77. Pandas for Panel Data#

77.1. Overview#

In an earlier lecture on pandas, we looked at working with simple data sets.

Econometricians often need to work with more complex data sets, such as panels.

Common tasks include

  • Importing data, cleaning it and reshaping it across several axes.

  • Selecting a time series or cross-section from a panel.

  • Grouping and summarizing data.

pandas (derived from ‘panel’ and ‘data’) contains powerful and easy-to-use tools for solving exactly these kinds of problems.

In what follows, we will use a panel data set of real minimum wages from the OECD to create:

  • summary statistics over multiple dimensions of our data

  • a time series of the average minimum wage of countries in the dataset

  • kernel density estimates of wages by continent

We will begin by reading in our long format panel data from a CSV file and reshaping the resulting DataFrame with pivot_table to build a MultiIndex.

Additional detail will be added to our DataFrame using pandas’ merge function, and data will be summarized with the groupby function.

77.2. Slicing and Reshaping Data#

We will read in a dataset from the OECD of real minimum wages in 32 countries and assign it to realwage.

The dataset can be accessed with the following link:

url1 = 'https://raw.githubusercontent.com/QuantEcon/lecture-python/master/source/_static/lecture_specific/pandas_panel/realwage.csv'
import pandas as pd

# Display 6 columns for viewing purposes
pd.set_option('display.max_columns', 6)

# Reduce decimal points to 2
pd.options.display.float_format = '{:,.2f}'.format

realwage = pd.read_csv(url1)

Let’s have a look at what we’ve got to work with

realwage.head()  # Show first 5 rows
Unnamed: 0 Time Country Series Pay period value
0 0 2006-01-01 Ireland In 2015 constant prices at 2015 USD PPPs Annual 17,132.44
1 1 2007-01-01 Ireland In 2015 constant prices at 2015 USD PPPs Annual 18,100.92
2 2 2008-01-01 Ireland In 2015 constant prices at 2015 USD PPPs Annual 17,747.41
3 3 2009-01-01 Ireland In 2015 constant prices at 2015 USD PPPs Annual 18,580.14
4 4 2010-01-01 Ireland In 2015 constant prices at 2015 USD PPPs Annual 18,755.83

The data is currently in long format, which is difficult to analyze when there are several dimensions to the data.

We will use pivot_table to create a wide format panel, with a MultiIndex to handle higher dimensional data.

pivot_table arguments should specify the data (values), the index, and the columns we want in our resulting dataframe.

By passing a list in columns, we can create a MultiIndex in our column axis

realwage = realwage.pivot_table(values='value',
                                index='Time',
                                columns=['Country', 'Series', 'Pay period'])
realwage.head()
Country Australia ... United States
Series In 2015 constant prices at 2015 USD PPPs In 2015 constant prices at 2015 USD exchange rates ... In 2015 constant prices at 2015 USD PPPs In 2015 constant prices at 2015 USD exchange rates
Pay period Annual Hourly Annual ... Hourly Annual Hourly
Time
2006-01-01 20,410.65 10.33 23,826.64 ... 6.05 12,594.40 6.05
2007-01-01 21,087.57 10.67 24,616.84 ... 6.24 12,974.40 6.24
2008-01-01 20,718.24 10.48 24,185.70 ... 6.78 14,097.56 6.78
2009-01-01 20,984.77 10.62 24,496.84 ... 7.58 15,756.42 7.58
2010-01-01 20,879.33 10.57 24,373.76 ... 7.88 16,391.31 7.88

5 rows × 128 columns

To more easily filter our time series data, later on, we will convert the index into a DateTimeIndex

realwage.index = pd.to_datetime(realwage.index)
type(realwage.index)
pandas.core.indexes.datetimes.DatetimeIndex

The columns contain multiple levels of indexing, known as a MultiIndex, with levels being ordered hierarchically (Country > Series > Pay period).

