Research design, Methods and Data Collection

Lecture 8. Quantitative methods 1: Foundations

Youssouf Merouani

2024-02-13

Structure of the lectures

45 minute block – 10 minute break – 45 minute block
Last 5 minutes of class: Open for questions
Ask for clarifications throughout
Discussions and reflections

Content of the lectures

Lecture 8 – 13/02
- Quantitative data
- Univariate and Multivariate analysis in economics
- Models and Research questions
Lecture 9 – 16/02
- Content analysis and Surveys
- Sampling and Imputation
Lecture 10 – 20/02
- Identification and Causal Diagrams
- Experiments and Quasi-experimental methods

Doing quantitative research requires the use of `quantitative data`.

What is quantitative data?

`Two dimensions` are useful to explain what it is, what it is not, and the gray areas.

Variable types

We quantify by defining variables that take the form of (different) numbers.
An instrument decides the measure (“number”) of a variable.
Levels (sophistication) of measurement explain the inherent order of the variable.

Categorical variables

Entities are divided into distinct categories:
- Binary variable: only two categories (e.g., dead or alive)
- Nominal variable: more than two categories (e.g., omnivore, vegetarian, vegan, or fruitarian).
- Ordinal variable: Nominal with logical order (e.g., grades in A, B, C, D, E, F)

Continuous variables

Entities get a distinct score:
- Interval variable: Equal intervals on the variable represent equal differences in the property being measured (e.g., the difference between 6 and 8 is equivalent to the difference between 13 and 15).
- Ratio variable: Interval but with a meaningful “0”, which gives meaningful ratios (e.g., score 16 on an anxiety scale means that the person is twice as anxious as someone with an 8)

What do you do with these variables?

You have two roads:
`univariate` analysis or `multivariate` analysis.

Univariate Analysis: Exploring Data One Variable at a Time

Definition: Analyzing one variable at a time to produce descriptive statistics, giving data meaning through numerical summaries.
Common Tools:
- Frequency Tables: Show how often each value occurs; include counts and percentages.
- Diagrams: Bar charts, pie charts, histograms, and infographics display data visually.
- Measures of Central Tendency: Mean, median, and mode identify typical values within data.
- Measures of Dispersion: Range and standard deviation measure variability among data.
- Boxplots: Visual summaries showing both central tendency (median) and dispersion (range), highlighting outliers.

Let’s break down univariate analysis. It’s about looking at one thing at a time. Imagine you’re taking a photo of a bird. You focus on the bird to understand what it looks like, right? That’s univariate analysis for data. You pick one variable and dig into it.

Now, how do we do this? First, frequency tables. They’re like counting how many birds are in different parts of your yard. Easy way to see what’s going on.

Diagrams come next. Think of them as different ways to show your bird photos. Bar charts and pie charts are great for simple categories—like bird types. Histograms are for when things can vary more, like bird weights.

Then, we talk about finding an ‘average’ bird. That’s where mean, median, and mode come in. They help us summarize what a typical bird might look like in numbers.

Dispersion measures, like range and standard deviation, tell us how different the birds are from each other. Is your yard visited by mostly the same kind of bird, or is there a wide variety?

Lastly, boxplots. They put all this info into one picture—showing the average bird, the range of birds, and if there are any unusual birds, all at once.

So, when we analyze data one variable at a time, we’re focusing on understanding each piece of the puzzle in depth, like getting to know each bird in your yard.

When to use univariate analysis?

As part of a multivariate analysis to provide an understanding of your variables.
As part of a qualitative study to provide additional context (turns the study into mixed methods if used extensively)
In its own right as an explorative study with new data (example: you have constructed a new and impressive dataset about a phenomenon we previously didn’t know much about)

Example 1: Evolution of patenting activity

Women-linked Patents: 1791-1900, France. Source: (Merouani and Perrin, 2024)

Example 1: Evolution of patenting activity

Women-linked Patents: 1791-1900, France. Source: (Merouani and Perrin, 2024)

Example 2: How does the gender patenting gap evolve over time?

Gender Patenting Gap: 1791-1900, France. Source: (Merouani and Perrin, 2024)

Example 3: How does the `connectivity` of inventors evolve?

Average degree evolution for two networks. Source: (Merouani, 2024)

Example 4: How does `collaboration` differ across sectors and gender?

Average Degree Per IPC Sector. Size of the circles represent the relative share of connections within that sector compared to others. Source: (Merouani, 2024)

Studying economic phenomena from a `multivariate perspective`? Look into econometrics!

Econometrics

Econometrics: Utilizes statistical methods to uncover relationships between economic variables.

While key in predicting macroeconomic variables (interest rates, inflation, GDP), with applications extending to politics, education, and beyond.
Purpose is not to predict, but to understand relationships underlying economic phenomena.
Addresses the challenges of working with nonexperimental data (i.e., observation data) through ceteris paribus.

Econometrics is the application of statistics to economics. Some use it to predict, forecast. Yes, forecasting things like inflation rates or GDP growth is part of what some econometricians use econometrics for. But, the heart of econometrics is really about digging into how different parts of the economy affect each other. Why does this matter? Because understanding these relationships helps us test economic theories and see if certain policies might work or not.

We often deal with data that isn’t from experiments. Imagine trying to set up an experiment to see how a policy affects the entire economy - it’s not easilly feasible. For instance, if we want to have an answer to how tax structure affects GDP. So, we work with the data we can observe from the real world. So, we rely on observational data, which comes with its own set of challenges, like dealing with data that wasn’t collected under controlled conditions.

UFO and patenting activity

Avoid the pitfals of spurious relationships 😊

How?
Quantitative research is `deductive`.
So, `start from theory`!

… or just simple `"economic understanding"` 🤯

What do you want to explain?

