Introductory Econometrics - Unit 1
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Questions and Answers

What type of variable is 'Wage' classified as?

  • Nominal
  • Ordinal
  • Binary
  • Cardinal (correct)

Which variable type is 'Highest grade attended' categorized under?

  • Ordinal (correct)
  • Nominal
  • Cardinal
  • Binary

How is the variable 'Sex' best classified?

  • Ordinal
  • Continuous
  • Cardinal
  • Nominal (correct)

Which of the following variables is considered nominal?

<p>Race (D)</p> Signup and view all the answers

What does the variable 'No. of own kids' represent in terms of variable type?

<p>Cardinal (D)</p> Signup and view all the answers

What is the maximum wage recorded in the dataset?

<p>50000 (A)</p> Signup and view all the answers

How many individuals in the dataset are identified as female?

<p>7 (D)</p> Signup and view all the answers

Which individual has the highest age in the dataset?

<p>75 (A)</p> Signup and view all the answers

What is the most common level of education indicated in the dataset?

<p>1 (C)</p> Signup and view all the answers

How many people in the dataset are married?

<p>9 (B)</p> Signup and view all the answers

What is the age of the youngest individual in the dataset?

<p>1 (B)</p> Signup and view all the answers

Which of the following individuals works the most hours?

<p>Individual 17 (B)</p> Signup and view all the answers

How many children does the individual with the highest wage have?

<p>3 (C)</p> Signup and view all the answers

What is the null hypothesis for testing if the expected value of BMI is significantly different from 25?

<p>H0: E[BMI] = 25 (C)</p> Signup and view all the answers

In a two-sided t-test with a significance level of 5%, what are the critical values?

<p>-1.96 and 1.96 (B)</p> Signup and view all the answers

Why are one-sided t-tests reasonable in certain economic considerations?

<p>They focus on extreme deviations from the null hypothesis. (D)</p> Signup and view all the answers

What is the t-value computed for the BMI based on the given expected value and standard deviation in the example?

<p>29.63 (B)</p> Signup and view all the answers

If the absolute value of the calculated t-value is larger than the critical value in a hypothesis test, what should be the decision?

<p>Reject the null hypothesis. (C)</p> Signup and view all the answers

What does the notation H1: E[BMI] ≠ 25 signify in hypothesis testing?

<p>The expected value of BMI is different from 25. (C)</p> Signup and view all the answers

What is the significance level used in the t-test example provided for BMI?

<p>5% (A)</p> Signup and view all the answers

Which statistic is used to determine whether to reject the null hypothesis in a t-test?

<p>t-value (B)</p> Signup and view all the answers

What data method is used in the example provided for wages in different years?

<p>Pooled cross-sectional data (A)</p> Signup and view all the answers

What is a characteristic of the GSOEP sample from Germany?

<p>It includes a representative sample of private households. (D)</p> Signup and view all the answers

Which scale of measurement describes realizations that can be ranked but have no meaningful differences?

<p>Ordinal scale (D)</p> Signup and view all the answers

What type of data is represented by industry classes according to the data scale?

<p>Nominal scale (D)</p> Signup and view all the answers

When were Eastern Germans added to the GSOEP sample?

<p>1994/1995 (D)</p> Signup and view all the answers

Which of the following best describes Cardinal/interval scale data?

<p>Data expressed as multiples with meaningful intervals (D)</p> Signup and view all the answers

What kind of questions does the GSOEP survey include in the yearly changing topics?

<p>Environmental behavior (D)</p> Signup and view all the answers

In the context of data maintenance, what can additional samples be used for?

<p>To analyze only specific subgroups of the population (A)</p> Signup and view all the answers

What equation represents the confidence interval for the population mean when the population variance is unknown?

<p>$P(X̄ - t_{α/2} · \frac{σ̂_X}{√N} ≤ µ_X ≤ X̄ + t_{α/2} · \frac{σ̂_X}{√N}) = 1 - α$ (A)</p> Signup and view all the answers

When the expected value µ_X is unknown, which method is commonly used to estimate it?

<p>Using the sample mean $XÌ„$. (A)</p> Signup and view all the answers

What is the main purpose of constructing a confidence interval?

<p>To provide a range in which the population parameter likely lies. (A)</p> Signup and view all the answers

In a 95% confidence interval, which critical value is typically used?

<p>1.96 (B)</p> Signup and view all the answers

What happens to the confidence interval as the sample size N increases?

