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Summary Empirical Finance, P1 MSc Finance $8.88
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  3. Vrije Universiteit Amsterdam (VU)
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  5. Empirical Finance (E_FIN_EF)

Summary

Summary Empirical Finance, P1 MSc Finance

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  • Course
  • Empirical Finance (E_FIN_EF)
  • Institution
  • Vrije Universiteit Amsterdam (VU)

Summary for the course Empirical Finance, given in period 1 of the Master of Finance at the VU. This summary greatly covers all theoretical subjects which are taught in this course .

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Document information

  • January 15, 2023
  • 63
  • 2022/2023
  • Summary

Subjects

  • linear regression
  • logit
  • panel data
  • endogeneity
  • difference in difference
  • misspecification
  • event studies
  • unit roots
  • univariate linear time series models
  • univariate volatility models

Written for

  • Vrije Universiteit Amsterdam (VU)
  • Finance
  • Empirical Finance (E_FIN_EF)
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Empirical Finance Summary
MSc Finance ’22 – ’23, period 1


Contents


Part I – Linear regression ....................................................................................................................4
1.1 Explanation of linear models and transformation ......................................................................4
1.2 Dummies...................................................................................................................................5
1.3 Model adequacy and outliers (𝑅2, 𝑅2, 𝐴𝐼𝐶 & 𝐵𝐼𝐶) ....................................................................6
1.4 OLS framework..........................................................................................................................7
1.5 t-test & F-test ............................................................................................................................8
Part II – Logit ....................................................................................................................................10
2.1 Limited dependent variable models ........................................................................................ 10
2.2 Logit/Probit models and their estimation through maximum likelihood .................................. 10
2.3 Parameter interpretation and marginal effects ........................................................................ 10
2.4 Model adequacy: R2 and ROC/CAP curve ................................................................................. 11
2.5 Other Logit/Probit models ...................................................................................................... 13
Part III – Panel data ..........................................................................................................................14
3.1 Motivation for panel data........................................................................................................ 14
3.2 Pooled regression.................................................................................................................... 14
3.3 Fixed effects models................................................................................................................ 15
3.4 Within and between estimator ................................................................................................ 16
3.5 Random effects models ........................................................................................................... 16
3.6 Take fixed effects or random effects? ...................................................................................... 16
3.7 Clustered standard errors ........................................................................................................ 17
Part IV – Endogeneity and Diff-in-Diff ..............................................................................................18

, 4.1 Endogeneity explanation ......................................................................................................... 18
4.2 Source 1: Measurement error ................................................................................................. 18
4.3 Source 2: Omitted variable bias ............................................................................................... 19
4.4 Solution 1: Instrumental Variables (IV) .................................................................................... 20
4.5 Solution 2: Diff-in-Diff approach .............................................................................................. 20
Part V – Misspecification ..................................................................................................................22
5.1 Assumption 0a; correction specification .................................................................................. 22
5.2 Assumption 0b; no perfect multicollinearity ............................................................................ 23
5.3 Assumption 1; zero mean errors.............................................................................................. 24
5.4 Assumption 4’; non-random regressors ................................................................................... 24
5.5 Assumption 4; no covariance between errors and regressors .................................................. 24
5.6 Assumption 5; normality ......................................................................................................... 24
5.7 Assumption 2; homoskedasticity ............................................................................................. 25
5.8 Assumption 3; No cross-correlation ......................................................................................... 26
Part VI – Event studies .....................................................................................................................27
6.1 Motivation and overview ........................................................................................................ 27
6.2 Event study methodology ........................................................................................................ 27
6.3 Cross-sectional regressions ..................................................................................................... 29
6.4 Extensions and some important aspects .................................................................................. 29
Part VII – Univariate linear time series models ................................................................................31
7.1 Specification of AR, MA & ARMA models ................................................................................. 31
7.2 (Partial) Autocorrelations ........................................................................................................ 32
7.3 Diagnostics checking ............................................................................................................... 37
7.4 Forecasting with univariate time series models ....................................................................... 39
7.5 Forecasting an AR(1) model  Empty sheet to write on .......................................................... 40
7.6 Forecasting an ARMA(2,1) model  Empty sheet to write on ................................................. 41
7.7 Evaluation of forecasts ............................................................................................................ 42
Part VIII – Unit roots.........................................................................................................................44
8.1 Motivation .............................................................................................................................. 44
8.2 Non-stationarity and unit roots ............................................................................................... 44
8.3 Testing for unit roots ............................................................................................................... 48
Part IX – Univariate volatility models ...............................................................................................51
9.1 Motivation and overview ........................................................................................................ 51
9.2 Different types of volatility ...................................................................................................... 51
9.3 ARCH and GARCH models, their varieties and motivation ........................................................ 52
9.4 Estimation and diagnostics ...................................................................................................... 56

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Empirical Finance summary

, 9.5 Forecasting and evaluation...................................................................................................... 58
Part X – Extra: Overview tables ........................................................................................................61
10.1 OLS Assumptions ................................................................................................................... 61
10.2 Linear probability model overview ........................................................................................ 62
10.3 Various models overview ...................................................................................................... 62




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Empirical Finance summary

, Part I – Linear regression


1.1 Explanation of linear models and transformation

Most simple model to explain a relationship between certain factors:
𝑌𝑖 = 𝛽0 + 𝛽1 𝑋𝑖 + 𝛽2 𝑋𝑖 + 𝜖𝑖
This is also called the ‘’Classical Linear Regression Model’’ (CLRM), and it consist of
the following main components:
 Dependent variable  Is observed and random
 Parameters  Are fixed & non-random, however they are not known,
therefore we estimate them.
 Regressors  Are observed and could be random or non-random
 Error term  Is unobserved and random
Anything that depends on data will be (a) random (variable) and will have
distributional properties.
This linear relationship can also be described through vector notation:
First standard notation: 𝑦𝑖 = 𝑥𝑖′ 𝛽 + 𝜖𝑖
where the beta’s and regressors are stored in column vectors:

𝛽0 1
𝛽 = (𝛽1 ) , 𝑥𝑖 = (𝑋…1 ) Note that the Xi vector needs to be transposed in order to
….
βi 𝑋𝑖

make matrix multiplication possible.
The second standard notation stacks all the observations i = 1, …., 3010:
𝑦 = 𝑋𝛽 + 𝜖




A linear regression can be done when the model is linear in the parameters, e.g.:
𝑊𝑎𝑔𝑒𝑖 = 𝛽0 + 𝛽1 𝐸𝑑𝑢𝑐𝑖 + 𝜖𝑖



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Empirical Finance summary

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