02 Methodology

Methodology for measuring relationships¶

flowchart LR
et[Hypothesis] -->
mm -->
em -->
dc[(Data<br/>Collection)] -->
Estimation -->
ht[Hypothesis<br/>Testing] -->
Forecasting -->
p[Policy to<br/>affect behavior]

subgraph Model
    mm[Mathematical]
    em[Economic]
end

Theory/Logic¶

Hyphothesis¶

Theoretical assertion whose truth can be tested

Logical reasoning on how variables would be related, ie what could be the factors

This is also called as specification of relationship. We need to make appropriate specification.

An increase in \(x\) will cause an increase in \(y\)

• Null Hypthosis
• Alternate Hypthosis

Problem with social sciences (business, economics, etc) is that there may be number of factors, but it is not feasible to incorporate all the features

Some theories¶

Structural changes¶

Population shifting from primary sector (agriculture) to secondary sector(manufacturing, construction)

Economic sectors are highly-interconnected.

flowchart LR

Primary -->
|Inflation of Raw Materials| Secondary -->
|Inflation of Tools| Primary

Population Sentiment¶

People will spend money because they feel secure.

Govt¶

Govt gives out many schemes and development projects, in order to mitigate the effect of decreased private interest.

Moral Hazard¶

Insurance will actually cause people to be less cautious.

Check in India if the direct monetary support to infected bank agents actually increased the amount of cases.

Mathematical Model¶

Expressing theory in terms of mathematical equations.

❌ Assumes that the relationship is perfect

Let’s say that, height of wife is a function of height of husband, but not vice-versa; it is a male-dominated society

• height of husband is independent
• height of wife is dependent

Let’s say that, height of wife is a function of height of husband, but vice-versa is also applicable, then it is a equal society.

• height of husband is independent
• height of wife is independent

Econometric Model¶

Similar to Mathematical Model, but understands that relationships are not perfect. There will remain some change unexplained by our mathematical model.

The real world is complex and continuously changing, but human knowledge is limited.

Specifying inexact relationships¶

• \(y\) is actual value of the dependent variable

• \(\beta_1 + \beta_2 x\) is the estimated/forecasted/predicted component of \(y\)

  • \(B_1\) is the value of \(y\) even when \(x=0\) It is the value of \(x\), that is independent of \(x\)

  • For eg, consumption can be non-zero even if income is 0 (called as autonomous consumption spending)

  • \(B_2\) is the change in \(y\) for a unit change in \(x\)

• \(u\) is the residual/error/disturbance/unexplained component of \(y\)

  • difference between estimated value and actual value
  • component not explained by your initial mathematical model in terms of only \(x\)
  • it is different for each point

Linear vs Non-Linear Model¶

We have to decide based on theory and logic

If you are not aware about the theory, then visualize and use trial-error

Types of Regression¶

Data¶

Why do we need data?¶

To estimate numerical values, we need data.

Types¶

Basics - Refer other notes

• Cross Sectional Data

  • Marks of all students in 1 year

• Time Series Data

  • Marks of 1 student from all years

• Panel Data

  • Marks of all students from all years

• Scale Data

  • Qualitative data
  • Ratings: Good-Poor

Sources of Data¶

Primary Data¶

Data collected on your own, using sensors/surveys

Secondary Data¶

Data collected by someone else

Data Frequency¶

How often the data is collected

• High Frequency: Stock Prices (recorded every second)
• Low Frequency: GDP (recorded monthly)

High Frequency data is preferred over Low Frequency¶

This is because, monthly data does not capture small changes appearing between 2 time periods, those small changes may not even be visible if you collect low frequency data.

Data Quality¶

We must check the following properties of the data

• Verify Characteristics
  • Mean
  • Standard Deviation
  • Skewness

• Ensure Reliability

  • Sensors are working correctly
  • Calculations were made correctly

• No Bias

  • There should be no researcher bias

  • Picking a particular sample

  • Ensuring participants of survey have been unbiased

  • For ex: Satisfaction of students in UAE

Sample Estimation¶

Obtain the values of parameters/coefficients, using a sample of data

Types¶

We have to choose a method based on

• Nature of relationship
• Distribution of variables

OLS¶

Assumes normal distribution

Finds the best fit to reduce error term

Maximum Likelihood¶

Assumes normal or other distribution

Finds the best fit to pick the data point corresponding to highest probability of occurance for each data point

Hypothesis Testing¶

Testing if our hypothesis holds true

Is our sample representative?

Sample Evidence and Statistical Inference¶

Is estimated value statistically closer to hypothesized/assume value?

Here, we are only interested in the existence of a relationship.

• \(H_0: B_1 = 0\) (there exists a relationship)
• \(H_1: B_1 \ne 0\) (there exists no relationship)

Localization of Hypothesis¶

Forecast/Prediction¶

Using the estimated equation

Types¶

Evaluation¶

Error is the deviation between predicted and actual value

Policy Purpose/Impact Analysis¶

Understand the impact of a policy decision

Multiplier¶

An initial increase in income will increase the aggregate income to \(M\) times the initial aggregate income.

Disposal Income¶

Income ready for spending

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