<p>It becomes narrower. (D)</p> Signup and view all the answers

Which assumption is made when using the t-distribution to create a confidence interval?

<p>The sample comes from a normally distributed population. (C)</p> Signup and view all the answers

Which formula represents the standardized sample mean when using the estimated variance?

<p>$Z̄ = \frac{X̄ - µ_X}{(σ̂_X/√N)}$ (A)</p> Signup and view all the answers

What does the symbol $t_{α/2}$ represent in the context of confidence intervals?

<p>The critical value from the t-distribution. (C)</p> Signup and view all the answers

What happens to the variance of the sample mean as the number of observations increases?

<p>It decreases and converges to zero. (A)</p> Signup and view all the answers

What is the formula used to calculate the unbiased estimator for the variance of a random variable?

<p>$\hat{\sigma}<em>X^2 = \frac{1}{N-1} \sum</em>{i=1}^{N} (X_i - \bar{X})^2$ (B)</p> Signup and view all the answers

What does $plim \bar{X} = E(X)$ signify in the context of the sample mean?

<p>The sample mean converges to the expected value of the random variable. (B)</p> Signup and view all the answers

What is the role of degrees of freedom in the estimation of variance?

<p>They adjust the estimate to account for the number of estimated parameters. (D)</p> Signup and view all the answers

In the formula for the variance of the sample mean, what does $N$ represent?

<p>The sample size. (A)</p> Signup and view all the answers

Which statement about the average of a random variable is correct?

<p>The average can converge to the expected value as sample size increases. (C)</p> Signup and view all the answers

What does the notation $\sigma_X^2$ represent?

<p>The variance of the population distribution. (D)</p> Signup and view all the answers

How is the variance of a sample mean expressed in terms of the population variance?

<p>$Var(\bar{X}) = \frac{\sigma_X^2}{N}$ (D)</p> Signup and view all the answers

Flashcards

Confidence Interval for µX

A range of values likely to contain the true population mean µX, given a sample mean X̄.

Sample Mean (XÌ„)

The average value of a sample.

Population Mean (µX)

Average value of the entire population.

Standard Deviation (σX)

Measurement of data dispersion around the population mean.

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t-distribution

Probability distribution used in statistical inference when population variance is unknown.

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Critical Value (tα/2)

A threshold value from the t-distribution corresponding to a given confidence level.

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Estimating Variance (σ̂X)

Estimating population variance using sample data when it's unknown.

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Confidence Level (1-α)

Probability that the confidence interval contains the true population parameter.

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Variable Coding

Assigning numerical values to categorical variables for analysis

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Variable Names

Descriptive names for variables in a dataset.

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Nominal Variable (e.g., sex)

Categorical variables without inherent order (e.g., male/female).

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Ordinal Variable (e.g., education)

Categorical variables with a meaningful order (e.g., less than high school, high school, college).

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Cardinal Variable (e.g., age)

Numerical variables with a meaningful scale and a specific value

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t-test

A statistical test used to determine if a sample mean significantly differs from a hypothesized value.

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Null Hypothesis (H0)

The assumption that there's no significant difference between a sample and a known value.

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Alternative Hypothesis (H1)

The opposite of the null hypothesis (e.g., there is a significant difference).

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Critical Value (t)

A value from the t-distribution used to determine if the calculated t-value is statistically significant.

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t-value

A calculated value used to assess the statistical significance of the difference between the sample mean and hypothesized value.

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Significance Level

Probability of rejecting a true null hypothesis (e.g., 5%).

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Degrees of Freedom

The number of independent values in a sample used in t-test calculations.

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One-sided t-test

A t-test where the alternative hypothesis specifies a direction of difference(either greater than or less than).

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Data Set

A collection of data points, often organized in rows and columns.

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Pooled cross-sectional data

Data collected from different groups (cross-sectional) over multiple time periods (pooled) to understand how variables change across time and groups.

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GSOEP Data

A representative German survey of households, tracking employment, family history, life satisfaction, and other topics annually.

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Variable 'age'

Represents age of individuals in a dataset.

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Variable 'female'

Indicates gender of individuals in a dataset (0=male, 1=female).

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Nominal Scale

Qualitative data where order doesn't matter (e.g., industry classes).

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Ordinal Scale

Qualitative data where order matters, but differences between values are meaningless (e.g., education levels).

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Variable 'wage'

Represents the salary or earnings of each individual in the data set.

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Cardinal/Interval Scale

Quantitative data where order, differences, and multiples are meaningful (e.g., income).

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Variable 'hours'

Represents the number of working hours.

