Basic concepts of econometrics

1. PRESENTATION ON TOPIC:
BASIC CONCEPTS OF ECONOMETRICS AND
PROGRAMMING METHODS
Done by-
Bisakha Mondal(Roll:10)
Soumili Bera(Roll:58)

2.  The word econometrics means "economic measurement".The purpose of
econometrics is to quantify and verify predictions from economic theory. It is a
mixture of economic theory, mathematical economics, and statistics.
Econometrics is the quantitative application of statistical and mathematical
models using data to develop theories or test existing hypotheses in economics
and to forecast future trends from historical data.
 JanTinbergen is one of the two founding fathers of econometrics.The other,
Ragnar Frisch, also coined the term .
 The econometric relationship depict the random behavior of economic
relationships which are generally not considered in economics and
mathematical formulations.

3.  Econometric theory is a mixture of Mathematical, statistical and economic theory.
 Mathematical theory: Firstly, mathematical economics is concerned with expressing
economic theory in equations. It is algebra of the kind where variables can be subtracted,
added, multiplied and divided in an equation. But it is not concerned with measurability
or empirical verification.
 Statistical theory: whose concern is to collect, process and present economic data.
Many developed countries have government agencies whose job it is to collect and
distribute economic data, such as the U.S. Bureau of Labor Statistics, which publishes
data on unemployment, inflation, productivity, etc.The Bureau releases this information
to the public and it is often used by other levels of government, social scientists, and
interested laymen.
 Economic theory: A general law or rule formulated.

4.  There are two branches of econometrics: theoretical econometrics and applied
econometrics.
Theoretical econometrics: concerned with methods, both their properties and
developing new ones. It is closely related to mathematical statistics, and it states
assumptions of a particular method, its properties.

Applied econometrics :applies econometric theory to branches within economics,
such as unemployment figures, portfolio theory, demand and supply functions, etc.
 Econometric theory uses statistical theory and mathematical statistics to evaluate
and develop econometric methods
Applied econometrics uses theoretical econometrics and real-world data for
assessing economic theories, developing econometric models, analysing economic
history, and forecasting.

5.  Econometric models are statistical models used in econometrics. An econometric
model specifies the statistical relationship that is believed to hold between the various
economic quantities pertaining to a particular economic phenomenon.
 An econometric model consists of
 Set of equations derived from economic model and have two parts –
 observed variables and disturbances.
 Statement about observed in the values of the variables.
 Specification of the probability distribution of disturbances
Steps of formulating an econometric model:
1.Statement of theory
2.Formulation and specification of econometric models by using observational
or experimental data
3. Obtaining Data
4. Estimation and testing of models using the data
5. Hypothesis testing
6.Forecasting and prediction
7. Use of model for policy making
EconomicTheory
Mathematical model
Econometric model
Data collection and
estimation
HypothesisTesting
Forecasting
Application by creating
a suitable model

6.  Step 1: Statement of economic theory: AccordingTo Keynes,The marginal propensity to consume, the rate of
change of consumption for a unit change in income is greater than zero but less than 1.
 Step 2: Specification of Mathematical model: A positive relationship between consumption and income,
Y=β1+β2X 0<β2<1; whereY=consumption expenditure X= income. Β2 and β1 are parameters as well as
intercept and slope respectively.
Specification of the model:The econometricians have modified the deterministic consumption function.
Y= β1+β2X+u ;Where u is the error terms having well defined probabilities
Step 3: Obtaining data: Obtaining numerical value of β1 and β2
Step 4: Estimation of econometric model: Statistical techniques of regression analysis is the main tool to obtain
these estimates
Step 5: Hypothesis testing:Assuming the null hypotheses that the fitted model is a good approximation of
reality, we have to test whether this is true or not
Step 6:Forecasting: if it abides by the hypothesis, the value of dependent variable(Y) on the known value of
variable X can be predicted.
Step 7: Use of model:The estimated model is used to create policies by the government, e.g. Fiscal or Monetary
policies to control variable X for a desired value ofY.

7.  The β2 measures the MPC.
Consumption is linearly
related to income.The
relationship between
consumption and income is
consumption function.The
variable appearing on left
side( consumption is
dependant while on the right
side, income is an explanatory
variable.

