6th week

• combines cross-sectional and time series data

• it contains for the same observation units (cross-section) data for several points in time (time series)

• the total number of observations T*N

-> small N can be compensated by large T

• Balanced panel: all observation units have measurements for all time periods

• Unbalanced panel: measurements are not available for all units for all time periods

T = 5 (Years)

N = 3 (Movies)

Now we have two sources:

• between units (cross section data(/ movies)

• within each unit (variation between different points in time)

• high external and internal validity

• more degreed of freedom -> higher efficency

• contol impact of unobserved heterogenity

  -> reduces problem of potential omitted variable bias

• facilitate constructing and testing more complex hypotheses -> study dynamics. treatment can not be observed in one period of time or with one person, it needs multiple persons over multiple periods of time

• Data collection is costly and time-consuming

• ”Panel mortality” or “panel attrition”: units drop out of the panel, firm lose interest, disappear excluding them -> might result in a bias (there is a reason why they disappeared)

• Missing observations → ”unbalanced panel”

• Similar problems as for time series data (e.g., autocorrelation, seasonal effects etc.)

• heterogenity = omitted variable

Movie effects:

• Some movies are of higher quality (but as this is difficult to measure, we do not observe this) (we call this unobserved heterogeneity)

• So what is influencong the amount of hours streamed? Is it really the marketing money we spent for the film? Or do we unknowingly spend moer for films with higher quality, whih means the amount of streams is dependet of the Quality not the marketing money spent

Time-related effects:

• we already know that during some months people watch less -> If we decide to advertise movies during those months, our analysis might again suffer from an omitted variable bias

• fixed effects

• random effects

• Pooled OLS

Use the Hausman Test ->The Hausman test checks if your unobserved individual effects (αᵢ) are correlated with your explanatory variables (X).

Adding entity/unit dummies

• -> für jeden Film die Qualität bestimmen -> Rechenleistung intensiv

First Differences:

• Using “first differences” between successive time periods eliminates 𝛼𝑗 as it is time independent.

Qualität pro Film bleibt gleich über Zeit -> verschwindet

Within group fixed effects:

• We can also eliminate 𝛼𝑗 by subtracting from each variable for each unit its mean value (over time)

Adding seasonal dummies:

• Add a dummy variable 𝐴𝑚 for each month (𝐴𝑚 equals 1 only for the observation unit j)

• The different constants capture the combined effects of several (or many) unknown time-related effects that are different between periods but constant for all observation units (e.g., winter effect)

-> Often, unit-fixed effects and time-fixed effects are combined.

In a random effects regression, we assume that 𝛼 is purely random, uncorrelated with the observed variables 𝑋𝑘𝑖𝑡. This means a random effects model considers 𝛼 as a random variable.

Important!

𝑢𝑖𝑡 will be subject to autocorrelation:

• OLS is inefficient and the standard errors it computes are wrong

• Alternative approach: Generalized least square (GLS)

• not so much an analysis method but a type of data set or data structure

• Many types of models can be used with panel data:

  • OLS

  • Logit, probit

  • Autoregressive models

  • Other time series models

• Correlation is not causality! (see next slide)

• we actually want to make are recommendations to managers and policymakers -> need causality: increasing A leads to an increase in B

• To prove that a causal mechanism created the correlation, we need to be able to make a ceteris paribus statement

• Ceteris paribus statement: ”keeping all other factors equal increasing A increases B.”