Econometrics - What is Econometrics?

Question 1

What’s ‘Econometrics’?

Answer 1

The interaction of economic theory, observed data and statistical methods

Question 2

Explain the importance of Econometrics

Answer 2

Economic theory tends to make qualitative statements about the relationships between economic
variables, e.g. we know that if the price of a good decreases then the demand for that good should
increase, ceteris paribus, or that the more education an individual receives, the more money they
will earn. These theories do not provide a numerical measure of the relationship; they simply state
that the variables are linked and whether the relationship is negative or positive. It is the
econometrician’s job to provide the numerical or empirical content to the economic theory.
Econometricians are therefore responsible for the empirical verification of economic theories. To
do this they use mathematical equations to express economic theories and use real economic data
to test these theories.

Question 3

Describe how the methodology in Econometrics might follow. Then, apply this methodology to Keynesian theory of consumption

Answer 3

1. Statement of economic theory or hypothesis
2. Specification of the theory in an equation
3. Specification of the econometric model
4. Obtaining the data
5. Estimation of the parameters of the econometric model
6. Hypothesis testing
7. Beyond inference

Let’s consider each step using a particular economic theory, the Keynesian theory of consumption.
1. The theory is that on average, people increase their consumption as their income increases,
but by a smaller amount than the increase in income. Essentially, Keynes was stating that the
relationship is positive (income and consumption move in the same direction) and that the
Marginal Propensity to Consume (MPC) which measures how much of a rise in income gets
consumed, is less than 1 (consumption increases by less than the increase in income).
2. The economist might suggest a simple way to specify this Keynesian consumption function
using the equation of a straight line as follows:
𝑌 = 𝛽0 + 𝛽1𝑋 (1)
J. S. Ercolani
What is Econometrics?
2
In this function we call 𝑌 the dependent variable (in this case consumption) and 𝑋 is the
explanatory variable, sometimes called the regressor (in this case income). Equation (1) explicitly
states the direction of causality, i.e. changes in income determine changes in consumption, not
the other way around. The terms 𝛽0 and 𝛽1 are the parameters of the model. The 𝛽0 parameter
is the intercept coefficient and 𝛽1 is the slope coefficient. The slope is very important as it
reflects how much influence the 𝑋 variable has on the 𝑌 variable. In the consumption function
above, 𝛽1 is interpreted as the MPC because it is the coefficient on income and so directly
reflects how income affects consumption. We would expect 0 < 𝛽1 < 1 to signal both the
positive relationship between income and consumption (𝛽1 > 0) and the MPC being less than
one (𝛽1 < 1).
In a diagrammatic representation of this, the function is upward sloping.X (income)
Y (consumption)0 =1 MPC
3. Equation (1) is an exact relationship. In practice however, economic relationships are rarely
exact. If we could collect data on income and consumption for many different households, it
is unlikely that all households would lie exactly along the line drawn above. Firstly, income is
not the only determinant of consumption (the model is a simplification of true economic
behaviour) and secondly there is randomness in human behaviour such that two people on
the same income do not necessarily consume the same amount. So, equation (1) and the
diagram depict the general trend of the relationship between the two variables, rather than the
behaviour of each individual. To reflect that the economic relationship is not exact, we
transform (1) into an econometric model by adding a disturbance or error term so that
𝑌 = 𝛽0 + 𝛽1𝑋 + 𝜀 (2)
The term is a random variable, also called a stochastic variable. It is used to represent all
of the factors that affect consumption that we have not included explicitly in the model
(maybe because they are variables that cannot be measured or observed) as well as the fact
that there is inherent randomness in people’s behaviour.
J. S. Ercolani
What is Econometrics?
3
4. The next step is to collect data that are relevant to the model. In this example, we would
collect data on consumption and income. You can find many sources of economic data on
the internet. For the consumption function example, one could do a micro-level analysis by
using data on the income and consumption behaviour of the individuals living in a particular
country. This would be called a cross-sectional regression. Or one could do a macro-level analysis
using aggregate economy data where the data are observed over time, say 1950-2016. This
would be a time-series regression.
5. Once you have specified your model and have an appropriate set of data, we bring the two
together and estimate the unknown parameters 𝛽0 and 𝛽1 in the regression model. This is one
of the main topics of this module and we will deal with the procedures used for estimation in
detail later. For now, let’s suppose that we have applied an estimation technique and our
estimates are 𝛽̂0 = 184.28 and 𝛽̂1 = 0.71, so that the estimated model can be written as
𝑌̂𝑖 = 184.28 + 0.71𝑋𝑖
where the ^ denotes an estimated value. The 𝑖 subscript here denotes the individuals over
which the data are observed. If we have 1000 people in our sample, so 1000 pairs of
observations of income and consumption, then 𝑖 = 1, … ,1000. We have now provided some
empirical content to Keynes’ theory. The parameter 𝛽1 represents the MPC, and this has been
estimated to have a value of 0.71. This means that for every £1 increase in income, on average
this leads to an increase in consumption of 71p (assuming the data are for individuals who
live in the UK).
6. Once we have estimated the parameters as above, we can test various hypotheses to see if the
economic theory actually holds. In this case, Keynes’ theory was that the MPC is positive but
less than 1. Although the value obtained is 0.71 and therefore satisfies the requirements, we
need to ensure that the value is sufficiently above 0 and sufficiently below 1 that it could not
have occurred by chance or because of the particular data set that we have used. What we
want to make sure of is that 0.71 is statistically above 0 and statistically below 1. This is where
hypothesis testing comes in. Again, we will not go into details here but this does form another
major component of this module.
7. Beyond this inference, once we have shown that the economic theory stands up to empirical
scrutiny, econometricians can use their estimates to predict values for the dependent variable
based on values of the explanatory variable(s). Ultimately the inference may help government
to formulate better policies. From simply knowing the value estimated for the MPC the
government can manipulate the control variable 𝑋 to produce a desired level for the target
variable 𝑌