8.  1.Time series data
Time series data give information about the numerical values of same variables from period to period and are
collected over time. For example, the data during the years 1990-2010 for monthly income constitutes a time
series of data.
 2. Cross-section data
The cross-section data give information on the variables concerning individual agents (e.g., consumers or
produces) at a given point of time. For example, a cross-section of a sample of consumers is a sample of
family budgets showing expenditures on various commodities by each family, as well as information on
family income, family composition and other demographic, social or financial characteristics.
 3. Panel data:
The panel data are the data from a repeated survey of a single (cross-section) sample in different periods of
time. Combination ofTime Series data and Cross sectional data.
 4. Dummy variable data
When the variables are qualitative in nature, then the data is recorded in the form of the indicator function.
The values of the variables do not reflect the magnitude of the data.They reflect only the presence/absence
of a characteristic. For example, variables like religion, sex, taste, etc. are qualitative variables.The variable
`sex’ takes two values – male or female, the variable `taste’ takes values-like or dislike etc. Such values are
denoted by the dummy variable.

9.  One of the very important roles of econometrics is to provide the tools for modeling on the basis of given data.
The regression modeling technique helps a lot in this task.The regression models can be either linear or non-
linear based on which we have linear regression analysis and non-linear regression analysis.
 Linear regression model
 Suppose the outcome of any process is denoted by a random variable y , called as dependent (or study) variable,
depends on k independent (or explanatory) variables denoted by X1, X2, ... Xk .Suppose the behaviour of y can be
explained by a relationship given by-
 y= f(X1,X2,….Xk,β1, β2, …..βk)+ε
 where f is some well-defined function and values of β are the parameters which characterize the role and
contribution of values of X, respectively. Ε represents the stochastic relationship between variables.
 A model or relationship is termed as linear if it is linear in parameters and non-linear, if it is not linear in
parameters.
 if all the partial derivatives of y with respect to each of the parameters β1,β2,…..β are independent of the
parameters, then the model is called as a linear model.
 If any of the partial derivatives of y with respect to any of the β1,β2,….βk is not independent of the parameters,
the model is called non-linear.

10.  .Without data and statistics, we cannot analyse how the nation is prospering.
 Without knowing economic status of the country in a nutshell, we cannot solve its
existing problems.

12.  Linear programming is a widely used mathematical modeling technique to determine the optimum allocation of scarce
resources among competing demands.The technique is very powerful and found especially useful because of its
application to many different types of real business problems in areas like finance , production , sales and distribution ,
personnel, marketing and many more areas of management.
 As its name implies ,the linear programming model consists of linear objectives and linear constrains , which means that
the variables in a model have a proportionate relationship. For example ,an increase in manpower resource will result in
an increase in work output.
 Usage in agricultural economics: In linear programming models the objective of the typical farm that is maximization of
net profit or cost minimization is achieved through optimal plan generated from its solution. hence it is that method of
determining the best for optimal plant to a given farm under the given linear constraints.
 the objective function specified that is profit maximization or cost minimization is linear inform and constraints on
resource restrictions are specified in in non linear form for power form
 it has been used in agriculture since 1950s. it provides prudent solutions to hold farm planning.

13. For a given problem situation, there are certain essential conditions that need to be
solved by using linear programming.
 1. Limited resources: limited number of labour, material equipment and finance
 2. Objective: refers to the aim to optimize (maximize the profits or minimize the
costs).
 3. Linearity: increase in labour input will have a proportionate increase in output
 4. Homogeneity: the products, workers' efficiency, and machines are assumed to be
identical
 5. Divisibility: it is assumed that resources and products can be divided into fractions.
(in case the fractions are not possible, like production of one-third of a computer, a
modification of linear programming called integer programming can be used).
 Other assumptions are: additivity of the resources and activities divisibility of the
activities as well as resources finiteness of the activity and resource restriction single
value expectation, non negativity of decision variables etc.

14.  A company manufactures two types of boxes, corrugated and ordinary cartons.The boxes undergo
two major processes: cutting and pinning operations.The profits per unit are Rs. 6 and Rs. 4
respectively. Each corrugated box requires 2 minutes for cutting and 3 minutes for pinning
operation, whereas each carton box requires 2 minutes for cutting and 1 minute for pinning.The
available operating time is 120 minutes and 60 minutes for cutting and pinning machines.The
manager has to determine the optimum quantities to be manufacture the two boxes to maximize
the profits.
 A general representation of LP model is given as follows:
Maximize or Minimize, Z = P1 X1 + P₂ X₂……………..Pn Xn
Subject to constraints,
W11 X₁ +W12 X₂ ..............W1n Xn ≤or =or ≥W₂............ .(i)
W21 X₁ +W22X₂ +......W2nXn ≤ or = or ≥W2…………(ii)
Wm1X₁ +Wm2 X₂+......... .Wmn Xn ≤or = or ≥Wm………..(iii)
Non-negativity constraint, Xi≥0 (where i=1,2,3.....n)