A MultiIndex is the simplest and most flexible way to manage panel data in pandas

type(realwage.columns)
pandas.core.indexes.multi.MultiIndex
realwage.columns.names
FrozenList(['Country', 'Series', 'Pay period'])

Like before, we can select the country (the top level of our MultiIndex)

realwage['United States'].head()
Series In 2015 constant prices at 2015 USD PPPs In 2015 constant prices at 2015 USD exchange rates
Pay period Annual Hourly Annual Hourly
Time
2006-01-01 12,594.40 6.05 12,594.40 6.05
2007-01-01 12,974.40 6.24 12,974.40 6.24
2008-01-01 14,097.56 6.78 14,097.56 6.78
2009-01-01 15,756.42 7.58 15,756.42 7.58
2010-01-01 16,391.31 7.88 16,391.31 7.88

Stacking and unstacking levels of the MultiIndex will be used throughout this lecture to reshape our dataframe into a format we need.

.stack() rotates the lowest level of the column MultiIndex to the row index (.unstack() works in the opposite direction - try it out)

realwage.stack().head()
Country Australia Belgium ... United Kingdom United States
Series In 2015 constant prices at 2015 USD PPPs In 2015 constant prices at 2015 USD exchange rates In 2015 constant prices at 2015 USD PPPs ... In 2015 constant prices at 2015 USD exchange rates In 2015 constant prices at 2015 USD PPPs In 2015 constant prices at 2015 USD exchange rates
Time Pay period
2006-01-01 Annual 20,410.65 23,826.64 21,042.28 ... 20,376.32 12,594.40 12,594.40
Hourly 10.33 12.06 10.09 ... 9.81 6.05 6.05
2007-01-01 Annual 21,087.57 24,616.84 21,310.05 ... 20,954.13 12,974.40 12,974.40
Hourly 10.67 12.46 10.22 ... 10.07 6.24 6.24
2008-01-01 Annual 20,718.24 24,185.70 21,416.96 ... 20,902.87 14,097.56 14,097.56

5 rows × 64 columns

We can also pass in an argument to select the level we would like to stack

realwage.stack(level='Country').head()
Series In 2015 constant prices at 2015 USD PPPs In 2015 constant prices at 2015 USD exchange rates
Pay period Annual Hourly Annual Hourly
Time Country
2006-01-01 Australia 20,410.65 10.33 23,826.64 12.06
Belgium 21,042.28 10.09 20,228.74 9.70
Brazil 3,310.51 1.41 2,032.87 0.87
Canada 13,649.69 6.56 14,335.12 6.89
Chile 5,201.65 2.22 3,333.76 1.42

Using a DatetimeIndex makes it easy to select a particular time period.

Selecting one year and stacking the two lower levels of the MultiIndex creates a cross-section of our panel data

realwage.loc['2015'].stack(level=(1, 2)).transpose().head()
Time 2015-01-01
Series In 2015 constant prices at 2015 USD PPPs In 2015 constant prices at 2015 USD exchange rates
Pay period Annual Hourly Annual Hourly
Country
Australia 21,715.53 10.99 25,349.90 12.83
Belgium 21,588.12 10.35 20,753.48 9.95
Brazil 4,628.63 2.00 2,842.28 1.21
Canada 16,536.83 7.95 17,367.24 8.35
Chile 6,633.56 2.80 4,251.49 1.81

For the rest of lecture, we will work with a dataframe of the hourly real minimum wages across countries and time, measured in 2015 US dollars.

