1
Q
What is econometrics?
A
- a set of statistical methodologies aiming at defining and measuring causal relationships between economic variables
2
Q
What is causality?
A
- Causal relationship between X and Y indicated that X is an explanatory variable for Y
3
Q
What are the necessities for causality?
A
- Association between variables (statistical relationship)
- An appropriate time order (cause before effect)
- The elimination of alternative explanations
4
Q
What is the difference between experimental and non-experimental data?
A
- Experimental: conduct and observe experiment
- Non-experimental: use data (surveys)
5
Q
How is a function set up?
A
Y=f(X1,X2,X3)+ε
Y= Outcome of interest
X= theoretically relevant determinants
f() = function
+ε = error term
6
Q
What types of data are there?
A
Experimental data
Non experimental data?
7
Q
What is meant by randomisation in experimentation and what are its benefits?
A
- Building treatment and control groups, so that they are similar in their characteristics
Benefits: - Reduction of selection bias
- Reduce accidental bias
- Permits use of probability theory to analyse the difference of outcome
8
Q
What is meant by CETERIS PARIBUS?
A
“All other things remain equal”
9
Q
What is a counterfactual?
A
The unobserved outcome
10
Q
What is the difference between qualitative and quantitative data?
A
Qualitative: Types, groups and categories –> education level
Quantitative: Amounts of magnitudes –> GDP
11
Q
What are the different datatypes?
A
- Numeric (Numbers)
- String (Text)
- Continuous (Can take many values)
- Binary (Can be 0 or 1)
12
Q
What are the different between cross-sectional, time series and panel databases?
A
- Cross-sectional: Many units, one point in time (income of a country over 1 year)
- Time series: One Unit, many points in time (Income of one person over 10 years)
- Panel: Many Units, over many points in time (Wages of individuals over years)
13
Q
What are the two subcategories of qualitative data?
A
- Nominal (no natural ordering) –> religion
- Ordinal (natural ordering) –> firm size
14
Q
What are the two subcategories of quantitative data?
A
- Continuous (Include fractional values)
- Discrete (integer values)
15
Q
What is descriptive analysis ?
A
- Summarises raw data to make it interpretable (What does the data show)
–> Focus on: patterns, tendencies, relationships, & variability
16
Q
What is data distribution?
A
- Shows how values in a dataset are spread across the range of possible values
–> Focus on: Shape of distribution, centre, spread & outliers
17
Q
What types of distributions are there?
A
- Normal distribution
- Skewed distribution (left or right)
- Uniform distribution
- Bimodel distribution
18
Q
What does a normal distribution look like?
A
- Bell shaped, evenly distributed
19
Q
What does a left/negative skewed distribution look like?
A
- Lump of data on right side
- long tail decreasing to the left
20
Q
What does a right/positive skewed distribution look like?
A
- Lump of data on left side
- long tail decreasing to the right
21
Q
What does a uniform distribution look like?
A
- All values have a similar frequency
- almost flat line
22
Q
What does a bimodal distribution look like?
A
- Two peaks indicating two subgroups in the data
23
Q
Why does distribution matter?
A
- Helps choose appropriate statistical methods
- Reveals data quality issues
- Aids transfromation decisions
- Informs modelling assumptions
24
Q
What is meant by central tendency?
A
Tendency of values to cluster around some central value
25
What are measures to describe the central tendency of a dataset?
- Mean
- Median
- Mode
26
Where do mean median and mode lie on a right and on a left skewed distribution?
- Mode is at the peak
- Median is in the direction of the skew
- Mean is somewhere in the middle of the skew
27
What is meant by spread and how can it be measured?
- The difference between the min and the max (max-min)
Measured through:
- Standard deviation
- Variance
28
What does a high vs a low variance indicate?
- Low variance strong centrality
- High variance low centrality
29
What are outliers?
Values that fall far outside the general range of data
30
What is a correlation, and what types are there?
- Measures the strength and direction of a relationship between two numeric values
Types:
- Positive: When one grows the other does too
- Negative: When one grows the other shrinks
- Non: when one grows the other stays the same
31
What is a spurious correlation?
- Apparent correlation due to coincidence or a hidden third variable
32
What is a non-linear relationship?
- effect of one variable on the other is not constant
--> may require transformation or regression to analyse
33
What is cross-tabulation?
- Matrix of data analysing the relationship between two or more categorical variables
34
What is a truncated y-axis?
not starting the axis at 0
---> leads to deception
35
What is meant by mean skewed by outliers?
When the mean is skewed by few outliers
--> average pay top 1% earn a lot
36
What variable is the dependent variable?
The variable affected
37
What is the explanatory variable??
The variable affecting another variable
38
What is the conditional mean?
E(y|x) or μy∣x or ^I (in estimation)
- the conditional mean is the expected average value of y when x is fixed
39
What is the intercept?
