3.1 Data structure

• Sample data which consists of multiple units ($i=1,~2,~3,...,n$) observed at a single point in time or one time interval, represents cross-sectional data or spatial data

• Conversely, if the values of the variables for a single unit are observed over time ($t=1,~2,~3,...,T$) these are known as time-series or historical data

• Data observed for same multiple units across same multiple time periods are known as panel data, which are indexed by two subscripts $i$ and $t$, where the total number of observations is $n\times T$.

TABLE 3.1: Cross-sectional data vs time-seris data

Country Life expec. Poverty rate Bulgaria 71.4 31.7 Czech 77.2 10.7 Estonia 77.2 22.2 Croatia 76.7 20.9 Italy 82.7 25.2 Latvia 73.1 26.1 Hungary 74.3 19.4 Poland 75.5 16.8 Romania 72.8 34.4 Slovenia 80.7 13.2

Years Life expec. Poverty rate 2013 77.8 25.3 2014 77.9 24.9 2015 77.5 24.4 2016 78.2 23.5 2017 78.1 23.7 2018 78.2 22.1 2019 78.6 20.8 2020 77.8 20.5 2021 76.7 20.9 2022 77.7 19.9

Exercise 10. According to above tables in which year the cross-sectional data are observed? For which country the time-series data are observed?

Solution

BBy finding a matching pair of life expectancy and poverty rate [$76.7, ~ 20.9$], we conclude that the cross-sectional data were observed in the year 2021, while the time-series data pertain to Croatia.

TABLE 3.2: Panel data

Country	Year	Life expec.	poverty rate
Bulgaria	2013	74.9	NA
Bulgaria	2014	74.5	NA
Bulgaria	2015	74.7	43.3
Bulgaria	2016	74.9	41
Bulgaria	2017	74.8	38
Bulgaria	2018	75	33
Bulgaria	2019	75.1	33.2
Bulgaria	2020	73.6	33.5
Bulgaria	2021	71.4	31.7
Bulgaria	2022	74.3	32.2
Czech	2013	78.3	NA
Czech	2014	78.9	NA
Czech	2015	78.7	13
Czech	2016	79.1	12.4
Czech	2017	79.1	12.1
Czech	2018	79.1	11.8
Czech	2019	79.3	12.1
Czech	2020	78.2	11.5
Czech	2021	77.2	10.7
Czech	2022	79.1	11.8
…	…	…	…
…	…	…	…

• Panel data are repeated measurements of the same cross-sectional units

• If there are missing values, they are referred to as unbalanced panel data