To create our filtered dataframe (realwage_f), we can use the xs method to select values at lower levels in the multiindex, while keeping the higher levels (countries in this case)

realwage_f = realwage.xs(('Hourly', 'In 2015 constant prices at 2015 USD exchange rates'),
                         level=('Pay period', 'Series'), axis=1)
realwage_f.head()
Country Australia Belgium Brazil ... Turkey United Kingdom United States
Time
2006-01-01 12.06 9.70 0.87 ... 2.27 9.81 6.05
2007-01-01 12.46 9.82 0.92 ... 2.26 10.07 6.24
2008-01-01 12.24 9.87 0.96 ... 2.22 10.04 6.78
2009-01-01 12.40 10.21 1.03 ... 2.28 10.15 7.58
2010-01-01 12.34 10.05 1.08 ... 2.30 9.96 7.88

5 rows × 32 columns

77.3. Merging Dataframes and Filling NaNs#

Similar to relational databases like SQL, pandas has built in methods to merge datasets together.

Using country information from WorldData.info, we’ll add the continent of each country to realwage_f with the merge function.

The dataset can be accessed with the following link:

url2 = 'https://raw.githubusercontent.com/QuantEcon/lecture-python/master/source/_static/lecture_specific/pandas_panel/countries.csv'
worlddata = pd.read_csv(url2, sep=';')
worlddata.head()
Country (en) Country (de) Country (local) ... Deathrate Life expectancy Url
0 Afghanistan Afghanistan Afganistan/Afqanestan ... 13.70 51.30 https://www.laenderdaten.info/Asien/Afghanista...
1 Egypt Ägypten Misr ... 4.70 72.70 https://www.laenderdaten.info/Afrika/Aegypten/...
2 Åland Islands Ålandinseln Åland ... 0.00 0.00 https://www.laenderdaten.info/Europa/Aland/ind...
3 Albania Albanien Shqipëria ... 6.70 78.30 https://www.laenderdaten.info/Europa/Albanien/...
4 Algeria Algerien Al-Jaza’ir/Algérie ... 4.30 76.80 https://www.laenderdaten.info/Afrika/Algerien/...

5 rows × 17 columns

First, we’ll select just the country and continent variables from worlddata and rename the column to ‘Country’

worlddata = worlddata[['Country (en)', 'Continent']]
worlddata = worlddata.rename(columns={'Country (en)': 'Country'})
worlddata.head()
Country Continent
0 Afghanistan Asia
1 Egypt Africa
2 Åland Islands Europe
3 Albania Europe
4 Algeria Africa

We want to merge our new dataframe, worlddata, with realwage_f.

The pandas merge function allows dataframes to be joined together by rows.

Our dataframes will be merged using country names, requiring us to use the transpose of realwage_f so that rows correspond to country names in both dataframes

realwage_f.transpose().head()
Time 2006-01-01 2007-01-01 2008-01-01 ... 2014-01-01 2015-01-01 2016-01-01
Country
Australia 12.06 12.46 12.24 ... 12.67 12.83 12.98
Belgium 9.70 9.82 9.87 ... 10.01 9.95 9.76
Brazil 0.87 0.92 0.96 ... 1.21 1.21 1.24
Canada 6.89 6.96 7.24 ... 8.22 8.35 8.48
Chile 1.42 1.45 1.44 ... 1.76 1.81 1.91

5 rows × 11 columns

We can use either left, right, inner, or outer join to merge our datasets:

  • left join includes only countries from the left dataset

  • right join includes only countries from the right dataset

  • outer join includes countries that are in either the left and right datasets

  • inner join includes only countries common to both the left and right datasets

By default, merge will use an inner join.

Here we will pass how='left' to keep all countries in realwage_f, but discard countries in worlddata that do not have a corresponding data entry realwage_f.

This is illustrated by the red shading in the following diagram

_images/venn_diag.png

We will also need to specify where the country name is located in each dataframe, which will be the key that is used to merge the dataframes ‘on’.

Our ‘left’ dataframe (realwage_f.transpose()) contains countries in the index, so we set left_index=True.

