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Technical Assessment > Econometrics - Panel/TS & hetero/autocorrelation > Flashcards

Econometrics - Panel/TS & hetero/autocorrelation Flashcards

1
Q

What is heteroskedasticity and why is it a problem?

A

Non-constant variance in errors - violates a classical assumption

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2
Q

What are 6 reasons heteroskedasticity occurs?

A
  1. Error-learning models
  2. Real income grows through time
  3. Improved data collection over time
  4. Outliers in a sample of data
  5. An incorrectly specified model
  6. Skews in distribution in an X variable
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3
Q

What are the consequences of heteroskedasticity?

A

No longer minimum variance so inefficient estimator, not BEST anymore so there can be another estimator that can produce smaller variance, there will be a breakdown in inference (std errors no longer unbiased so issues w t-tests)

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4
Q

What are the 3 main tests for heteroskedasticity?

A
  1. Goldfeld-Quandt Test (GQ test)
  2. Breusch-Pagan Test (BP test)
  3. White’s Test
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5
Q

How does the Breusch-Pagan test work?

A

Fit regression, then calculate the squared residuals, and fir a new model using the squared residuals, then calculate the chi-square test stat and p-value, and compare to sig level. Null hypothesis is homoskedasticity.

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6
Q

How can you correct for heteroskedasticity?

A
  1. Transform model e.g. logs/squares/inverse
  2. Robust standard errors
  3. Generalised Least Squares/Weighted Least Squares (GLS/WLS)
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7
Q

What is autocorrelation/serial correlation and why is it a problem?

A

Errors correlated with their previous value - violates classical assumption

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8
Q

When does serial correlation occur?

A
  1. Time-series data
  2. Spatially organised data
  3. Can be in cross section but less common
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9
Q

What causes serial correlation?

A
  1. Omitted lagged variables
  2. Economic shocks that have persistent effects
  3. Transformations applied to data
  4. Model misspecification
  5. Error term being truly dynamic
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10
Q

What is first-order autocorrelation?

A

Assume that the errors is correlated linearly only with its value in the previous period

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11
Q

What are the consequences of autocorrelation?

A

Residuals don’t have minimum variances so OLS isn’t BLUE.
R-squared may seem high
Standard errors may be baised downwards - OLS is inefficient and incorrect inferences may be made

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12
Q

What does the Durbin Watson Test test for?

A

First-order correlation

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13
Q

What values of the Durbin Watson test statistic indicate first-order autocorrelation?

A

DW -> 0 = positive autocorrelation
DW -> 2 = no autocorrelation
DW -> 4 = negative autocorrelation

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14
Q

What are 3 limitations of the Durbin Watosn test?

A
  1. Not valid in dynamic models as test stat biased to 2
  2. Only applies to first-order autocorrelation
  3. Bounds test doesn’t offer exact critical values so an element of doubt
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15
Q

What is a better test for serial correlation?

A

Bresuch-Godfrey Lagrange Multiplier Test

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16
Q

How is a Bresuch-Godrey LM test conducted?

A

Estimate OLS and obtain residuals, estimate auxiliary regression and then either compute LM test stat and compare to ch-squared dist OR use an F-test

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17
Q

What can be done to correct for serial correlation?

A

Employ robust standard errors (HAC standard errors)

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18
Q

What do hetertoskedasticity autocorrelated consistent (HAC) standard errors do?

A

Larger standard errors so less statistical significance

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19
Q

What is the difference between a True and Natural experiment

A

True = observations randomly assigned to different groups
Natural = not randomly assigned

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20
Q

What is the equations for a Difference-in-Difference model?

A

Y = b0 + b1Gi + b2Ri + b3(G.R) + error, where G=1 in treatment group, otherwise 0, and R=1 if observation is observed in period 2, otherwise 0

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21
Q

What is the interpretation of b3 in a general D-in-D?

A

Average treatment effect (ATE), captures the policy effect

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22
Q

What are the advantages of using panel data? (5)

A
  1. More information, more variability, less collinearity, greater degrees of freedom - hence more efficient
  2. Consider dynamic changes
  3. Detect/measure effects that can’t be observed in other data types
  4. Better model specific types of economic behaviour
  5. Large panels less likely to produce biased estimates
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23
Q

What are the 4 main types of panel models?

A
  1. Pooled OLS
  2. Fixed Effects Least Squares Dummy Variable Model (LSDV)
  3. Fixed Effects Within-Group Model
  4. Random Effects Model
24
Q

Explain pooled OLS?

A

Pools data and estimates simple OLS - disregards time and entity dimensions

25
Q

Explain LSDV model?