Y	X
Dependent variable	Independent variable
Explained variable	Explanatory variable
Response variable	Control variable
Predicted variable	Predictor variable
Regressand	Regressor

Example of Job Training and Worker Productivity

Examine the effects of job training on worker productivity.
Discuss with your classmates the following:
- How can we measure training?
- How can we measure worker productivity?
- What other things do we need to control for? (ceteris paribus)

Example: Job Training and Worker Productivity

Job Training -> weeks/hours spent in job training 🤸‍♀️
Worker Productivity -> wage (hourly wage) 💰
(other) Big things that affect productivity:
- Education: years of formal education 👩‍🎓
- Experience years of working experience 🏢
We add an error term that captures “all other things” 🤷‍♀️
💰 = 👩‍🎓 + 🏢 + 🤸‍♀️ + 🤷‍♀️

\[ \text{wage} = \beta_0 + \beta_1 \text{educ} + \beta_2 \text{exp} + \beta_3 \text{training} + u \]

Reflection: Why did we choose a regression model for that RQ?

Example: Explain Women’s patenting

\[ Pr(Y_i = 1) = \Phi\left(\beta_0 + \beta_1 \cdot \text{Year1844}_i + \beta_2 \cdot \text{PatentLength}_i + \beta_3 \cdot \text{TeamSize}_i + \sum_{j=1}^{J} \beta_{4j} \cdot \text{Sector}_{ji} + \sum_{k=1}^{K} \beta_{5k} \cdot \text{Education}_{ki} + \varepsilon_i\right) \]

\(Y_i = 1\) indicates women-linked patent

Financial resources
Team size
Female oriented sectors
Human capital

Good RQ bridge theory and reality.

Crafting a Good Research Question (1)

Essential Criteria:
- Answerable: Must be possible to answer with empirical evidence.
- Informative: Should enhance understanding of how the world works.

Key Components:
- Clarity: Avoids ambiguity, allowing for specific evidence to answer.
- Relevance: Connects to broader theories or explanations of phenomena.
- Feasibility: Data necessary for answering the question can realistically be obtained.

From Theory to Hypothesis: A good question bridges theory (why things happen) to hypothesis (what specifically will be observed).

When we’re setting up a research question for quantitative research, we’re not just asking anything that pops into our head. We need a question that’s actually answerable with real, tangible evidence. Think about it like this: asking “what’s the best James Bond movie?” isn’t going to cut it because “best” is too subjective. But asking “which era of Bond movies sold the most tickets?” is something we can dig into with data.

A solid research question should do more than just seek an answer; it should aim to improve our understanding of the world. It’s about connecting dots between what we observe and the bigger picture, like how theories about societal behaviors can be supported or challenged by our findings.

But how do we know if a question is good? First, it has to be clear enough that we can envision what evidence would answer it. It also needs to be relevant, tying back to broader concepts or theories that give context to our inquiry. And importantly, it must be feasible – we need to be able to gather the data to address it.

Let’s say we’re curious about the impact of TV watching on childhood curiosity. We can formulate this into a research question: “Does watching a lot of TV as a child dull your curiosity as an adult?” This question passes our checks – it’s specific, it connects to broader discussions about media consumption, and it’s something we can study by tracking TV habits and adult curiosity levels.

Crafting a Good Research Question (2)

Where we find them: Curiosity and oppotunity.

Evaluating Questions:
- Does it provide new insights?
- Can unexpected results challenge or refine our understanding?

References

Clark, T., Foster, L., Bryman, A., and Sloan, L. 2021. Bryman’s Social Research Methods, Oxford University Press

Huntington-Klein, N. 2022. The effect: An introduction to research design and causality, Boca Raton, CRC Press, Taylor & Francis Group

Merouani, Y. and Perrin, F. 2024. Women Inventors: On the Origins of the Gender Patenting Gap, Lund Papers in Economic History, vol. 255

Wooldridge, J. M. 2020. Introductory econometrics: A modern approach, Boston, MA, Cengage Learning

Research design, Methods and Data Collection

Structure of the lectures

Content of the lectures

Doing quantitative research requires the use of quantitative data.

What is quantitative data?

Two dimensions are useful to explain what it is, what it is not, and the gray areas.

Variable types

Categorical variables

Continuous variables

What do you do with these variables?

You have two roads:univariate analysis or multivariate analysis.

Univariate Analysis: Exploring Data One Variable at a Time

When to use univariate analysis?

Example 1: Evolution of patenting activity

Example 1: Evolution of patenting activity

Example 2: How does the gender patenting gap evolve over time?

Example 3: How does the connectivity of inventors evolve?

Example 4: How does collaboration differ across sectors and gender?

Studying economic phenomena from a multivariate perspective? Look into econometrics!

Econometrics

Avoid the pitfals of spurious relationships 😊

How? Quantitative research is deductive. So, start from theory!

… or just simple "economic understanding" 🤯

What do you want to explain?

Example of Job Training and Worker Productivity

Example: Job Training and Worker Productivity

Reflection: Why did we choose a regression model for that RQ?

Example: Explain Women’s patenting

Good RQ bridge theory and reality.

Crafting a Good Research Question (1)

Crafting a Good Research Question (2)

References

Doing quantitative research requires the use of `quantitative data`.

`Two dimensions` are useful to explain what it is, what it is not, and the gray areas.

You have two roads:
`univariate` analysis or `multivariate` analysis.

Example 3: How does the `connectivity` of inventors evolve?

Example 4: How does `collaboration` differ across sectors and gender?

Studying economic phenomena from a `multivariate perspective`? Look into econometrics!

How?
Quantitative research is `deductive`.
So, `start from theory`!

… or just simple `"economic understanding"` 🤯