The analysis of data-sets at a fixed point in time
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Cross-sectional data analysis is when you analyze a data set at a fixed point in time. Surveys and government records are some common sources of cross-sectional data. The datasets record observations of multiple variables at a particular point in time.
Financial analysts may, for example, want to compare the financial position of two companies at a specific point in time. To do so, they would compare the two companies’ balance sheets.
Below are Amazon’s and Apple’s End of Year Consolidated Balance Sheets. An analyst could use them to look at their 2018 financial position. However, the slight difference in reporting period ending dateas could necessitate making a few adjustments.
Gross Domestic Product (GDP) of North American countries in 2012 – The economic unit of analysis is a country from North America. The economic unit of analysis is for the time period 2012. A typical entry from the dataset would be (the United States of America, $16.16 trillion).
GDP per capita of European countries in 2010 – The economic unit of analysis is a country from Europe. The economic unit of analysis is for the time period 2010. A typical entry from the dataset would be (Germany, $41,700).
Total steel exported by Asian countries in 2015 – The economic unit of analysis is a country from Asia. The economic unit of analysis is for the time period 2015. A typical entry from the dataset would be (India, $3.17 billion).
Total oranges eaten by households in Ghana in 2018 – The economic unit of analysis is a household in Ghana. The economic unit of analysis is for the time period 2018. A typical entry from the dataset would be (Household 302, 200 oranges).
Uses of Cross-Sectional Data
Cross-sectional datasets are used extensively in economics and other social sciences. Applied microeconomics uses cross-sectional datasets to analyze labor markets, public finance, industrial organization theory, and health economics. Political scientists use cross-sectional data to analyze demography and electoral campaigns.
Financial Analysts will typically compare the financial statements of two companies, a cross sectional analysis would be to compare the statements of two companies at the same point in time. Contrast that to time-series data analysis, which would compare the financial statements of the same company across multiple time periods.
Random sampling framework is a statistical framework that is widely used in data analysis. The random sampling method works under the assumption that there exists a close link between the population and a sample taken from that population.
Consider the example of orange consumption by Ghanaian households described above. It would take a lot of resources (both time and money) to measure the actual orange consumption of every household in Ghana. It would be much cheaper to only measure the orange consumption of 1,000 households in Ghana. In such a case, the population consists of every household in Ghana, and the sample consists of the 1,000 households whose orange consumption data is known.
Econometric analysis of cross-sectional data sets usually assumes that the data is independently generated and that the observations are mutually independent. Such an assumption of independently generated data is violated when the economic unit of analysis is large, relative to the population.
Suppose we want to analyze the GDP of all countries in North America. Our population, in this case, consists of 23 countries. Any sample we construct from the population can’t possibly support the construction of a mutually independent random sample. For example, it is extremely likely that the GDP of the United States is correlated with the GDP of Canada.
Random Sample in Cross-Sectional Data Analysis
Consider a cross-sectional dataset that measures K characteristics for N different economic entities at time t. An individual observation in the cross-sectional dataset is of the form:
Un is the nth economic unit of analysis
X1n is the ith characteristic for the nth economic unit
t is the time
The cross-sectional dataset was created using a random sample drawn from the population (F, X, t), where F is the joint distribution of all (U,X) in the population at time t.
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