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Topic: Subject, method and problems "econometrics"
Summary of the lesson:
Econometrics and its place among mathematical statistics and economic
theory
Basic concepts of econometric modeling
Main applied purposes of econometric researches
Basic stages of econometric researches
1. Econometrics and its place among mathematical statistics and economic
theory
The name "econometrics" was introduced in 1926 by the Norwegian economist
and statistician R. Frisch. In the USSR econometrics was not taught, as there was no
base for it: there was no high-grade economic theory, and there was no objective
economic statistics. Now this situation has changed, economic theory "was allowed"
and there was a necessity for market economy analysis. Since 1992 econometrics
has been taught in Moscow State University.
Let's define the following.
Econometrics is a science which gives a concrete quantitative expression to
the qualitative laws caused by economic theory. For this purpose econometrics
uses economic theory, economic statistics and mathematical statistics.
The basic product of activity of an econometrician is an econometric model.
An econometric model is a statistical model describing functioning of a
concrete economic system.
For example, economic theory considers production functions to be an abstract
production mode. A concrete production function describing the economy of the
Astrakhan area during last 25 years is an econometric model.
Economic theory reveals objective qualitative laws and connections between
economic parameters and offers some approaches to their formalization. It plays the
main role in econometric model creation.
Economic statistics gives information for estimating econometric models. An
econometrician often makes the work of a statistician, but we are not going to touch
this part of his activity in the book.
Our attention will be concentrated on application of mathematical statistics to
economic event investigations. We will touch upon the following sections of applied
statistics.
Regression analysis.
The analysis of time series.
The systems of simultaneous equations.
We will pay great attention to the analysis of accuracy of constructed models.
2. Basic concepts of econometric modeling
The following concepts concern the basic points of econometric modeling.
Initial statistical data.
Variables.
Function of regression.
The equation of regression.
Initial assumptions.
Initial statistical data in general are represented as a sequence of matrixes
«object - property».
The top index is the number of property, an attribute or a parameter. The bottom
index is the number of observation or an object. Letter t designates the moment of
time.
In such a general view the data are rarely used. One of the following special
cases is more often used.
Cross-sectional data.
Time-series data.
Cross-sectional data appears, when the moment of time is fixed, i.e. the data are
gathered only once, and there are a lot of objects of inspection. Time-series data
appears, when there is only one object of inspection, and the data are gathered
repeatedly, for example, annually. Time series have a lot of features, but in the
beginning we will operate with them as with cross-sectional data. Thus the moment
of time will play the role of an observation number. Only in the second part of our
book we will take up the theory of time series in details.
Let's describe economic system functioning by the following sets of variables.
Explanatory variables.
Independent variables.
Regressors.
Exogenous variables.
This group of variables describes system functioning conditions with their
values fixed on the system entrance.
Dependent variables.
Endogenous variables.
This group of variables characterizes results of system functioning. The
efficiency of real system functioning is described by a number of interconnected
resulting parameters; however in the beginning we will consider models which have
one dependent variable. It will allow to essentially simplify the model and to reveal
most important points in the econometric model study.
Disturbance terms.
Disturbance terms determine a specific character of econometric models as
statistical models.
It is possible to represent the set of variables describing an econometric model
on the following scheme in which the economic system itself is considered as «a
black box».
The following element of an econometric model is the function of regression.
The function of regression describes the change of the conditional expected
value of a dependent variable according to the change of explanatory variables.
The construction of the function of regression is the main task in econometric
model construction.
The equation of regression:
The main problem of econometric modeling is to find out which items bring the
greater contribution to y value formation. If the basic contribution is made with the
function of regression, and the contribution of a disturbance term is insignificant,
then the constructed model describes the behaviour of a dependent variable well. If
the basic contribution is made with a disturbance term, the quality of the model is
unsatisfactory.
Initial assumptions are one more element of an econometric model. They can
refer to various parts of a model, but basically they describe prospective behaviour
of a disturbance term.
Example.
The dependence of a monthly increase of savings (y) depending on monthly
income (x) is considered in the example. Within the investigation individuals with
the income of 5, 10, 20 and 40 thousand rubles were sorted out. The increase of
savings was also measured in thousands of rubles. The data of the investigation are
given in the table below.
Let's represent the initial data on the graph.
We see that at the fixed value of х values of y are subjected to some random
scatter. At the same time it is possible to see some tendency describing the
dependence of y on х. It is possible to assume, that the increase of savings is
proportional to squared income, i.e. the equation of regression looks like the
following
In this equation α and β are unknown parameters which are estimated according
to initial statistical data.
3. Main applied purposes of econometric researches
Basically there are two purposes of this kind.
Forecast.
Investigation and management.
The vast majority of econometric researches are carried out to forecast the
values of dependent variables according to known values of explanatory variables.
Confidential intervals are usually constructed here. To solve this problem the
function of regression itself has the subordinated value. Only the values of function
are of any interest here. The solution of the problem is usually interesting from the
practical view point.
Occasionally econometric models are made to reveal causal relationships
between explanatory variables and dependent variables. Revealed causal
relationships are used to fulfill the purpose of management. The choice of the
correct type of the function of regression plays the main role. First of all, such
researches represent scientific interest.
4. Basic stages of econometric researches
Basic stages of econometric researches are the following
Installated stage.
An aprioristic stage.
An information stage.
Correlation analysis.
Specification.
Identifiability.
Identification.
Verification.
At an initial stage the researcher defines: 1) purposes of the research; 2)
economic parameters; 3) the set of objects of the research; 4) the set of objects
which will be affected with the results of the research; 5) expenses. The leading role
at this stage is played by the customer.
An a priori stage consists of substantial essence analysis of a modeled
phenomenon, the formulation of hypotheses and initial assumptions. This stage
exists in customer - econometrician interaction.
An information stage is statistical data gathering.
Correlation analysis allows us to answer whether in general there is any
connection between variables and in case there is some how close it is. This stage is
almost completely automated.
At the stage of specification the class of functions which the function of
regression belongs to is sorted out. After such a choice the function of regression
depends on lines of parameters which numerical values are unknown and are subject
to estimation. This stage is the most difficult and the least developed. Here it is
necessary to take into account economic theory. At this stage the cooperation of the
subject expert and econometrician is required.
The problem of identifiability consists in the following: whether it is possible to
establish exact values of unknown parameters of the model with the data available.
If not, we come back to the stage of specification. There are two principal causes
preventing from parameter defining. The first is insufficient quantity of
observations. The second is the dependence of variables on each other. Both these
reasons create deficiency of information. At this stage an econometrician’s skills are
important.
Identification is a calculation of estimation of unknown parameters. This stage
includes a choice of criteria of approximation quality, and then estimations of
unknown parameters are searched as the solution of an extreme problem of the
criterion optimization. This stage should have good mathematic and software
maintenance.
Verification is the act of control of model adequacy and the analysis of its
accuracy. Adequacy is model conformity with objective reality. Let’s assume that
the dependence of demand for some goods on a set of other parameters was studied,
and the factor at a price index appeared positive. It means that the increase of price
causes demand increase. Such conclusion contradicts economic theory. Probably
while constructing the model we made a mistake. The constructed model only
approximately describes real economic system. Therefore the calculated estimations
of factors and forecasts have rough character as well. Hence it is necessary to
investigate the accuracy of these estimations and forecasts.