1. ECF 230: Introduction to Econometrics
Chapter # 1: Introduction
Damodar N. Gujarati (2003), Basic Econometrics, McGraw – Hill
Mr. Teddy K. Funyina
School of Business: University of Lusaka
2016.

2. 1.1 Nature and Scope of Econometrics
What is Econometrics? Definition 1: Economic measurement. This is too broad a definition to be of any use because most of economics is concerned with measurement. We measure our gross national product, employment, money supply, exports, imports, price indexes, and so on. Thus, what we mean by econometrics is: Definition 2: 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 them or refuting them (Maddala, 1992). Definition 3: The application of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics and obtain numerical results (Tinter, 1968). Definition 4: The social science in which the tools of economic theory, mathematics, statistical inference are applied to the analysis of economic phenomena (Arthur, 1971).

3. Econometrics Economic Theory Mathematical Economics Economic
Statistics
Mathematic
Statistics

4. 1.2 Why a separate discipline?
Economic theory makes statements that are mostly qualitative in nature, while econometrics gives empirical content to most economic theory
Mathematical economics express economic theory in mathematical form (equations) without empirical verification of the theory, while econometrics is mainly interested in the later
Economic Statistics is mainly concerned with collecting, processing and presenting economic data in the form of charts and tables. It is not concerned with using the collected data to test economic theories
Mathematical statistics provides many of the tools for economic studies, but econometrics supplies the later with many special methods of quantitative analysis based on economic data

5. 1.3 Methodology of Econometrics
Given an economic problem, how do econometricians proceed in their analysis? Or what is their methodology? There are several schools of thought on econometric methodology, however, we present the traditional or classical methodology, which still dominates empirical research in economics and other social sciences. Traditional econometric methodology proceeds in the following lines:
Statement of theory or hypothesis
Keynes stated: ”Consumption increases as income increases, but not as much as the increase in income”. Implying that “The marginal propensity to consume (MPC) for a unit change in income is greater than zero but less than unit”
2. Specification of the mathematical model of the theory
Keynes postulated a positive nexus between consumption and income, but did not specify the precise functional form of the relationship between the two. For simplicity, a mathematical economist might suggest the Keynesian consumption function as follows:
C = ß1+ ß2I ; < ß2< 1 ……………………………………………….. (1)
C= consumption expenditure
I= income
ß1 and ß2 are parameters; ß1 is intercept, and ß2 is slope coefficients

7. 3. Specification of the econometric model of the theory
The mathematical model of the consumption function given in Eq. (1) is of limited interest to the econometrician, as it assumes that there is an exact or deterministic relationship between consumption and income. However, relationships between economic variables are inexact.
Thus, if we obtained data on consumption expenditure and disposable income of a sample, say, 200 Zambian families and plot these data on a graph, we would not expect all 200 observations to lie exactly on the straight line of Eq. (1) because , in addition to income, other variables affect consumption expenditure. For instance, family size, ages of family members, family religion, etc., are likely to exert some influence on consumption
To allow for the inexact relationship between economic variables, the econometrician would modify the deterministic consumption function (1) as follows:
C = ß1+ ß2I + u ………………………………………………………….. (2)
u is disturbance term or error term. It is a random or stochastic variable that has well-defined probabilistic properties. The error term u may well represent all those factors that affect consumption but are not taken into account explicitly.
Equation (2) is an example of an econometric model

9. 4. Obtaining Data
To estimate the econometric model in Eq. (2) and obtain the numerical values of 𝛽 1 and 𝛽 2 , we need data.

10. 5. Estimation of the Econometric Model
Now that we have the data, we estimate the parameters of the consumption function. The numerical estimates of the parameters give empirical content to the consumption function. Using the statistical technique of regression analysis, we obtain the following estimates
𝛽 1 =− 𝑎𝑛𝑑 𝛽 2 = , thus the estimated consumption function is
𝐶 =− 𝐼 …………………………………………………………… (3)
The hat on the C indicates that it is an estimate. From this figure we see that for the period 1982–1996 the slope coefficient (i.e., the MPC) was about 0.70, suggesting that for the sample period an increase in real income of 1 dollar led, on average, to an increase of about 70 cents in real consumption expenditure. We say on average because the relationship between consumption and income is inexact; as is clear from Figure 3; not all the data points lie exactly on the regression line. In simple terms we can say that, according to our data, the average, or mean, consumption expenditure went up by about 70 cents for a dollar’s increase in real income.

12. 6.Hypothesis Testing
Are the estimates in accord with the expectations of the theory that is being tested? Is MPC < 1 statistically? If so, it may support Keynes’ theory.
Keynes expected the MPC to be positive but less than 1. In our example we found the MPC to be about But before we accept this finding as confirmation of Keynesian consumption theory, we must enquire whether this estimate is sufficiently below unity. In other words, is 0.70 statistically less than 1? If it is, it may support Keynes’ theory.
Confirmation or refutation of economic theories based on sample evidence is object of Statistical Inference (hypothesis testing).
7. Forecasting or Prediction
If the chosen model does not refute the hypothesis or theory under consideration, we may use it to predict the future value(s) of the dependent, or forecast, variable Y on the basis of known or expected future value(s) of the explanatory, or predictor, variable X.
Suppose we want to predict the mean consumption expenditure, given the income for 1997 is billion dollars ( 𝐼 1997 =$ billion). Consumption expenditure would be
𝐶 ̂ 1997 = (7,269.8)= $4,951 billion ………………….(4)

13. 8. Use of the Model for control or Policy purposes
Given the consumption function in eq. (3), Suppose further the government believes that consumer expenditure of about 4900 billions dollars will keep the unemployment rate at its current level of about 4.2 percent (early 2000). What level of income will guarantee the target amount of consumption expenditure?
If the regression results given in (I.3.3) seem reasonable, simple arithmetic will show that
4900 = − I (5)
which gives I = 7197, approximately. That is, an income level of about 7197 billion dollars, given an MPC of about 0.70, will produce an expenditure of about 4900 billion dollars.
As these calculations suggest, an estimated model may be used for control, or policy, purposes. By appropriate fiscal and monetary policy mix, the government can manipulate the control variable I to produce the desired level of the target variable C.