Our ‘right’ dataframe (worlddata) contains countries in the ‘Country’ column, so we set right_on='Country'

merged = pd.merge(realwage_f.transpose(), worlddata,
                  how='left', left_index=True, right_on='Country')
merged.head()
2006-01-01 00:00:00 2007-01-01 00:00:00 2008-01-01 00:00:00 ... 2016-01-01 00:00:00 Country Continent
17.00 12.06 12.46 12.24 ... 12.98 Australia Australia
23.00 9.70 9.82 9.87 ... 9.76 Belgium Europe
32.00 0.87 0.92 0.96 ... 1.24 Brazil South America
100.00 6.89 6.96 7.24 ... 8.48 Canada North America
38.00 1.42 1.45 1.44 ... 1.91 Chile South America

5 rows × 13 columns

Countries that appeared in realwage_f but not in worlddata will have NaN in the Continent column.

To check whether this has occurred, we can use .isnull() on the continent column and filter the merged dataframe

merged[merged['Continent'].isnull()]
2006-01-01 00:00:00 2007-01-01 00:00:00 2008-01-01 00:00:00 ... 2016-01-01 00:00:00 Country Continent
NaN 3.42 3.74 3.87 ... 5.28 Korea NaN
NaN 0.23 0.45 0.39 ... 0.55 Russian Federation NaN
NaN 1.50 1.64 1.71 ... 2.08 Slovak Republic NaN

3 rows × 13 columns

We have three missing values!

One option to deal with NaN values is to create a dictionary containing these countries and their respective continents.

.map() will match countries in merged['Country'] with their continent from the dictionary.

Notice how countries not in our dictionary are mapped with NaN

missing_continents = {'Korea': 'Asia',
                      'Russian Federation': 'Europe',
                      'Slovak Republic': 'Europe'}

merged['Country'].map(missing_continents)
17.00        NaN
23.00        NaN
32.00        NaN
100.00       NaN
38.00        NaN
108.00       NaN
41.00        NaN
225.00       NaN
53.00        NaN
58.00        NaN
45.00        NaN
68.00        NaN
233.00       NaN
86.00        NaN
88.00        NaN
91.00        NaN
NaN         Asia
117.00       NaN
122.00       NaN
123.00       NaN
138.00       NaN
153.00       NaN
151.00       NaN
174.00       NaN
175.00       NaN
NaN       Europe
NaN       Europe
198.00       NaN
200.00       NaN
227.00       NaN
241.00       NaN
240.00       NaN
Name: Country, dtype: object

We don’t want to overwrite the entire series with this mapping.

.fillna() only fills in NaN values in merged['Continent'] with the mapping, while leaving other values in the column unchanged

merged['Continent'] = merged['Continent'].fillna(merged['Country'].map(missing_continents))

# Check for whether continents were correctly mapped

merged[merged['Country'] == 'Korea']
2006-01-01 00:00:00 2007-01-01 00:00:00 2008-01-01 00:00:00 ... 2016-01-01 00:00:00 Country Continent
NaN 3.42 3.74 3.87 ... 5.28 Korea Asia

1 rows × 13 columns

We will also combine the Americas into a single continent - this will make our visualization nicer later on.

To do this, we will use .replace() and loop through a list of the continent values we want to replace

replace = ['Central America', 'North America', 'South America']

for country in replace:
    merged['Continent'].replace(to_replace=country,
                                value='America',
                                inplace=True)

Now that we have all the data we want in a single DataFrame, we will reshape it back into panel form with a MultiIndex.

We should also ensure to sort the index using .sort_index() so that we can efficiently filter our dataframe later on.

