Arrays & Vectorisation

ECON 3209 · Week 3, Lecture 1 · Kerala Agricultural University

Department of Development Economics, KAU

Autumn 2026

Learning Outcomes

By the end of this lecture, you will be able to:

1. Create and inspect NumPy arrays using ndarray
2. Index and slice arrays efficiently
3. Perform element-wise vectorised operations
4. Use boolean masks and broadcasting in economic examples
5. Explain why vectorisation is valuable in econometrics

Why NumPy for Economics?

• Economic data often comes as columns of numbers
• Python lists are flexible but not ideal for heavy numerical work
• NumPy stores numbers in efficient arrays called ndarray
• It supports fast vectorised operations on entire datasets
• Most scientific Python libraries are built on top of NumPy

In econometrics, NumPy lets us think in vectors and matrices rather than one observation at a time.

Creating Arrays

• np.array() converts a Python list into an array
• np.zeros() and np.ones() create standard arrays quickly
• np.arange() is useful for evenly spaced integer sequences
• NumPy arrays usually contain one numeric type throughout

Shape, Size, and Data Type

• .shape tells us rows and columns
• .size counts total elements
• .ndim shows number of dimensions
• .dtype tells us the numeric type such as int64 or float64
• These properties matter when preparing data for models

Indexing and Slicing

• NumPy uses zero-based indexing like Python lists
• Slices use the pattern [start:stop]
• The stop position is excluded
• Indexing and slicing help isolate years, districts, or variables

Vectorised Arithmetic

• Operations happen element by element
• No explicit loop is needed
• This is called vectorisation
• It is faster and often easier to read than manual looping

Broadcasting

• Broadcasting lets NumPy combine arrays of compatible shapes
• A single number can be applied to every element of an array
• This is useful for inflation adjustments, tax changes, or subsidies
• NumPy expands smaller objects automatically when rules match
• Understanding shapes prevents broadcasting errors

Boolean Masks

• A boolean mask is an array of True and False
• It filters values using economic rules
• This is a powerful alternative to writing manual loops
• We often combine masks when cleaning or subsetting data

Vectorised Growth Calculations

• deposits[1:] means all but the first observation
• deposits[:-1] means all but the last observation
• Vectorisation lets us compute growth for all adjacent years at once
• This pattern appears in finance, prices, and productivity analysis

Why Vectorisation Beats Manual Loops

Conceptual Benefits

• Closer to mathematical notation
• Less repetitive code
• Easier to combine with linear algebra
• Lower chance of indexing mistakes

Practical Benefits

• Faster for large datasets
• Works well with pandas and statsmodels
• Easy to debug intermediate arrays
• Standard in scientific Python workflows

Applied Example: Fertiliser Subsidy Shock

• Here each district has its own subsidy rate
• NumPy still handles the operation element by element
• This is a natural way to model policy differences across observations
• Arrays make policy simulation much easier

Exercise

Create a NumPy array called yields with values 3000, 3200, 2900, 3600, 3400.

1. Add 200 to every value to represent improved irrigation.
2. Create a boolean mask for yields above 3300.
3. Print only the improved yields above 3300.

Summary

• ✅ NumPy arrays store numerical data efficiently
• ✅ Array attributes like .shape and .dtype describe structure
• ✅ Vectorised operations work on whole arrays at once
• ✅ Boolean masks make filtering elegant and fast
• ✅ Broadcasting applies smaller objects across larger arrays
• ✅ NumPy is the numerical foundation for econometrics in Python

Next Lecture

Linear Algebra with NumPy

• We will extend arrays into vectors and matrices
• You will learn matrix multiplication, solving systems, and eigenvalues
• These tools connect directly to regression algebra