β1 or b1
- The expected value of y when x = 0
40
What is the slope?
β2 or b2
-The change in conditional mean of y when x changes by 1 unit
41
What is the function of a simple regression?
E(y|x) = β1 + β2x + ε ----> ^i=b1+b2xi+ ε
- E(y|x) = conditional mean
- β1 = intercept
- β2 = slope
- x = value of x at that point
- ε = error term
42
What is the error term?
ε
represents all other factors influencing y other than x
43
What are the three core assumptions of the simple regression?
SR1: y=β1+β2x+ε
--> the value of y, for each value of x is:
SR2: E(y)=β1+β2x
--> the expected value of the random error is 0 meaning that:
SR3: Var(ε)=σ2=Var(y)
--> the variance of random error is equal to that of y
44
What is homoskedasticity?
- Models explain y equally well at all levels of x
- All levels have bell shaped curve with same variance
45
What is heteroskedasticity?
- The model fits some ranges of x better than others
- Variability of y depends on x
46
What are the three additional assumptions of simple regressions?
SR4: The covariance between any pair of random errors is:
- Cov(εi,εj)=0 (i !=j) -->errors from different observations are unrelated
SR5: The variable x is not random and must take at least 2 values
SR6: (optional) The values of ε are normally distributed about their mean
47
What is the Gauss–Markov Theorem?
Under the assumption's of SR1-SR5
--> Model is correctly specified
--> Errors behave nicely
--> Regressors are exogenous (not related to x)
Then:
No other linear unbiased estimator can systematically do better than OLS in terms of precision.
48
What is OLS?
- Ordinary Least Squared
--> A rule to determine the "best" line through the data to estimate β1 and β2
49
What is the least square principle?
To fit a line to the data values we should make the sum of the squares of the vertical distances from each point to the line as small as possible.
Meaning:
- Difference between actual y and line y at value x is squared (because they can be negative and positive)
- should be as low as possible
50
What does R-squared (R2) measure?
The proportion of variation in y explained by x in your model
--> closer to 1 = better
51
What does the Coefficient show, and where is it in a regression?
How much y changes if x increases by 1 unit
First intercept then coefficient
52
What does the test/t-statistic shows?
How many standard errors away from 0 the estimate is
|t|>2 = significant
53
What does the prob. part of the model show?
the p-value
-> if there where no effect, what is the probability of seeing an effect this large by coincidence?
p< 0.10 Weak/moderate evidence
p< 0.05 significant
54
What are residuals and what do they show?
The residuals show how much the model got wrong
--> difference between slope y and actual y
-->positive = under-predicted
-->negative = over-predicted
55
What do we want to see in a good residual?
- Residuals are scattered randomly
- Residuals are entered around 0
- Roughly the same spread everywhere
- No patterns
56
What does heteroskedasticity look like on residuals?
- Residual spread increases with increasing fitted values
57
What does nonlinearity look like on residuals?
- Systematic patterns
- systematically above and below 0
58
What is H0?
The null hypothesis --> H0:β2=0
- Nothing special is going on, everything we see is due to random noise
59
What is H1?
The alternative hypothesis --> H0:β2!=0
- Opposite of null hypothesis --> something is going on
60
What are the three possible alternative hypothesis?
1. Two-sided: H1:β2!=0
2. One-sided:
- H1:β2<0
- H1:β2>0
61
What is the rejection region?
The range of values of the t-statistic in which we reject H0
62
What is the usual level of significance (𝜶) chosen ?
0.01
0.05
0.10
63
What types of hypothesis testings are there?
One-tail test with alternative
64
What is a one-tail test with alternative?
Either:
𝐻1 ∶ 𝛽𝑘 > 𝑐 --> We reject H0 when the t-statistic is larger than the critical value for the level of significance 𝜶
or
𝐻1 ∶ 𝛽𝑘 < 𝑐 --> We reject H0 when the t-statistic is smaller than the critical value for the level of significance 𝜶
65
What is a two-tail test with alternative?
𝐻1 ∶ 𝛽𝑘 ≠ 𝑐 --> We reject H0 when the t-statistic is either larger or smaller than the critical value for the level of significance 𝜶
66
What are the 5 things needed for hypothesis testing?
1. Null hypothesis
2. Alternative hypothesis
3. Test statistic (t-statistic)
4. Rejection region
5. Conclusion
67
What is the t distribution ?
The point where only 5% lie above or below it
--> the cutoff point for the null hypothesis
68
How do you compute the t statistic?
t= b2−c / se(b2)
slope - H0 value
/ standard deviation
69
How is a multiple linear regression model build up?
y = β₁ + β₂x₂ + β₃x₃ + … + β_k x_k + ε
70
What is meant by partial differentiation?
when there are two factors being tested, the effect of one without the other changing
71
What happens to R2 if we add more variables?
it usually rises
72
How can we model non-linear relationships?