By default, levels will be sorted top-down

merged = merged.set_index(['Continent', 'Country']).sort_index()
merged.head()
2006-01-01 2007-01-01 2008-01-01 ... 2014-01-01 2015-01-01 2016-01-01
Continent Country
America Brazil 0.87 0.92 0.96 ... 1.21 1.21 1.24
Canada 6.89 6.96 7.24 ... 8.22 8.35 8.48
Chile 1.42 1.45 1.44 ... 1.76 1.81 1.91
Colombia 1.01 1.02 1.01 ... 1.13 1.13 1.12
Costa Rica NaN NaN NaN ... 2.41 2.56 2.63

5 rows × 11 columns

While merging, we lost our DatetimeIndex, as we merged columns that were not in datetime format

merged.columns
Index([2006-01-01 00:00:00, 2007-01-01 00:00:00, 2008-01-01 00:00:00,
       2009-01-01 00:00:00, 2010-01-01 00:00:00, 2011-01-01 00:00:00,
       2012-01-01 00:00:00, 2013-01-01 00:00:00, 2014-01-01 00:00:00,
       2015-01-01 00:00:00, 2016-01-01 00:00:00],
      dtype='object')

Now that we have set the merged columns as the index, we can recreate a DatetimeIndex using .to_datetime()

merged.columns = pd.to_datetime(merged.columns)
merged.columns = merged.columns.rename('Time')
merged.columns
DatetimeIndex(['2006-01-01', '2007-01-01', '2008-01-01', '2009-01-01',
               '2010-01-01', '2011-01-01', '2012-01-01', '2013-01-01',
               '2014-01-01', '2015-01-01', '2016-01-01'],
              dtype='datetime64[ns]', name='Time', freq=None)

The DatetimeIndex tends to work more smoothly in the row axis, so we will go ahead and transpose merged

merged = merged.transpose()
merged.head()
Continent America ... Europe
Country Brazil Canada Chile ... Slovenia Spain United Kingdom
Time
2006-01-01 0.87 6.89 1.42 ... 3.92 3.99 9.81
2007-01-01 0.92 6.96 1.45 ... 3.88 4.10 10.07
2008-01-01 0.96 7.24 1.44 ... 3.96 4.14 10.04
2009-01-01 1.03 7.67 1.52 ... 4.08 4.32 10.15
2010-01-01 1.08 7.94 1.56 ... 4.81 4.30 9.96

5 rows × 32 columns

77.4. Grouping and Summarizing Data#

Grouping and summarizing data can be particularly useful for understanding large panel datasets.

A simple way to summarize data is to call an aggregation method on the dataframe, such as .mean() or .max().

For example, we can calculate the average real minimum wage for each country over the period 2006 to 2016 (the default is to aggregate over rows)

merged.mean().head(10)
Continent  Country      
America    Brazil          1.09
           Canada          7.82
           Chile           1.62
           Colombia        1.07
           Costa Rica      2.53
           Mexico          0.53
           United States   7.15
Asia       Israel          5.95
           Japan           6.18
           Korea           4.22
dtype: float64

Using this series, we can plot the average real minimum wage over the past decade for each country in our data set

import matplotlib.pyplot as plt
import seaborn as sns
sns.set_theme()
merged.mean().sort_values(ascending=False).plot(kind='bar',
                                                title="Average real minimum wage 2006 - 2016")

# Set country labels
country_labels = merged.mean().sort_values(ascending=False).index.get_level_values('Country').tolist()
plt.xticks(range(0, len(country_labels)), country_labels)
plt.xlabel('Country')

plt.show()
_images/9414e44d51d728a2f6f3d91d4e9016e540c0160c32a6ff818e1d52e05657b10a.png

Passing in axis=1 to .mean() will aggregate over columns (giving the average minimum wage for all countries over time)

merged.mean(axis=1).head()
Time
2006-01-01   4.69
2007-01-01   4.84
2008-01-01   4.90
2009-01-01   5.08
2010-01-01   5.11
dtype: float64

We can plot this time series as a line graph

merged.mean(axis=1).plot()
plt.title('Average real minimum wage 2006 - 2016')
plt.ylabel('2015 USD')
plt.xlabel('Year')
plt.show()
_images/5148ae57ad1923223e21ee73e645459a76affa9d764b40aa9f2388aa1f712513.png

