for proving causality has a low , a good model for predicting Y has a low R2
Multiple Variable Tests
Reparametrisation
1.
2. For showing
3. Let
4. Thus,
5.
6. Now, let
7. Thus,
8. Now, run a new regression and do the usual hypothesis...
...Classical Linear Regression Models and Relaxing their Assumptions
Seid Nuru seidnali@yahoo.com
August 2012
>
The Classical Linear Regression Models
Introduction The Simple Regression Model The Multiple Linear Regression Models Violations of the Assumptions of CLRMs
Definition
•
Econometrics is the application of statistical, and mathematical techniques to the analysis of economic data with a purpose of verifying or refuting economic theories.
Theory Mathematical Model Econometric Model
As income increases, consumption also increases, but not as much as income.
yi = f ( xi ) = β0 + β1xi
y i = f ( x i ) = β0 + β1x i + εi
2
>
The Classical Linear Regression Models
Introduction The Simple Regression Model The Multiple Linear Regression Models Violations of the Assumptions of CLRMs
Definition
•
Why do we need to include the stochastic (random) component, for example in the consumption function? function?
— Omission of variables leads to misspecification problem. For example, income is not the only determinants of consumption. — There may be measurement error in collecting data. — We may use poor proxy variables. — The functional form may not be correct.
3
>
The Classical Linear Regression Models
Introduction The Simple Regression Model The Multiple Linear Regression Models Violations of the Assumptions of CLRMs
Some Concepts: Regression,...
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