BACHELOR OF COMMERCE (HONS) DEGREE IN FINANCE
INTRODUCTION TO FINANCIAL ECONOMETRICS AND DATA
ANALYSIS [CFI 4208]
(2022)
LECTURER – Z. CHIKAZA
Introduction
▪ The application of mathematical statistics to
economic data to lend empirical support to models
constructed by mathematical economics and to
obtain numerical estimates (Samuelson et al.,
Econometrica,1954).
▪ Financial econometrics is the application of
statistical techniques to problems in finance.
▪ It is the quantitative measurement and analysis of
actual economic and business phenomena.
▪ Econometrics is used for:
– Estimating Economic Relationships
– Testing Economic Theories
– Evaluating & Implementing Policy
– Forecasting
What Econometrics Addresses
▪ There are three basic types of econometric
questions namely:
⮚ Descriptive Questions - Descriptive statistics is
analysis of data that helps describe, show or
summarize data in a meaningful way such that
patterns might emerge from the data. Eg
⮚How much do men and women earn annually on
average in the Zimbabwe?
▪ Forecasting Questions - is the process of
making predictions for the future.
⮚Which Political Party will wins elections in
Zimbabwe in the next 10 years?
⮚What is the expected growth of GDP for SSA
countries in the next 2 years?
▪ Highly visible applications of forecasts are
macroeconomic indicators (interest rates,
inflation, GDP etc.)
▪ Causal Questions - Causation or causality is the
capacity of one variable to influence another.
⮚If the federal reserve lowers interest rates
today, what will happen to inflation
tomorrow?
⮚How much more money will you earn as a
result of taking this course?
▪ The presence of a causal link is suggested by
economic theory (or common sense), the goal
of econometric analysis is either to empirically
verify or quantify this causal link.
Types of Economic Data
▪ All empirical analysis requires data. There are
different structures of data that you come
across if you do empirical analysis in economics:
▪ The special features of the data sets must be
accounted for or should be exploited to make
correct predictions.
⮚Cross-sectional data
⮚Time series data
⮚Pooled cross sections
⮚Panel (or longitudinal) data
Cross-Sectional Data
▪ A cross-sectional dataset consists of a sample of
individuals, households, firms, … taken at a
given point in time
▪ Cross-sectional datasets are often obtained
from random sampling from the underlying
population.
▪ Cross-sectional data are usually collected from
respondents making up the sample within a
relatively short time frame (field period).
▪ In a cross-sectional study, time is assumed to
have random effect that produces only
variance, not bias.
Example 1
Example 2
Time Series Data
▪ A time series data set consists of observations on
one or several variables over time.
▪ Unlike the arrangement of cross-sectional data,
the chronological ordering of observations in a
time series is important.
▪ A key feature of time series data that makes them
more difficult to analyze than cross-sectional data
is that observations are unlikely to be
independent over time.
▪ One can quote numerous examples: monthly
unemployment, weekly measures of money
supply, daily closing prices of stock indices, and so
on.
▪ The interval between observations can be any
time interval (hours within days, days, weeks,
months, years, etc).
Example
Some examples of time series are:
▪
▪
▪
▪
Monthly closings of the stock exchange index
Malaria incidence or deaths over calendar years
Daily maximum temperatures
Hourly records of babies born at a maternity
hospital
Pooled Cross-Sections
▪ Some datasets have both cross-sectional and
time series features.
▪ Example: household surveys from 1985 and
1990 which are combined to yield one dataset
containing observations from both years.
▪ May be a useful basis for analysis of change of
policy, for example, we often include time (year)
as an additional explanatory variable in
regressions based on pooled cross-sections
Panel Data / Longitudinal Data
▪
Panel
Data
is
data
in
which
we
observe
repeated
cross-sections
of
the
same individuals.
▪ Fortunately all of the standard techniques and
analysis in econometrics are equally valid for time
series and cross sectional data
▪ Have dimensions of both time series and cross sections
▪ Examples:
⮚ Annual unemployment rates of each state over
several years
⮚ Quarterly sales of individual stores over
several quarters
⮚ Wages for the same worker, working at several
different jobs
Example
▪ The key feature of panel data is that we
observe the same individual in more than one
condition.
▪ In pure panel data, we are following the same
units i.e. the same households or individuals
over time.
Steps in Empirical Model Building
▪ There is need to come up with an appropriate
economic analysis to have reliable results.
1. Formulate the Question of Interest.
▪ The first important step in conducting any
regression analysis is to specify the problem
and the objectives to be addressed by the
regression analysis.
▪ The wrong formulation or the wrong
understanding of the problem will give the
wrong statistical inferences.
▪ The choice of variables depends upon the
objectives of study and understanding of the
problem.
2. Choice of Relevant Variables
▪ It has to be kept in mind that the correct
choice of variables will determine the
statistical inferences correctly.
▪ For example, in any agricultural experiment,
the yield depends on explanatory variables
like quantity of fertilizer, rainfall, irrigation,
temperature etc.
▪ These variables are denoted by 1 2 , ,..., XX Xk
as a set of k explanatory variables.
Step 3: Collection of data on relevant variables
▪ One important aspect is to collect data on such
relevant variables.
▪ The data is essentially the measurement on
these variables.
▪ It is also important to decide that whether the
data has to be collected on variables as
quantitative variables or qualitative variables.
Step 4: Find a suitable economic model.
▪ The experimenter or the person working in the
subject usually help in determining the form of the
model.
▪ If a model contains only one explanatory variable,
then it is called as simple linear regression model.
▪ When there are more than one independent
variables, then it is called as multiple regression
model.
