Panel analysis GudangMovies21 Rebahinxxi LK21

      Panel (data) analysis is a statistical method, widely used in social science, epidemiology, and econometrics to analyze two-dimensional (typically cross sectional and longitudinal) panel data. The data are usually collected over time and over the same individuals and then a regression is run over these two dimensions. Multidimensional analysis is an econometric method in which data are collected over more than two dimensions (typically, time, individuals, and some third dimension).
      A common panel data regression model looks like




      y

      i
      t


      =
      a
      +
      b

      x

      i
      t


      +

      ε

      i
      t




      {\displaystyle y_{it}=a+bx_{it}+\varepsilon _{it}}

      , where



      y


      {\displaystyle y}

      is the dependent variable,



      x


      {\displaystyle x}

      is the independent variable,



      a


      {\displaystyle a}

      and



      b


      {\displaystyle b}

      are coefficients,



      i


      {\displaystyle i}

      and



      t


      {\displaystyle t}

      are indices for individuals and time. The error




      ε

      i
      t




      {\displaystyle \varepsilon _{it}}

      is very important in this analysis. Assumptions about the error term determine whether we speak of fixed effects or random effects. In a fixed effects model,




      ε

      i
      t




      {\displaystyle \varepsilon _{it}}

      is assumed to vary non-stochastically over



      i


      {\displaystyle i}

      or



      t


      {\displaystyle t}

      making the fixed effects model analogous to a dummy variable model in one dimension. In a random effects model,




      ε

      i
      t




      {\displaystyle \varepsilon _{it}}

      is assumed to vary stochastically over



      i


      {\displaystyle i}

      or



      t


      {\displaystyle t}

      requiring special treatment of the error variance matrix.
      Panel data analysis has three more-or-less independent approaches:

      independently pooled panels;
      random effects models;
      fixed effects models or first differenced models.
      The selection between these methods depends upon the objective of the analysis, and the problems concerning the exogeneity of the explanatory variables.


      Independently pooled panels



      Key assumption:
      There are no unique attributes of individuals within the measurement set, and no universal effects across time.


      Fixed effect models


      Key assumption:
      There are unique attributes of individuals that do not vary over time. That is, the unique attributes for a given individual



      i


      {\displaystyle i}

      are time



      t


      {\displaystyle t}

      invariant. These attributes may or may not be correlated with the individual dependent variables yi. To test whether fixed effects, rather than random effects, is needed, the Durbin–Wu–Hausman test can be used.


      Random effects models



      Key assumption:
      There are unique, time constant attributes of individuals that are not correlated with the individual regressors. Pooled OLS can be used to derive unbiased and consistent estimates of parameters even when time constant attributes are present, but random effects will be more efficient.
      Random effects model is a feasible generalised least squares technique which is asymptotically more efficient than Pooled OLS when time constant attributes are present. Random effects adjusts for the serial correlation which is induced by unobserved time constant attributes.


      Models with instrumental variables


      In the standard random effects (RE) and fixed effects (FE) models, independent variables are assumed to be uncorrelated with error terms. Provided the availability of valid instruments, RE and FE methods extend to the case where some of the explanatory variables are allowed to be endogenous. As in the exogenous setting, RE model with Instrumental Variables (REIV) requires more stringent assumptions than FE model with Instrumental Variables (FEIV) but it tends to be more efficient under appropriate conditions.
      To fix ideas, consider the following model:





      y

      i
      t


      =

      x

      i
      t


      β
      +

      c

      i


      +

      u

      i
      t




      {\displaystyle y_{it}=x_{it}\beta +c_{i}+u_{it}}


      where




      c

      i




      {\displaystyle c_{i}}

      is unobserved unit-specific time-invariant effect (call it unobserved effect) and




      x

      i
      t




      {\displaystyle x_{it}}

      can be correlated with




      u

      i
      s




      {\displaystyle u_{is}}

      for s possibly different from t. Suppose there exists a set of valid instruments




      z

      i


      =
      (

      z

      i
      1


      ,

      ,

      z

      i
      t


      )


      {\displaystyle z_{i}=(z_{i1},\ldots ,z_{it})}

      .
      In REIV setting, key assumptions include that




      z

      i




      {\displaystyle z_{i}}

      is uncorrelated with




      c

      i




      {\displaystyle c_{i}}

      as well as




      u

      i
      t




      {\displaystyle u_{it}}

      for



      t
      =
      1
      ,

      ,
      T


      {\displaystyle t=1,\ldots ,T}

      . In fact, for REIV estimator to be efficient, conditions stronger than uncorrelatedness between instruments and unobserved effect are necessary.
      On the other hand, FEIV estimator only requires that instruments be exogenous with error terms after conditioning on unobserved effect i.e.