A

Pools data and gives each entity its own intercept dummy

26
Q

Explain fixed effects (within group) ?

A

Each entity given its own intercept, but each variables is expressed as deviation from mean value

27
Q

Explain random effects model?

A

Assumes intercepts are random draws from a bigger population

28
Q

Problems of LSDV model?

A
  1. Time-invariant - can’t consider variables over time
  2. Too many dummies can reduce degrees of freedom
  3. Lots of dummies = multicollineaity
  4. Can have issues with error term
29
Q

How is random effects different from fixed effects?

A

Random effects doesn’t estimate an individual effect for each observation, it estimates an overall estimate of the intercept that captures the average effect within the sample of data

30
Q

What are the 2 error terms in a random effects model?

A
  1. cross section/individual specific error component
  2. combine time series and cross section error comportment - idiosyncratic error term (always in a regression)
31
Q

When should REM be used over FEM?

A

If you think differences across firms influence dependent variables

32
Q

What does the Hasuman test test for? What is the null/alternate hypothesis?

A

Tests whether the unique errors are correlated with the regressors. The null hypothesis is that there is no correlation and so estimates are consistent and REM is preferred.

33
Q

What type of estimator is used for REM and why?

A

Generalised Least Squares (GLS) - cannot use OLS as would yield inefficient estimators.

34
Q

What models can be employed if you have a binary/limited dependent variable?

A
  1. Linear Probability Model
  2. Logit Model
  3. Probit Model
  4. Tobit Model
35
Q

What type of estimation the is Probit Model?

A

Maximum-Likelihood estimator

36
Q

What is the interpretation of a Probit Model?

A

Have to calculate marginal effects and the results are a change in probability, in software marginal effects are the slope value

37
Q

What is the interpretation of a Logit Model?

A

Coefficients are a partial slope coefficient, the measure change in logit for a unit change in X

38
Q

How do you decide between a Logit and a Probit?

A
  1. Measure of fit, R-squared
  2. Hypothesis test
  3. Model interpretation (marginal effects)
39
Q

What is a Tobit Model used for?

A

Limited dependent variables, where the value is continuous but is cut-ff/censored at a particular value

40
Q

How does the Tobit Model work?

A

Uses maximum likelihood estimation that treats the cutoff/censor values differently

41
Q

What is the general equation for a simultaneous equation model?

A
42
Q

How do you estimate a reduced form equation?

A

Use the relationship between the 2 simultaneous equations e.g. Qd = Qs and rearrange to get a reduced form equation. Treat as a normal simultaneous equation

43
Q

What is the problem with using OLS with simultaneous equation models? What is the solution?

A

Simultaneity bias, use two stage least squares (2SLS) instead

44
Q

How do you conduct a 2SLS

A

Identify exogenous and endogenous variables, use an instrumental variables approach where regressors = endogenous variables and the instruments = exogenous variables

45
Q

What makes a good instrument?

A

Z (insturment) must be exogenous in the equation , but related to X (endogenous variable)

46
Q

What is the difference between static and dynamic time series data?

A

Static =change in X at time t has an immediate effect on y e.g. Phillips curve
Dynamic = where change in X at time t doesn’t have an immediate effect on y, lags are included in the model to account for the time it takes for the change in X to be full absorbed by Y

47
Q

In TS data - what additional classical assumption is needed?

A

Strict exogenity = for each time period the expected value of the error term given all explanatory variables for all time periods is 0

48
Q

What problem will you have if stricy exogeneity is not achieved?

A

biased OLS estimates

49
Q

How can you prove consistency?

A

Stationarity and weak dependence

50
Q

What does stationarity mean?

A

Probability distribution is stable over time - the statistical properties of a process generating a time series do not change over time. (the series changes over time but the WAY it changes does not itself change over time)

51
Q

What are 2 problems with dynamic models?

A
  1. High mutlicollinearity
  2. Loss of degrees of freedom
52
Q

What is an autoregressive model? Why is it used?

A

Replace lagged values of independent variables with lagged dependent variables. Used to mitigate issues with dynamic models

53
Q

What happens when TS data is not weakly dependent?

A

Random walk - which is highly persistent and non-stationary

54
Q

What is it called when you have highly persistent TS data with a trend?

A

Random walk with drift

55
Q

How can you make a problematic series stationary and have weak dependence?

A

First-differencing the data series

56
Q

What model can you employ if you have serial correlation in TS?

A

Feasible Generalized Least Squares

57
Q

How do you test for a unit root? What is the null/alternate hypothesis?

A

Dickey-fuller test (uses special DF critical values)
H0 = there is a unit root, data is non-stationary
H1 = there is not a unit root, the data is stationary

Technical Assessment (19 decks)

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