1.Logs: x --> ln(x)
2. powers: x --> x2
73
What does the Log-log model look like ?
ln(y)=β1+β2ln(x)
74
What does the Log-level model look like?
ln(y)=β1+β2x
75
What does the Level-log model look like?
y=β1+β2ln(x)
76
What does the quadratic model look like?
y=β1+β2x^2+β3x
77
What questions do log models answer?
1. If x increases by 1%, how much does y change?
2. Does each extra unit of x matter less than the previous one?
78
What does the Log-log model do?
--> compares the percentage change in y to the percentage change in x
If x increases by 1%, y increases by B2 percent
79
What do B1 and B2 mean in a log model?
B1: Baseline of y
B2: Elasticity (increase in 1% --> B2% increase in y)
80
When is the Log-Log model used?
- When each percent increase leads to a percent increase in y
E.g.
each percent of income increase leads to y% increase in food spending
81
When is the Log-Level model used?
When each unit increase leads to a percentage increase
E.g.
1 year of education leads to y% increase in income
82
When is the Level-log model used?
When each percent increase leads t a unit increase
e.g.
1% income increase leads to y increase in food spending
83
In a level log model, what Is the effect on y if x rises by 1%?
B2/100 = effect on y if 1% change in x
84
In a log level model, what Is the percent-change in y if x rises by 1 unit?
B2*100 = effect on y if 1 unit change in x
85
In a log-log model, what Is the effect on y if x rises by 1%?
B2 =effect on y% if 1% change in x
86
What are the benefits of using logs?
-Convenient percentage/elasticity interpretation
- Mitigates outliers
- Helps with normality and homoscedasticity
87
What should generally be logged?
- Wages
- Salaries
- Sales
- Market value
- Population
88
What should generally not be logged?
- Variables measured in years
- Ratios and percentages
- Zero or negative values
89
What does the quadratic model look liked?
𝑃𝑅𝐼𝐶𝐸 = 𝛽1 + 𝛽2x + 𝛽3x2 + 𝜀
90
What does the quadratic model account for?
Allows the effect of x on y to change with the level of x
91
What are the three scenarios of the quadratic model?
B3=0 --> Marginal effect of X is constant --> linear shape
B3>0 --> Marginal effect of X increases with X --> U-shaped
B3<0 --> Marginal effect of X decreases with X --> reverse U-shaped
92
What are interaction terms?
β3X2
Terms that allow us to depend the effect of one variable on the outcome on another variable
93
What are indicator variables?
δD --> Dummy or binary variables
--> variables that take only 2 values, 0 or 1 (True/False)
94
What are indicator variables used for?
- Turning qualitative content int quantitative variables
95
How can indicators enter a regression?
1. As a regressor --> Y=β1+δD+β2x+e
2. As interaction term --> Y=β1+δD+β2x+γ(B2x × D)+e
96
How is the indicator interprets in level and log regressions?
Level: change in outcome compare to baseline
Log: percentage change relative to baseline
97
What is the dummy variable trap?
When for every possibility there is a dummy leading to there not being a baseline
98
What are binary choice models and which are there?
Models that allow to explore choices and decisions are labelled binary choice models:
- Linear probability model
- Probit/Logit models
99
When are binary variables usually used as dependent variables?
When we model individuals and firms choices
100
What is the linear probability model?
A model where y captures a choice that individuals make
Y= ( 1 if first alternative, 0 if second alternative)
101
How can we tell whether a model is binary or not?
binary if Y= 2 values
102
How can we interpret a coefficient in a linear probability model?
A 1-unit change in x leads to a B% increase in y
103
What are the benefits of a linear probability model?
- Easy to add duties, interactions and controls
- Coefficients are directly interpretable as change in probability
104
What are limitations of the linear probability model?
- Model is heteroskedastic by design as error term changes with X
- Can get p-values lower than 0 or greater than 1
-
105
What is the difference of non-linear probability models to linear probability models? (when using binary dependant variables)
- They adjust the change of x on probability so it doesn't exceed 100% or get below 0%
--> therefore the effect of x on y changes depending on where on the curve you are
106
How do non-linear probability models work?
They use 𝐺(𝛽0 + 𝛽1𝑥1 + ⋯ + 𝛽𝑘𝑥𝑘) which cramps the score of linear probability models on a scale of 0 to 1, preventing numbers above 1 or below 0
107
What is the G function called?
The likelihood function
108
What are the rule of thumbs on probit and logit estimates?
logit = 4Blpm
Bprobit = 2.5Blpm
logit=1.6Bprobit
109
110
When is each function used?
-Level-Level: linear relationship
-Log-Level: y grows proportionally
-Level-Log: diminishing effects of x
-Log-Log: Both grow proportionally
-Quadratic: Effect of x on y depends on x —> you expect an optimum or turning point
Bocconi Semester 1
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