### 1.1 Definition Of Econometrics

The word econometrics has two parts. The first part Econo’ has come from the word Economics’ and the last part metrics’ is a Greek word which means measurement. So, Literally Econometrics means Economic measurement. Besides this we can define Econometrics more precisely as follows.

Econometrics is a subject which borrows Technique from mathematics and statistics to estimate numerical result of economic phenomena.

Econometrics may be defined as social science in which Mathematical tools and statistical inference are used to quantify.

In short, Econometrics is the study of expressing economic relation in number and it will convert qualitative statement to quantitative statement which is more realistic.

More simply, measuring and analyzing any economic theory is what we say Econometrics’

We can show Econometrics as follows by using a diagram:

### 1.2 Forms Of Econometrics

Econometrics is also divided into 2 sorts broadly speaking,

- Theoretical econometrics
- Applied econometrics

#### (1) Theoretical Econometrics:

The econometrics that discusses concerning the method for measuring economics relationships, assumption of the method, its properties and happens to those properties once one or additional of the assumption of the method don’t seem to be fulfilled is named theoretical econometrics. it’s additionally 2 sorts,

- Classical
- Bayesian

#### (2) Applied Econometrics:

The econometrics during which we have a tendency to use the tools of theoretical econometrics to review some special fields of economic and business like the production function, investment function, demand and supply function, portfolio theory etc is named applied econometrics. it’s additionally 2 types:

- Classical
- Bayesian

#### At a look we are able to show the kinds of econometrics as follows:

### 1.3 Importance Of Separate Discipline

Though Econometrics is an amalgam of economics, Mathematics and Statistics, it deserves to be studied in its own right for the following reasons

From the economics we can get qualitative statements, For example: according to the demand Law of Microeconomics- other things remain the same, if the price decrease then the quantity of demand of a commodity increase. For example, This economic theory shows a negative relationship between the price and quantity of demanded of a commodity. But the theory itself does not provide any numerical result between the two. It is econometrics from where we can get the numerical value of this economic theory. Thus econometrics provides the value of most economic theory of numbers.

The uses of economics are to express economic theory in equation from without regard any empirical verification. The econometricians lend these equations and convert them into econometrics equations with a great deal of practical skill.

The main job of the economic statistician are to collect, processing and presenting economic data in the form of charts and tables. They are responsible for collecting economic data like GNP, employment, prices and so on. But they are not concerned with using collected data to test economic theories. One who does the jobs of course becomes an econometrician.

So, to verify the economic theory numerically with the help of mathematical equation and statistical data, We have to read econometrics separately.

### 1.4 The Methodology Of Econometrics

The procedure to analyze any economic problem is called methodology of econometrics. There is several type of methodology for econometrics. But the methodology of traditional methodology is still dominating the economic research in the world

#### Which we will discuss now:

#### The steps of traditional methodology of econometrics:

- The declaration of economic theory or law.
- Framing the mathematical model of the theory.
- Specification the econometrics model.
- Collecting the data.
- Estimation of the parameters of the econometrics model.
- Test of hypothesis.
- Foretelling or prediction.
- Using the specified model for controlling policy.

#### Explanation of the proceeding steps:

Let us consider the well known Keynesian consumption theory.

#### 1. The declaration of economic theory or law

Suppose we want to proceed with Keynes consumption theory.

Keynes stated: The fundamental psychological law . . . is that men people are disposed, as a rule and on average, to increase their consumption as their income increases, but not as much as the increase in their income. In short, Keynes postulated that the marginal propensity to consume (MPC), the rate of change of consumption for a unit (say, a dollar) change in income, is greater than zero but less than 1 .

#### 2. Forming or constructing mathematical model of the theory.

According the Keynes consumption theory we are informed about the positive relationship between consumption (c) and income (Y); but we did not get any exact relationship between the two. It is possible to get the exact functional relationship from the mathematical model which is as follows:

Y=B_{1 }+ B_{2}X; o<B_{2}<1 . . . (1)

It is the consumption function of Economic.

Where,

y = Dependent variable which shows the consumption expenditure

X= Explanatory variable which shows Income.

B_{1}=Intercept; It is autonomous consumption.

B_{2}=Slope coefficient, which measure the MPC.

