econometrics Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...

, a multidimensional panel data is data of a phenomenon observed over three or more dimensions. This comes in contrast with

panel data In statistics and econometrics, panel data and longitudinal data are both multi-dimensional data involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time. Time series and ...

, observed over two dimensions (typically,

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...

and cross-sections). An example is a data set containing forecasts of one or multiple macroeconomic variables produced by multiple individuals (the first dimension), in multiple series (the second dimension) at multiple times periods (the third dimension) and for multiple horizons (the fourth dimension).

Analysis of multidimensional panel data

A multidimensional panel with four dimensions can have the form :

X_, \; i = 1, \dots, N, \; s = 1, \dots, S, \; t = 1, \dots, T, \; h = 1, \dots, H, \,

where ''i'' is the individual dimension, ''s'' is the series dimension, ''t'' is the time dimension, and ''h'' is the horizon dimension. A general multidimensional panel data

regression model In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...

is written as :

y_ = \alpha + X_ \beta + u_.\,

Complex assumptions can be made on the precise structure of the correlations among errors in this model. For example, serial correlation (error terms correlated across time) has multiple distinct meanings. Error terms can be correlated across time for the same series, individual, and horizon. They can be correlated across time and across series for the same individual and horizon, etc. Similarly,

heteroskedasticity In statistics, a sequence (or a vector) of random variables is homoscedastic () if all its random variables have the same finite variance. This is also known as homogeneity of variance. The complementary notion is called heteroscedasticity. The s ...

can be defined across individuals for the same series, time, and horizon, across individuals and different series for the same time and horizon, etc.

Data sets which have a multidimensional panel design

*Blue Chip

Survey of Professional Forecasters The Survey of Professional Forecasters (SPF) is a quarterly survey of macroeconomic forecasts for the economy of the United States issued by the Federal Reserve Bank of Philadelphia. It is the oldest such survey in the United States. The survey i ...

*Survey of Professional Forecasters (ASA-NBER)

References

* * * * *{{cite book , last=Hsiao , first=Cheng , year=2003 , title=Analysis of Panel Data , location=New York , publisher=Cambridge University Press , edition=Second , isbn=0-521-52271-4 Multivariate time series Statistical data types da:Paneldata es:Datos de panel fi:Paneeliaineisto

Analysis of multidimensional panel data

Data sets which have a multidimensional panel design

See also

References