      E
      [

      u

      i
      t




      z

      i


      ,

      c

      i


      ]
      =
      0
      [
      1
      ]


      {\displaystyle E[u_{it}\mid z_{i},c_{i}]=0[1]}

      . The FEIV condition allows for arbitrary correlation between instruments and unobserved effect. However, this generality does not come for free: time-invariant explanatory and instrumental variables are not allowed. As in the usual FE method, the estimator uses time-demeaned variables to remove unobserved effect. Therefore, FEIV estimator would be of limited use if variables of interest include time-invariant ones.
      The above discussion has parallel to the exogenous case of RE and FE models. In the exogenous case, RE assumes uncorrelatedness between explanatory variables and unobserved effect, and FE allows for arbitrary correlation between the two. Similar to the standard case, REIV tends to be more efficient than FEIV provided that appropriate assumptions hold.


      Dynamic panel models



      In contrast to the standard panel data model, a dynamic panel model also includes lagged values of the dependent variable as regressors. For example, including one lag of the dependent variable generates:





      y

      i
      t


      =
      a
      +
      b

      x

      i
      t


      +
      ρ

      y

      i
      t

      1


      +

      ε

      i
      t




      {\displaystyle y_{it}=a+bx_{it}+\rho y_{it-1}+\varepsilon _{it}}


      The assumptions of the fixed effect and random effect models are violated in this setting. Instead, practitioners use a technique like the Arellano–Bond estimator.


      See also


      Panel study
      Factor analysis
      Hausman test


      References

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    Overall Result of Panel Analysis | Download Scientific Diagram

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    Panel analysis - Wikipedia

    Panel (data) analysis is a statistical method, widely used in social science, epidemiology, and econometrics to analyze two-dimensional (typically cross sectional and longitudinal) panel data. [1] The data are usually collected over time and over the same individuals and then a regression is run over these two dimensions.

    Introduction to Regression Models for Panel Data Analysis ...

    Oct 7, 2011 · WIM Panel Data Analysis October 2011| Page 1 What are Panel Data? Panel data are a type of longitudinal data, or data collected at different points in time. Three main types of longitudinal data: Time series data. Many observations (large t) on as few as one unit (small N). Examples: stock price trends, aggregate national statistics.

    Panel Data Analysis - What It Is, Examples, Advantages, Methods

    Panel data analysis is a statistical method used to examine data collected over time from multiple entities comprehensively. It is instrumental in capturing within-subject variations and between-subject differences simultaneously.

    Panel Data Analysis - an overview | ScienceDirect Topics

    Panel Data Analysis refers to a research method that combines time series and cross-sectional data to study changes over time. It allows researchers in social sciences to conduct longitudinal analyses by considering dynamics and variations across different dimensions simultaneously.

    1 The basics of panel data - University of California, Berkeley

    In a panel data set we track the unit of observation over time; this could be a state, city, individual, rm, etc.. To help you visualize these types of data we’ll consider some sample data sets below.

    What Is Panel Data? (With Uses, Advantages and an Example)

    Oct 14, 2023 · Panel data is a type of data that professionals collect by observing particular variables over a period of time at a regular frequency. This data can help experts establish trends, make correlations and guide further analysis of the variables included in the panel data.

    Panel Data: Meaning and Analysis Methods - SPUR ECONOMICS

    Dec 13, 2024 · Panel data analysis combines the strengths of time series and cross-sectional data, enabling a deeper understanding of complex phenomena. Hence, it involves repeated measurements of the same variables across different entities, such as …