ES103 Introduction to Econometrics

Transcription

1 Anita Staneva May 16, ES Introduction to Econometrics.. Lecture 1 ES103 Introduction to Econometrics Lecture 1: Basic Data Handling and Anita Staneva Egypt Scholars Economic Society

2 Outline Introduction to "econometrics" 1 Introduction to "econometrics"

3 Anita Staneva, Ph.D. Post-Doctoral Research Fellow Research Profile: Empirical labour economics/applied microeconomics; development economics, child labour; well-being and psychological health of employees; evaluating intervention programs within the social welfare;

4 What is Econometrics? It is "the application of statistical and mathematical methods to the analysis of economic data, with a purpose of giving empirical content to economic theories and verifying or refuting them" (Maddala, 2001, p.3) "Economic measurement"; Combines economic theory, mathematical economics and statistics; An empirical analysis uses data to test a theory or estimate relationship;

5 Founders: Davenant and King in the 17th century; Econometric Society formed in 1933, defined econometrics: "Economic theory in its relation to statistics and mathematics" and its object as the "unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems" (Frisch, 1933)

6 Steps in empirical economic analysis The traditional and classical methodology in econometrics includes the following steps: Step 1: Careful formulation of the question of interest - relevant economic/business theory Step 2: Hypothesis Step 3: Mathematical formulae - use mathematical equations to describe the relationship of interest Step 4: Data collection Step 5: Econometric testing - use collected data to empirically test the theory

7 Anatomy of classical econometric modelling

8 Example: Statement of economic theory or hypothesis Keynes Postulates a positive relationship between income and consumption If an individual s income increases by $1, their consumption will increase but with less than the $1 Marginal propensity to consume 0 < MPC < 1 Mathematical model of consumption Y = β 1 + β 2 X Y = consumption expenditure (dependent variable); X = income (independent, or explanatory variable); β 1 and β 2 = parameters, where β 2 measures the MPC;

9 Obtaining Data To obtain the numerical values of β 1 and β 2, we need data. Look at data below, which relate to the personal consumption expenditure (PCE) Y and the Gross Domestic Product (GDP) X. The data are in "real" terms.

10 Type of economic data: Time series Data: Many macroeconomic data are collected at specific points in time; Data ordered by time is called time-series data. Eg, (Y t for t=1,...,t) collected over time for one economic unit; It is collected at regular time intervals - daily, weekly, monthly quarterly, annually, quinquennially, that is, every 5 years (e.g., the census of manufactures), or decennially (e.g., the census of population); Examples of time-series: stock price, money supply, consumer price index, GDP;

11 Example: Time-series line graph

12 Example: Time-series line graph

13 Type of economic data (count.) Cross-Sectional Data: Microeconomists and labor economists often work with data that are characterized by individual units. This is cross-sectional data: (Y i for i=1,...,n); Collected for a sample of individuals/households, firms, countries, at a given point in time;

14 Type of economic data (count.) Pooled Cross-Sectional Data: Have both cross-sectional and time series features Example: two cross-sectional surveys, say in 1985 and 1990 pooled together;

15 Type of economic data (count.) Panel Data or Longitudinal Data Panel data combines both time series and cross sectional components Eg.(Y it for i=1,..,n and t=1,...,t); Example: wage, education, employment history for a set of individuals followed over a ten-year period; Key distinguish feature from the pooled cross-section - the same units are followed over a given time period;

16 Qualitative vs Quantitative Data

17 Scatter Diagrams - XY plots Relationship between two or more variables: - Are higher education levels associated with higher earnings? - Do countries with high population density also tend to have high deforestation rates? Example: Deforestation and population density for 70 tropical countries: Plot of one variable versus another (e.g. deforestation on y-axis, population density is on x-axis); Each point on graph represents deforestation and population density for one country;

18 Scatter Diagrams: What the diagram shows? Positive relationship between X and Y; Countries with high population densities - have higher deforestation rate;

19 Descriptive Statistics Mean - statistical term for the average: Ȳ = N i=1 Y i N Example: Mean GDP per capita Ȳ = $5, 443.8; N=sample size (i.e. number of countries - 90); Median = middle value; splits distribution into two equal halves; Mode = most common value (if there is no most common value, the mode will be the highest point of the histogram);