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Variable 'kids'

Number of children for individuals in the sample.

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Data maintenance (GSOEP)

GSOEP continually updates data from samples to obtain a representative sample of German households.

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Representative Sample

A sample that accurately reflects the characteristics of the entire population it is drawn from.

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Record

A complete observation of all the variables for one individual.

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Data Scale

Different ways data can be grouped and measured (nominal, ordinal, interval/ratio).

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Introductory Econometrics

The study of using statistical analysis to understand economic issues.

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Variance of sample mean

The measure of how spread out the sample means are around the true population mean.

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Consistent estimator

An estimator that gets closer to the true value as the sample size increases.

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Unbiased estimator for population variance

An estimator(σ̂X2) where the average of the estimated values equals the true variance.

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Degrees of freedom

The number of independent pieces of information used to estimate a parameter.

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Sample variance formula

The sum of squared differences between data points and the sample mean divided by the degrees of freedom minus 1.

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Sample variance calculation

How to calculate the variance, the measure of data dispersion.

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Population variance

The average squared difference of each data point from the population mean.

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Estimating parameters

Using sample data to find estimates for population values.

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Study Notes

Introductory Econometrics - Course Information

  • Course Instructor: Simon Martin
  • University: University of Vienna
  • Term: Winter 2024-25
  • Slides: Courtesy of Tomaso Duso (DIW Berlin), Martin Halla (WU Vienna), Liyang Sun (CEMFI), Jesse M. Shapiro (Harvard and NBER), and Andrea Weber (CEU). Based on Wooldridge (2022), and Pearson on Stock and Watson (2020).
  • Errors: All errors are the instructor's responsibility.

Course Aims and Content

  • Understanding: Standard econometric methods.
  • Empirical Analysis: Modern empirical economic literature and performing one's own analysis of cross-sectional, time series, and panel data.
  • Methods: Includes Least Squares Estimation, Instrumental Variables Estimation, and Maximum Likelihood.
  • Target Audience: Master students in Applied Economics (913 [3]), Banking and Finance (974), Research in Economics and Finance (953 [1]), and Philosophy and Economics (642).
  • Prerequisites: Background in statistics, probability theory, mathematical statistics, and linear regression.

Course Schedule and Materials

Assignments and Evaluation

  • Attendance: Unexcused absence from the first session leads to deregistration. Notify instructor of absence in advance to remain in course.
  • Assessment:
    • 2 Tests (45% each) on November 15, 2024, and January 31, 2025 (each 60 minutes)
    • Homework assignments (2 exercises in groups of up to 4, for 5% each)
    • November 22nd and January 24th for homework due dates
    • Self-selected group submissions via Moodle
  • Retake Exam: Students who fail or miss a test are eligible for a retake on February 12, 2025. Registration by February 6, 2025. The worse of the two exams is replaced.

Examples of Topics

  • Field Experiments: General procedure, treatment and control groups, random (or quasi-random) assignment
  • Policy Evaluation: Identify Agglomeration Spillovers (Greenstone, Hornbeck and Moretti 2010)
  • Cash Transfer Program in Kenya: Panel A. Uganda, Panel B. Kenya, data on age sets societies
  • Forecasting: Methods for heavily used analysis forecasting tools.

Course Plan

  • Basic Econometric Tools: Linear regression model with single regressor, Multivariate regression, OLS estimator & its properties, Difference-in-difference, experiments, Problems with time series, Multicollinearity, heteroskedasticity, GLS, clustering, Panel data methods
  • Advanced Econometric Tools: Endogeneity and instrumental variables estimation (IV), Systems of Equations, Quasi-experiments, Maximum likelihood estimation, Discrete choice models, Sample selection, Advanced time series analysis, Forecasting, Dynamic causal effects
  • Unit 1: Introduction to estimation and testing

Literature

  • Books: Stock, J. H., and Watson, M. W. (2020), Wooldridge, Jeffrey M.(2020), Angrist, J.D. and Pischke, J.-S. (2009), Cunningham, Scott (2021), Greene, W.H. (2019), Wooldridge (2010), Hanck, C., et al (2020), Heiss, F. (2020).

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Related Documents

Introductory Econometrics PDF - Winter Term 2024-25

Description

This course aims to provide master students with a strong foundation in standard econometric methods. Participants will engage in empirical analysis of economic literature, working with various data types including cross-sectional, time series, and panel data. Core topics include Least Squares Estimation, Instrumental Variables, and Maximum Likelihood methods.

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