Static econometric model
A static econometric model is an econometric model in which the explanatory variables do not present lags.
The concept of a static econometric model as a distinction from a dynamic econometric model makes sense with time series data. In other words, there are models that present lags in explanations: dynamic econometric models. And, on the other hand, there are models that do not present lags in the explanatory variables: static econometric models. From now on, it will be the static econometric model that we will refer to at all times.
In this sense, to understand the term well, the essence of an econometric model must first be explained. And secondly, the concept of static can be written clearly and concisely.
An econometric model
A static econometric model is one in which all the explanatory variables contain data at the same moment in time. That is, it has the form:
Like all econometric models, this model contains the following variables:
Y: It is the explained variable. It can be any economic variable that we intend to predict, estimate or explain.
Beta zero: It is the constant term in the equation, it has no economic meaning. Its inclusion in the equation is for mathematical reasons.
Beta one: It is the coefficient whose value explains the relationship that the explanatory variable x1 has on the explained variable Y.
X1: As we have said before, it is one of the variables that tries to explain the behavior of the variable Y.
Beta two: It is the coefficient whose value explains the relationship that exists between the explanatory variable x2 and the fluctuations of the variable Y.
X2: It is the second variable that tries to explain the behavior of Y.
Subscript 't': refers to time. That subscript could well take values of a certain year or of a certain month. Later, in the example, we will see a case applied to economic reality.
In this regard, it is worth mentioning that, to properly understand and assimilate this concept (the static econometric model) it is essential to master the concepts of: Econometric model and regression model.
Now, having the concept of a clear econometric model, it is worth shedding light on the concept of ‘static’. In the case of the static models, there are no lags in the explanatory ones.What does it mean that there are no delays? It means that, if the variable Y is data from year 1, then the data from X1 and X2 will also be data from that same year, year 1. In the same way, if we want to explain the value of variable Y in the year 2, then we will use data from X1 and X2 from year 2. That is, from the same year.
Static Econometric Model Example
Suppose we have an econometric model that tries to explain the Gross Domestic Product (GDP) of a country. To explain it, we will use as explanatory variables two indices on unemployment rate and industrial production. We will work with indexes to simplify the example.
The model in question would be mathematically how:
GDP: It is the explained variable, it represents an index on the Gross Domestic Product.
Desem: It is the first explanatory variable, it refers to an index on the country's unemployment.
Prod: It is the second explanatory variable, and it is an index on the industrial production of that country.
t: Represents the reference year
Once the model has been calculated, let's imagine that the coefficients are such that:
Taking into account the above, why do we know that it is a static econometric model? Because all variables are found at the same moment in time: the 't' moment.
Next we are going to see several examples to see how the model is interpreted:
This means that the 1980 GDP index is explained in terms of this equation and its values. That is, keeping everything else constant, if the unemployment variable had been greater by one unit in 1980, the GDP variable would have been reduced by 0.36 units (note the minus sign in front of it).
On the other hand, keeping everything constant, if that same year, 1980, industrial production, instead of having the value it presents, had presented one more unit, the GDP variable would have increased by 0.68 units in 1980.
This means that the 1985 GDP index is explained in terms of this equation and its values. That is, keeping everything else constant, if the unemployment variable had been a larger unit in 1985, the GDP variable would have been reduced by 0.36 units (note the minus sign in front of it).
On the other hand, keeping everything constant, if that same year, 1985, industrial production, instead of having the value it presents, had presented one more unit, the GDP variable would have increased by 0.68 units in 1985.
Ultimately, from these last two examples, we come to a clear conclusion. Whatever year you want to see in the model, the explanatory variables will contain data from the same year as the explained variable. In other words, the values of all the variables, both explained and explanatory, are found at the same moment in time.
It is recommended to read: Dynamic econometric modelMathematical model