Geometrically, the consumption function is as follows:

**3. Constructing the econometric model of the consumption theory**

The econometricians are not much more interested to the pure mathematical model of the consumption expenditure given in equation . . . .(1) as there is an exact or deterministic relationship between the two. The economic variable shows generally the inexact relationships. Thus, according to equation . . . . (1) only income influence the consumption. But other variable like family size, family members, age, family religion also affect the consumption expenditure. So, The econometrician would modify the mathematical model of consumption to econometric model as follows;

Y= B_{1}+B_{2}X+U . . . . (2)

Where u = disturbance term / error term

The term U is a random variable which represents all those factors that affect consumption but are not expressed into the equation.

Geometrically, the econometric model of the consumption as shown below where we would not expect all observation to lie exactly on the straight line because of the influences of other variables.

#### 4. Obtaining Data:

We need data to get the numerical value of B_{1} and B_{2 }to estimate the econometric model given in equation (2). The data may be time series or cross sectional or pooled data.

#### 5. Estimation of Econometric model:

After collecting the data, our next tusk to estimate the parameters of the consumption function. The main tool to obtain numerical estimates of the parameters B_{1 }and B_{2} is ordinary least square method of regression analysis. Now using the data and technique suppose we get the estimators of B_{1} and B_{2} are as follows:

B_{1} = -231.8 and B_{2 }= 0.7194.

Then the estimated consumption function will be

Ŷ = -231.8 + 0.7194X————–(3)

The hat/cap on parameter and indicates that they are estimators.

The slope coefficient of the equation is about 0.72 ( i.e. MPC = 0.72) indicates that for sample period an increase in real income of one taka, on average, about 72 paisa real consumption expenditure will be increased. We use on average because the relationship between consumption and income is inexact.

#### 6.Test of hypothesis:

According to the Keynsian consumption theory the MPC is positive but less than 1. In our example, we get the MPC to be about 0.72. But before we accept the estimate we must enquire that this is not a chance occurrence or peculiarity of the particular data we have used. In other words, is MPC statistically less than 1? If yes, it may be support Keynes theory.

Such confirmation of economic a theory on the basic of sample evidence based on a branch of statistical theory known as statistical inference or test of hypothesis.

#### 7. Forecasting or prediction

If the model accepts the hypothesis we may use it to predict the future value of the dependent or forecast variable Y on the basis of the explanatory or independent variable X.

To illustrate, suppose we want to predict the expenditure for 2016-2017. The GDP value for 2016-2017 was 29,717 crore taka. Then the consumption expenditure of that year will be

Y = -231.8+0.7194(29717) . . . .(3)

= 21146.61

Thus, given the value of the GDP the mean or average consumption expenditure is about 21146.61 crore taka.

Besides this, using the estimated MPC = .7194 we can get **the income multiplier** M which is defined as follows;

M= 1/1-MPC

If we use the MPC is .72 then this multiplier becomes 3.36.

It means that an increase (decrease) a taka in investment will eventually lead to more than threefold increase (decrease) in income. Thus estimating MPC by using regression models, one can predict the future income, consumption expenditure and employment following a change in the government fiscal policy.

#### 8. Uses of the model for controlling policy:

Suppose, we have the estimated consumption function for 2016-17 is

Y = -231.8+0.7194X

Now our government believes that about 2500 crore taka will help to increase unemployment rate in the country. Then, the targeted GDP will be

2500= -231.8+ 0.7194 (GDP)

= 2500 + 231.8= o.7194 (GDP)

GDP= 2731.8÷ 0.7194

=3797.33 approximately that is, an income level of about 3797 crore taka given an MPC is about .72 will produce consumption expenditure 2500 crore taka which will increase employment rate.

Such a way, an estimated model may be used for controlling policy purposes. The government of any country can manipulate the control variable X to produce the target variable Y.

### 1.5 Econometric Model

An economist can show the relationship between economic variable theoretically. But he does not specify the functional relationship between the variables. It is possible to show the exact relationship by using the mathematical model of economic theory which is as follows:

Y_{1}= B_{1}+B_{2} X; where Y_{1} = consumption expenditure and X_{1}= Income. But the relationship between economic variables is generally inexact. Because the variables not explicit in the model like family size, religion etc also influence the consumption expenditure that should be taken consideration. When we consider the influence of these variables in the model it is called econometric model which is as follows:

Y_{1}=B_{1} + B_{2}X + U

Where, U = disturbance term/error term that represent all those factors that affect consumption but are not taken into account in the above model explicitly. More technically, it is an example of linear regression model.

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