ECON0019 (Quantitative Economics and Econometrics) Term 2 Summary - UCL Economics BSc Second Year

UNIVERSITY COLLEGE LONDON

DEPARTMENT OF ECONOMICS
Economics BSc (Econ)
Second Year – Term 2




QUANTITATIVE
ECONOMICS AND
ECONOMETRICS
ECON0019
Rodrigo Antón García



London, 2022

,
, Contents

Topic 1 – Potential Outcomes and Experiments. Wooldridge Chapter 2–7a and 3–
7e & Stock and Watson Chapter 13.1–13.3.


o Topic 1.1 – Econometrics of Causality and Experiments. 1
o Topic 1.2 – Randomization Based on Covariates. 6
o Topic 1.3 – Pros and Cons of Experiments in Economics. 8


Topic 2 – Instrumental Variables I. Wooldridge Chapter 15.1–15.2 & Stock and
Watson Chapter 12.


o Topic 2.1 – The Basics of Instrumental Variables. 13
o Topic 2.2 – Becoming an Instrumental Variables Pro I. 19


Topic 3 – Instrumental Variables II. Stock and Watson Chapter 13.6 and Appendix
13.2.


o Topic 3.1 – Becoming an Instrumental Variables Pro II. 24
o Topic 3.2 – Instrumental Variables in Experiments. 28


Topic 4 – Simultaneous Equations Models. Wooldridge Chapter 16.1–16.4.


o Topic 4.1 – Supply and Demand. 32
o Topic 4.2 – The General Case. 36
o Topic 4.3 – Maximum Likelihood Estimator (MLE). 41


Topic 5 – Limited Dependent Variables I. Wooldridge Chapter 17.1 & Stock and
Watson Chapter 11.


o Topic 5.1 – Limited Dependent Variables (LDV) Content. 45
o Topic 5.2 – Binary Response Models. 46
o Topic 5.3 – The Logit and Probit Binary Response Models. 46
o Topic 5.4 – Estimation of Logit and Probit: NLLS and MLE. 48
o Topic 5.5 – Interpret the Coefficients and Measuring Marginal Effects. 51
o Topic 5.6 – Generalizing Hypothesis Test and Quality of Fit. 54

,Topic 6 – Limited Dependent Variables II. Wooldridge Chapter 17.3–17.5.


o Topic 6.1 – The Poisson Regression Model. 59
o Topic 6.2 – Truncated Regression Models. 62


Topic 7 – Limited Dependent Variables III. Wooldridge Chapter 17.2, 17.4–17.5.


o Topic 7.1 – Incidental Truncation (Sample Selection) Models. 67
o Topic 7.2 – Censored Regression Models. 73
o Topic 7.3 – The Tobit Model for Corner Solution Responses I . 76


Topic 8 – Limited Dependent Variables IV and Regression with Time Series I.
Wooldridge Chapter 17.2 and 10.1–10.3.


o Topic 8.1 – The Tobit Model for Corner Solution Responses II. 80
o Topic 8.2 – Time Series Regression Models. 87


Topic 9 – Regression with Time Series II. Wooldridge Chapter 10, and 11.1–11.3 &
Stock and Watson Chapter 15 and 16.


o Topic 9.1 – OLS Finite Sample Properties in Time Series Regressions. 90
o Topic 9.2 – Functional Forms, Dummy Variables, Trends, Seasonality. 92
o Topic 9.3 – Stationarity and Weak Dependence. 95
o Topic 9.4 – Asymptotic Properties of OLS. 97
o Topic 9.5 – Highly Persistent Time Series. 98


Topic 10 – Serial Correlation and Heteroskedasticity. Wooldridge Chapter 12 &
Stock and Watson Chapter 16.


o Topic 10.1 – Properties of OLS with Serially Correlated Errors. 101
o Topic 10.2 – Serial Correlation-Robust Inference with OLS. 104
o Topic 10.3 – Heteroskedasticity in Time Series Regressions. 106
o Topic 10.4 – Testing for Serial Correlation. 107

, Quantitative Economics and Econometrics – ECON0019 Rodrigo Antón García



ECON0019: QUANTITATIVE ECONOMICS AND ECONOMETRICS – TERM 2

Topic 1 – Potential Outcomes and Experiments. Wooldridge Chapter 2–7a and 3–
7e & Stock and Watson Chapter 13.1–13.3.

o Topic 1.1 – Econometrics of Causality and Experiments.

• Why Regressions?

Regressions estimate associations between variables (specifically, the conditional
expectation). Economists are interested in regression for various reasons, some are:

1. To predict ! from "! , . . . , "" . Actually, this is rarely used in economic research.
Prediction is not something economists, in general, are precisely interested in. This is
more an issue of traders or central banks.
2. To estimate parameters of “structural” equations. For example, the demand
elasticity in a demand equation. This is something regression is used for but not a
particular easy use of regressions. This will be discussed later in three weeks.
3. To estimate causal effects of policies, interventions, treatments. For example, of
a smaller class size on test scores; or of a job training program on future wages.

We will now center on this third application of regressions. But first, what does “causal”
mean? When/why is regression appropriate? With which controls?

• Defining Causal Effects.

In the simplest case, we are interested in evaluating an intervention or policy that has
only two states of the world: a unit is subjected to the intervention or not. In other words,
those not subject to the intervention or new policy act as a control group and those
subject to the intervention as the treatment group.

Therefore, we consider some population and assume the treatment status " is binary:
1 = if treated (e.g., a person goes through job training), 0 = if not treated.

If we then define causal effects by an abstraction called potential outcomes, for each unit
) in the population there are outcomes in both states of the world, !# and !! .

- !# = outcome without intervention.
- !! = outcome with an intervention.
- *+$ = !! − !# = causal effect (usually a random variable, may vary across units).

There are a couple of noteworthy items about the casual effect *%$ ,

- It is not observed for any unit ) because it depends on both counterfactuals.
- Second, it can be negative, zero, or positive. It could be that the causal effect is
negative for some units and positive for others.



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