Question

As an Econometrics student, you have just been hired by the new Zambian government to evaluate the relationship between monetary policy rate and economic growth.

(I) Derive the OLS estimator for the intercept and slope to test the relationship between monetary policy rate and economic growth.

(II) What are the properties of these estimators?

(III) What steps will you undertake to obtain empirical evidence of the relationship between monetary policy and economic growth as well as be able to comment on the decision?

Answer 1

Step 1

1. The relationship between both variables may be studied by incorporating the econometrics model of regression. This is possible by using the OLS estimation method of regression. The economic growth of an economy is a dependent factor on the persisting monetary policy in that economy. Hence, economic growth is a dependent variable and monetary policy is an independent one.

For proceeding with OLS estimation we have basic requirements fulfilled of dependent and independent variables, now we'll modulate this-

$$ Y_{i t}=a_{0}+a_{1} \cdot X_{i t}+\varepsilon_{i t} $$

where, \(Y\) is for dependent variable, \(X\) is for independent variable and e for error term for the respective period of study.

However, the first term on the right hand side of the equation ' \(a 0^{\prime}\) is the intercept term and the coefficient of \(\mathrm{X}^{\prime} \mathrm{a} \mathrm{l}^{\prime}\) is the slope. Given the details, related to a situation, we can proceed with the regression estimation.

Precisely, the model depicting the relationship between monetary policy and economic growth will be-

$$ G D P_{i}=a_{0}+a_{1} . \text { Monetary policy variable }+\varepsilon_{i} $$

Since growth rates of an economy are measured through its GDP only so we've replaced it here. But for the monetary policy variable, we have four different instruments of monetary policy as it's sub-part and these are-

a. International reserve

b. Money and quasi-money

c. Interest rate

d. Required reserve ratios

So, by inculcating all these variables we can reframe our \(\underline{\text { OLS model as follows- }}\)

$$ G D P_{i}=a_{0}+a_{1} \cdot I R_{i}+a_{2}, M M_{i A}+a_{3} \cdot l R_{n}+a_{4} \cdot R R_{i x}+\varepsilon_{i t} $$

Hence, this is the required answer.

Step 2

2. The ultimate properties of the OLS regression estimators are given by BLUE i.e. best minimum variance, linear, and an unbiased estimator.

LINEAR-

This is the foremost requirement of an OLS estimator. This implies that OLS estimators should be linear only with respect to the dependent variables.

UNBIASEDNESS-

The estimator should ideally be an unbiased estimator of true parameter/population values. That is, for any of the coefficients, its expected value must always equate to the actual value.

The above-mentioned two properties are necessary ones to be fulfilled before carrying out the regression but these are not sufficient ones.

BEST MINIMUM VARIANCE-

It is believed that estimators with the least variance will have individual data points closer to the mean and this is why such variables are likely to give more accurate results.

Step 3

3. In order to solve for the practical implication of this model depicting the relationship between economic growth and monetary policy we are likely to follow the following steps:

Step-1: We first need to identify the instruments specifically for the economy we're concerned with. And will formulate our model accordingly.

Step-2: After identification and selection of the instruments of monetary policy, we'll get the list of independent variables in our model.

Step-3: Before proceeding with the OLS regression method, we'll first check for the "BLUE" properties of the estimators.

Step-4: Now after successfully getting the variables with all the properties, we'll now proceed with the regression model in order to get the regressed values of the variables and expected values of the coefficients.

Step-5: Finally, we'll interpret the results of the model.