We can also specify a level of the MultiIndex (in the column axis) to aggregate over

merged.groupby(level='Continent', axis=1).mean().head()
Continent America Asia Australia Europe
Time
2006-01-01 2.80 4.29 10.25 4.80
2007-01-01 2.85 4.44 10.73 4.94
2008-01-01 2.99 4.45 10.76 4.99
2009-01-01 3.23 4.53 10.97 5.16
2010-01-01 3.34 4.53 10.95 5.17

We can plot the average minimum wages in each continent as a time series

merged.groupby(level='Continent', axis=1).mean().plot()
plt.title('Average real minimum wage')
plt.ylabel('2015 USD')
plt.xlabel('Year')
plt.show()
_images/a74d4673a5d2175112b698ebd5e0216e131ca7e500b382eb49f5c7ce5bcb6db6.png

We will drop Australia as a continent for plotting purposes

merged = merged.drop('Australia', level='Continent', axis=1)
merged.groupby(level='Continent', axis=1).mean().plot()
plt.title('Average real minimum wage')
plt.ylabel('2015 USD')
plt.xlabel('Year')
plt.show()
_images/e113ef995952ca298abb675f8c25fa6bed8cc066ab66b912aa619ea472eaaa36.png

.describe() is useful for quickly retrieving a number of common summary statistics

merged.stack().describe()
Continent America Asia Europe
count 69.00 44.00 200.00
mean 3.19 4.70 5.15
std 3.02 1.56 3.82
min 0.52 2.22 0.23
25% 1.03 3.37 2.02
50% 1.44 5.48 3.54
75% 6.96 5.95 9.70
max 8.48 6.65 12.39

This is a simplified way to use groupby.

Using groupby generally follows a ‘split-apply-combine’ process:

  • split: data is grouped based on one or more keys

  • apply: a function is called on each group independently

  • combine: the results of the function calls are combined into a new data structure

The groupby method achieves the first step of this process, creating a new DataFrameGroupBy object with data split into groups.

Let’s split merged by continent again, this time using the groupby function, and name the resulting object grouped

grouped = merged.groupby(level='Continent', axis=1)
grouped
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x7ff559d9a710>

Calling an aggregation method on the object applies the function to each group, the results of which are combined in a new data structure.

For example, we can return the number of countries in our dataset for each continent using .size().

In this case, our new data structure is a Series

grouped.size()
Continent
America     7
Asia        4
Europe     19
dtype: int64

Calling .get_group() to return just the countries in a single group, we can create a kernel density estimate of the distribution of real minimum wages in 2016 for each continent.

grouped.groups.keys() will return the keys from the groupby object

continents = grouped.groups.keys()

for continent in continents:
    sns.kdeplot(grouped.get_group(continent).loc['2015'].unstack(), label=continent, fill=True)

plt.title('Real minimum wages in 2015')
plt.xlabel('US dollars')
plt.legend()
plt.show()
_images/00e547bc0f21411760d01689456c029d3ddff4f76768ae841a16ff5cd2804ac7.png

77.5. Final Remarks#

This lecture has provided an introduction to some of pandas’ more advanced features, including multiindices, merging, grouping and plotting.

Other tools that may be useful in panel data analysis include xarray, a python package that extends pandas to N-dimensional data structures.

77.6. Exercises#

Exercise 77.1

In these exercises, you’ll work with a dataset of employment rates in Europe by age and sex from Eurostat.

The dataset can be accessed with the following link:

url3 = 'https://raw.githubusercontent.com/QuantEcon/lecture-python/master/source/_static/lecture_specific/pandas_panel/employ.csv'

Reading in the CSV file returns a panel dataset in long format. Use .pivot_table() to construct a wide format dataframe with a MultiIndex in the columns.

Start off by exploring the dataframe and the variables available in the MultiIndex levels.

Write a program that quickly returns all values in the MultiIndex.

Exercise 77.2

Filter the above dataframe to only include employment as a percentage of ‘active population’.

Create a grouped boxplot using seaborn of employment rates in 2015 by age group and sex.