20 Descriptive Statistics - Example: Seven people report their income as: 18,000, 15,000, 9,000, 15,000, 16,000, 17,000, 20,000 Mean - 15,714; Median - 16,000 (half people have higher income and half lower; Mode - 15,000;

21 Measures of Dispersion (count.) S = Standard deviation (SD) - variation or dispersion of a set of data values; (Yi Y ) 2 N 1 Variance = square of standard deviation; These are measures of spread, variability and inequality;

22 Standard Deviation

23 Quantiles/Percentiles Quantile points in a distribution that relate to the rank order of values in that distribution; Percentile: descriptions of quantiles relative to 100; divides the data range up into hundredths; the Xth percentile is the data value such that X% of the observations have lower data values; Accordingly, the 50th percentile is the median value, 50th percentile is the minimum, 100th percentile is the maximum. Quartiles: Divides the data into quarters 1st quartile = 25th percentile = lower quartile; 2nd quartile = 50th percentile = median quartile; 3rd quartile = 75th percentile = upper quartile; 4th quartile = 100th percentile = maximum

24 Example-returns to education across earnings distribution

25 Other descriptive stats Interquartile range measures difference between 3th and 1st quartile; Example: 75% of countries have GDP per capita less $9,802 (3st) and 25% less than $1,162 (1st); $9,802- $1,162 = $8,640; Deciles: Divides data into tenths. eg. 1st decile = 10th percentile; 8th decile = 80th percentile; Range = maximum-minimum

26 Introduction to "econometrics" is an important way of numerically quantifying the linear relationship between two variables; Eg, between X and Y is symbolised by r or r XY ; [Using an XY plot is a good indication of correlation]

27 Properties of correlation r lies between 1 and +1; Positive values of r indicate positive correlation between X and Y, negative values indicate negative correlation, r = 0 implies X and Y are uncorrelated; Larger positive values of r indicate stronger positive correlation. r = 1 indicates perfect positive correlation; More negative values of r indicate stronger negative correlation. r = 1 indicates perfect negative correlation; The correlation between Y and X is the same as the correlation between X and Y; The correlation between any variable Y and itself Y is 1;

28 Understanding correlation through XY-plot Positive correlation - upward sloping patterns in XY-plots; Negative correlation - downward sloping patters; Strongly correlated variables fit on or close to a straight line; Weakly correlated variables are more scattered;

29 Perfectly correlated variables

30 Positively correlated variables, but not perfectly

31 Uncorrelated variables

32 Negatively correlated variables

33 versus Causality does not imply causality; Example: The correlation between workers education levels and wages is strongly positive; Does this mean education "causes" higher wages? We don t know for sure. Possibility 1: Education improves skills and more skilled workers get better paying jobs. Education causes wages to increase; Possibility 2: Individuals are born with quality A which is relevant for success in education and on the job (e.g. intelligence, talent, determination, etc.). Quality A (NOT education) causes wages to increase;

34 Why are variables correlated? Example: Suppose we collected data on many elderly people on how much they smoked (X), whether they had cancer (Y) and how much they drank (Z). What correlations would we find? r XY > 0 Smoking cause cancer (Direct causality) r XZ > 0 Heavy drinkers tend to smoke, but this does not mean that smoking causes people to drink; r YZ > 0 This does not imply that drinking causes lung cancer (does not reflect causality);

35 Direct versus Indirect Causality Example: High rural population density (X) causes farmers to clear new land in forested areas (Z) which in turn causes deforestation (Y); Here we would find r XY > 0 and r ZY > 0 X (population density) is an indirect (or proximate) cause of Y (deforestation); Z (agricultural clearance) is a direct (or immediate) cause of Y (deforestation);

36 versus Causality s can be very suggestive, but cannot on their own establish causality; and a sensible theory suggests (but does not prove) causality;

37 Summary Introduction to "econometrics" Econometrics and its importance Types of data sets Data representations: line graph; histogram; scatter diagrams etc. Descriptive statistics