15.  Decision variables completely describe the decisions to be made (in this case, by Manager). Manager must decide how
many corrugated and ordinary cartons should be manufactured each week.With this in mind, he has to define:
X1 be the number of corrugated boxes to be manufactured.
X2 be the number of carton boxes to be manufactured
 Objective function is the function of the decision variables that the decision maker wants to maximize (revenue or profit)
or minimize (costs). Manager can concentrate on maximizing the total weekly profit (z).
Here profit equals to (weekly revenues) - (raw material purchase cost)-(other variable costs).
Hence Manager's objective function is: Maximize z=6X2+4X2
 Constraints show the restrictions on the values of the decision variables. Without constraints manager could make a large
profit by choosing decision variables to be very large. Here there are three constraints:
a. Available machine-hours for each machine
b.Time consumed by each product
c. Sign restrictions are added if the decision variables can only assume nonnegative values

16.  Max Z=6X1 +4X2, (The Objective function)
 s.t. 2X1+ 3X1 ≤ 120 (cutting time constraint)
 2X1+ X2 <= 60 (pinning constraint)
 X1, X2 >= 0(Sign restrictions)
 A value of (X1,X2) is in the feasible region if it satisfies all the
constraints and sign restrictions.
This type of linear programming can be solve by two methods.
 1) Graphical method
 2) Simplex algorithm method

17.  Step 1: Convert the inequality constraint as equations and find co-ordinates of the line.
 Step 2: Plot the lines on the graph.
(Note: If the constraint is a type, then the solution zone lies away from the centre. If the constraint is
type, then solution zone is towards the centre.)
 Step 3: Obtain the feasible zone
 Step 4: Find the co-ordinates of the objectives function (profit line) and plot it on the graph
representing with a dotted line
 Step 5: Locate the solution point
(Note: If the given problem is maximization, Zmax then locate the solution point at the far most point of
the feasible zone from the origin and if minimization, Zmin then locate the solution at the shortest point
of the solution zone from the origin).
 Step 6: Solution type
i. If the solution point is a single point on the line, take the corresponding values of x1 and x2.
ii. If the solution point lies at the intersection of two equations, then solve for x1 and x2 using the two
equations
iii. If the solution appears as a small line, then a multiple solution exists.
iv. If the solution has no confined boundary, the solution is said to be an unbound solution.

18.  The inequality constraint of the first line is (less than or equal to) <= type
which means the feasible solution zone lies towards the origin.
 (Note: If the constraint type is ≥ then the solution zone area lies away from
the origin in the opposite direction). Now the second constraints line is
drawn.
 When the second constraint is drawn, you may notice that a portion of
feasible area is cut.This indicates that while considering both the constraints,
the feasible region gets reduced further. Now any point in the shaded portion
will satisfy the constraint equations.
 the objective is to maximize the profit.The point that lies at the furthermost
point of the feasible area will give the maximum profit.To locate the point,
we need to plot the objective function (profit) line
 Equate the objective function for any specific profit value Z
Consider a Z-value of 6o, i.e.,
6x1+4x2=60
Substituting x1=0, we get x2 =15 and if x2=0,then x1=10
 Therefore, the coordinates for the objective function line are (0,15),(0,10) as
indicated objective function line.The objective function line contains all
possible combinations of values of x1 and x2.
 Therefore , we conclude that to maximize profit , 15 numbers of corrugated
boxes and 30 numbers of carton boxes should be produced to get a maximum
profit. Substituting x1=15 and x2=30 in objective function we get Zmax
=6x1+4x2 =6(15)+4(30)
 Maximum profit : Rs 210.00

20.  So,asfarourbriefdiscussiononthistopic,welearnthowtointegratemathematicsandstatistics
ineconomics,andhowtoapplytheminreallifecasesinourpresenteconomicscenario.
 Inareasliketrade,growthanddevelopmentpatternaswellasmarketbehaviour,econometricsis
essential
 Undesirablesituationscanbeavoidedwiththehelpoftheforecastingnatureofeconometrics.
 Maximumutilizationof resourceswithhighestpossiblereturnscanbeensured.