ECONOMIC STATISTICS

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ECONOMIC STATISTICS

Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics,

Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE) Department of Economics, Eötvös Loránd University Budapest

Institute of Economics, Hungarian Academy of Sciences Balassi Kiadó, Budapest

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Author: Anikó Bíró Supervised by Anikó Bíró

June 2010

Week 2

Data types, descriptive statistics, indices Data types I

• Time series:

• Variables ordered in time

• Freqency of observations (e.g. monthly, yearly)

• Notation: Yt

• Examples (macroeconomic, financial – individual?)

• Cross sectional:

• Sample of economic agents at a given time point

• Examples (individuals, enterprises, countries)

• Notation: Yi

• Random sample

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Data types II

• Panel:

• Time series + cross sectional jointly

• Observation of the cross sectional sample throughout more time periods

• Notation: Yit

• Examples (GDP of European countries, panel of individual households)

Data types III

• Quantitative and qualitative

• Quantitative: e.g. inflation, income

• Qualitative: e.g. male/female, education level – code as numbers

• Level and dynamics

• E.g. number of employed vs. change in employment

) 100 change (

% 

^¹

 

t t t

Y

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Time series graphs

HUF/USD monthly exchange rate

50 100 150 200 250 300 350

1994. 1995. 1996. 1997. 1998. 1999. 2000. 2001. 2002. 2003. 2004. 2005. 2006. 2007. 2008. 2009.

EU27 population

440 450 460 470 480 490 500

1970 1975 1980 1985 1990 1995 2000 2005 2010

million

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Histograms

• Plotting cross sectional data

• Example: distribution of income per capita

• Equal intervals (brackets) – determine it in Excel according to the data

• Frequency within the intervals

Histogram, example

• Penn World: distribution of countries according to population (bracket size: 5000)

Population (thousand) histogram

0 10 20 30 40 50 60 70 80 90

0 15000 30000 45000 60000 75000 90000 105000 120000 135000

Frequency

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• SHARE: cross sectional sample of people aged 50+

• Value of the car, Austrian subsample (bracket size: 1000) 0

200 400 600 800 1000 1200 1400

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

F re q u e n c y

Euro

Histogram of car value – Austria, 50+

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Point diagram

• Relationship between two variables

• KSH: data on counties

0 2 4 6 8 10 12 14 16 18 20

0 1000 2000 3000 4000 5000 6000

GDP/capita (th HUF)

Unemployment rate (%)

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8 Eurostat: number of students and children in kindergarten by countries, 2007

Descriptive statistics

• Up to now: graphical methods

• Descriptive statistics: numerical summary of some characteristics of the variables

• Level? – mean, median, mode

• Variability? – standard deviation, range

0 500 1000 1500 2000 2500 3000 3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

# students

# children in kindergarten

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Mean

N Y Y

N

i



i



¹

• N: number of observations

• Example: mean of country population (Penn World Table) – ca. 34 million

Mode

Mode: most frequent observation

• Problem: does not always exist (e.g. one from each value), there can be more modes

• Possible solution: highest point of the histogram (depends on brackets) – center of the interval

Median, percentile

• Median: value in the middle – half of the observations below the median

• Xth percentile: X% of the observations below X

• Quartile: cuts the observations into four

• 1st quartile: 25% below, 2nd quartile = median

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Skewness

• Example: mean > median

• Some large values – mean is large

• Skewed to the left

• Long right tail

Standard deviation

• Range: difference between maximum and minimum

• Not reliable (outlier values)

• Variance: mean of squared differences from the mean

• Standard deviation:

• Difficult to interpret on its own

Population (thousand) histogram

0 10 20 30 40 50 60 70 80 90

0 15000 30000 45000 60000 75000 90000 105000 120000 135000

Frequency

1 ) (

1

2





 



N Y Y Var

s

N

i i

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Indices

• Price index

• Price level, average price are difficult to interpret

• Price index: price level as % of price level at the basic period

• Annual inflation: basic period changes yearly

Annual price indices, example

-5 0 5 10 15 20 25

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

%

Busz menetjegyBus ticket Fehér kenyér, kgWhite bread, kg

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Change of population

• Base: previous year

Change of population, EU27

1 1.001 1.002 1.003 1.004 1.005 1.006

1976 1980 1984 1988 1992 1996 2000 2004 2008

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Summary

• Data types:

• Time series, cross sectional, panel

• Quantitative, qualitative

• Graphical methods: time series, histogram, point diagram

• Descriptive statistics:

• Mean, mode, median

• Skewness

• Standard deviation

Data types, descriptive statistics, indices

Seminar 2

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Time series graphs

HUF/EUR exchange rate? – graph, analysis

HUF/USD monthly exchange rate

50 100 150 200 250 300 350

1994. 1995. 1996. 1997. 1998. 1999. 2000. 2001. 2002. 2003. 2004. 2005. 2006. 2007. 2008. 2009.

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Histograms

• Graphical analysis of cross sectional data

• Excel: Analysis ToolPak extension

• Equal intervals (brackets) – determine it in Excel according to the

• Frequency within the brackets

• Excel: missing observations cause problems – solution: sorting

Histogram, example

• Penn World: distribution of countries according to population

• Histogram of GDP/capital? Suggested bracket size: 2000 Population (thousand) histogram

0 10 20 30 40 50 60 70 80 90

0 15000 30000 45000 60000 75000 90000 105000 120000 135000

Frequency

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Point diagram

• Relationship between two variables

• KSH: data on counties

• GDP/capital and number of registered enterprises? – What is expected? What can be seen?

Mean

N Y Y

N

i



i



¹

0 2 4 6 8 10 12 14 16 18 20

0 1000 2000 3000 4000 5000 6000

GDP/capita (th HUF)

Unemployment rate (%)

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• N: number of observations

• Examples: average population of countries, average income/capital (Penn World Tables)

Mode

Mode: most frequent value Examples:

• Country populations

• GDP per capita

• Based on histograms!

Median, percentile

• Median: middle value – half of the observations below

• Xth percentile: X% of the observations below

• Excel: descriptive statistics (median) + percentile function

• Example: median, 3rd quartile of population and GDP/capita?

• E.g. Median=PERCENTILE(B3:B189;0.5)

Standard deviation

• Range: difference between maximum and minimum

• MIN(), MAX() functions

• Not reliable (outliers)

• Variance: mean of squared differences

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• Standard deviation:

1 ) (

1

2





 



N

Y Y Var

s

N

i

• Range, variance, and standard deviation based on Penn World GDP/capita data (descriptive statistics table + functions)

Indices

KSH data

Price indices of bread and bus ticket

• Fix base

• Yearly changing base

• Graphical analysis

Homework 1 (groups)

1. Graphical analysis of a time series variable

2. Analysis of an economic indicator of a cross sectional sample with the help of histogram

3. Analysis of the relationship between two indicators of a cross sectional sample with the help of point diagram

For all three tasks: graph + one paragraph analysis!