14. Anatomy of Econometric Modeling
Economic theory
Mathematical of the theory
Economic model of the theory
Data
Estimation of econometric model
Hypothesis Testing
Forecasting or prediction
Using the model for control or policy purpose

15. Types of Econometrics
Theoretical Econometrics
Concerned with the development of appropriate methods for estimating economic relationships specified by econometrics models,.e.g. OLS, VAR, VECM, GARCH, etc.
2. Applied Econometrics
use the tools of theoretical econometrics to study some specified field(s) of economics and business, such as the production function, investment function and demand and supply functions.

16. Basic Data Types used in Econometrics
There are 3 types of data which econometricians might use for analysis:
Time series data
is a set of observations on the values that a variable takes at different times. Such data may be collected at regular time intervals, such as daily (e.g., stock prices, weather reports), weekly (e.g., money supply figures), monthly [e.g., the unemployment rate, the Consumer Price Index (CPI)], quarterly (e.g., GDP), and annually (government budgets).
2. Cross-sectional data
are data on one or more variables collected at the same point in time, such as the census of population conducted by the Central Statistics Organisation (CSO) every 10 years (the latest being in year 2010), the basic food basket by JCTR and opinion polls by MUVI –TV and the Post Newspaper.
3. Panel data, a combination of 1. & 2.

17. 3. Pooled data, a combination of 1. & 2.
In pooled, or combined, data are elements of both time series and cross-section data. The table below is an example of pooled data.
Hypothetical Egg Production in Zambian:
Y1 = eggs produced in 2010 (millions)
Y2 = eggs produced in 2011 (millions)
X1 = price per tray(ZMK) in 2010
X2 = price per tray(ZMK) in 2011
For each year we have 10 cross-sectional observations and for each province we have two time series observations on output and prices of eggs, a total of 20 pooled (or combined) observations.
Province Y1 Y2 X1 X2
LUSAKA
100
150 20 22
COPPERBELT
200
280 19 21
CENTRAL 60 62 18
NORTHERN 50 53
18.5
19.5
SOUTHERN 44 48
MUCHINGA 10 28
N.WESTERN 65 90
20.5
WESTERN 30 35
EASTERN 55
LUAPULA 78

18. A Note on the Measurement Scales of Variables
The variables that will generally encounter fall into the following four broad categories:
Nominal Scale
nominal scales assign numbers as labels to identify objects or classes of objects. The assigned numbers carry no additional meaning except as identifiers. For example, the use of ID codes A, N and P to represent aggressive, normal, and passive drivers is a nominal scale variable. Note that the order has no meaning here, and the difference between identifiers is meaningless. In practice it is often useful to assign numbers instead of letters to represent nominal scale variables, but the numbers should not be treated as ordinal, interval, or ratio scale variables. Further, variables such as gender (male, female) and marital status (married, unmarried, divorced, separated) simply denote categories

19. 2. Ordinal Scale
Something measured on an "ordinal" scale does have an evaluative connotation. One value is greater or larger or better than the other. Product A is preferred over product B, and therefore A receives a value of 1 and B receives a value of 2.
Another example might be rating your job satisfaction on a scale from 1 to 10, with 10 representing complete satisfaction. With ordinal scales, we only know that 2 is better than 1 or 10 is better than 9; we do not know by how much. It may vary. The distance between 1 and 2 maybe shorter than between 9 and 10.
Other examples are grading systems (A, B, C grades) or income class (upper, middle, lower). For these variables the ordering exists but the distances between the categories cannot be quantified.
Students of economics will recall the indifference curves between two goods, each higher indifference curve indicating higher level of utility, but one cannot quantify by how much one indifference curve is higher than the others.

20. 3. Interval Scale
Interval scales build upon ordinal scale variables. In an interval scale, numbers are assigned to objects such that the differences (but not ratios) between the numbers can be meaningfully interpreted. Temperature (in Celsius or Fahrenheit) represents an interval scale variable, since the difference between measurements is the same anywhere along the scale, and is consistent across measurements. Ratios of interval scale variables have limited meaning because there is not an absolute zero for interval scale variables. The temperature scale in Kelvin, in contrast, is a ratio scale variable because its zero value is absolute zero, i.e. nothing can be measured at a lower temperature than 0 degrees Kelvin.
Time is an example of variable measured on the interval scale. The distance between 1 and 2 is equal to the distance between 9 and 10. Temperature using Celsius or Fahrenheit is a good example, there is the exact same difference between 100 degrees and 90 as there is between 42 and 32.

21. 4. Ratio Scale
Ratio scales have all the attributes of interval scale variables and one additional attribute: ratio scales include an absolute “zero” point. For example, traffic density (measured in vehicles per kilometer) represents a ratio scale. The density of a link is defined as zero when there are no vehicles in a link. Other ratio scale variables include number of vehicles in a queue, height of a person, distance traveled, accident rate, etc
Temperature measured in Kelvin is an example. There is no value possible below 0 degrees Kelvin, it is absolute zero. Weight is another example, 0 lbs. is a meaningful absence of weight. Your bank account balance is another. Although you can have a negative or positive account balance, there is a definite and non arbitrary meaning of an account balance of 0.