▪ When there are more than one study variables, the
regression is termed as multivariate regression.
▪ The simple and multiple regression are determined
by the number of explanatory variables whereas
univariate and multivariate regressions are
determined by the number of study variables.
Step 5: Choice of method for fitting the data
▪ After the model has been defined and the data have
been collected, the next task is to estimate the
parameters of the model based on the collected data.
▪ This is also referred to as parameter estimation or
model fitting.
▪ The most commonly used method of estimation is the
ordinary least squares method (OLS)
▪ Under certain assumptions, the least squares method
produces estimators with desirable properties.
▪ The other estimation methods are the maximum
likelihood method, ridge method, principal
components method
Step 6: Fitting of model
▪ The estimation of unknown parameters using
appropriate method provides the values of
the parameter.
▪ Substituting these values in the equation gives
us a usable model and this is termed as model
fitting .
▪ The fitted equation is used for prediction.
Step 7: Model criticism and selection
▪ The validity of statistical method to be used
for regression analysis depends on various
assumptions.
▪ These assumptions become essentially the
assumptions for the model and the data.
▪ The quality of statistical inferences heavily
depends on whether these assumptions are
satisfied or not
▪ The validation of the assumptions must be
made before drawing any statistical
conclusions.
EMPIRICAL ECONOMIC ANALYSIS
▪ They come into play either when we have an economic
theory to test or when we have a relationship in mind
that has some importance for business decisions or
policy analysis.
▪ Econometrics should always be linked to economic
reasoning
▪ An empirical analysis uses data to test a theory or to
estimate a relationship
▪ A common goal for applied economists is to estimate the
causal effect of one variable on some outcome of
interest.
▪ Ceteris paribus: other relevant factors being equal,
what is the effect of…
⮚ Price increase on consumer demand
⮚ Training on worker productivity
▪ In economic thinking, causal relations are
strongly
connected
with
the
notion of ceteris paribus (other things being
equal)
▪ example: consumer demand analysis –
increasing a price makes consumers buy less
ceteris paribus (however, if other factors change,
anything can happen)
▪ Therefore, if one could run an experiment with
ceteris paribus conditions enforced, it would be
easy to verify and evaluate the causal link.
Economic Model of Crime - Example
▪ Econometric model to specify the crime rate
1. crime is the frequency of criminal activity,
2. wagem is the wage that can be earned in legal
employment,
3. othinc is the income from other sources (assets,
inheritance)
4. freqarr is the frequency of arrests for prior infractions (to
approximate the probability of arrest)
5. freqconv is the frequency of conviction
6. avgsen is the average sentence length after conviction.
▪ The term u contains unobserved factors, such
as the wage for criminal activity, moral
character, family background and errors in
measuring things like criminal activity and the
probability of arrest.
Points to consider when using models
▪ Does the work involve testing or developing theory or
it is merely a technique to motivate certain issues.
▪ Are data of good quality and is it from a reliable
source and is the size of the sample large enough for
the model estimation task at hand.
▪ Have the techniques been validly applied. Have tests
been conducted for possible violations of any
assumptions made in the estimation of the model.
▪ Have the results been interpreted sensibly. Is the
strength of the results exaggerated . Do the results
actually obtained relate to the questions posed by
the author.
▪ Can the results be replicated by other researchers.
▪ Are the conclusions drawn appropriate given results
have been overstated.
Is Econometrics Necessary?
▪ Despite inherent inaccuracies in trying to use the
regression analysis, econometrics drives policy
setting and planning
▪ Econometrics is necessary to move forward in
today’s
ever-changing and highly interactive
business environment.
▪ It enables policy makers to formulate a skilful mix of
quantitative methods
which enable sound
judgement for the benefit of our economies.
▪ In most organizations, we find financial experts who
through ignorance
and fear of quantitative
techniques and computers
relies solely on
qualitative and fail to formulate good policies.
▪ Econometrician may acquire skills in
sophisticated data manipulation skills but
unwilling to relate that to the needs of the
organization.
▪ Analysis, judgement, common sense and
business experience should be combined to
generate good decisions for the firms.
Macroeconomic Considerations
▪ There is also a growing interest for predicting
or forecasting important variables for the
entire economy.
▪ Economic policy is based on projections of
important economic indicators.
▪ It is very necessary to improve forecasting
techniques
to
improve
economic
performance especially for African Economies.
TYPES OF FINANCIAL ECONOMETRICS
▪ Econometrics may be divided into two broad
categories: theoretical econometrics and
applied econometrics.
▪ Theoretical econometrics is concerned with
the development of appropriate methods for
measuring economic relationships specified
by econometric models. In this aspect,
econometrics leans heavily on mathematical
statistics.
▪ In applied econometrics we use the tools of
theoretical econometrics to study some
special field(s) of economics and finance, such
as the production function, investment
function, demand and supply functions,
portfolio theory etc.
▪ Applied econometric methods will be used for
estimation of important quantities, analysis of
economic outcomes, markets or individual
behaviour, testing theories and for
forecasting.
Classical
▪ The philosophical approach to model-building
used here throughout is based on classical
statistics.
▪ This involves postulating a theory and then
setting up a model and collecting data to test
that theory
▪ Based on the results from the model, the
theory is supported or refuted
Bayesian
▪ Here, the theory and model are developed
together
▪ The researcher starts with an assessment of
existing knowledge or beliefs formulated as
probabilities known as priors
▪ The priors are combined with the data into a
model
▪ The beliefs are then updated after estimating the
model to form a set of posterior probabilities (the
statistical probability that a hypothesis is true
calculated in the light of relevant observations).