Unemployment and Labor Markets over the Business Cycle¶
We will take a look at the data on unemployment and functioning of labor markets in the United States
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%matplotlib inline
import numpy as np
import pandas as pd
import statsmodels.api as sm
import matplotlib.pyplot as plt
from pandas_datareader.data import DataReader
In [2]:
from matplotlib import rcParams
# Restore old behavior of rounding default axis ranges
rcParams['axes.autolimit_mode'] = 'round_numbers'
rcParams['axes.xmargin'] = 0
rcParams['axes.ymargin'] = 0
Below we are downloading two datasets.
The first dataset, fred, contains monthly data on:
- whether in a given month the US economy was in a recession state (
1) or not (0) -USREC - number of people in labor force in thousands -
CLF16OV - number of unemployed people in thousands -
UNEMPLOY - unemployment rate in percent -
UNRATE - number of job openings (vacancies) in thousands -
JTSJOL - job vacancy rate -
JTSJOR
The second dataset, hours, contains quarterly data on:
- real GDP in billions of 2009 dollars -
GDPC1 - total hours worked in the nonfarm business sector (index) -
HOANBS - average hours worked per employee in the nonfarm business sector (index) -
PRS85006023 - number of employees in the nonfarm business sector (index) -
PRS85006013
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# Get FRED data
fred = DataReader(['USREC','CLF16OV','UNEMPLOY','UNRATE','JTSJOL','JTSJOR'],
'fred', start='1947-01', end='2020-01')
hours = DataReader(['GDPC1','HOANBS','PRS85006023','PRS85006013'],
'fred', start='1947-01', end='2020-01')
Separate trend and cyclical components of GDP, hours and employment
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hp_cycle, hp_trend = sm.tsa.filters.hpfilter(100*np.log(hours[['GDPC1','HOANBS','PRS85006023','PRS85006013']]).dropna())
cf_cycle, cf_trend = sm.tsa.filters.cffilter(100*np.log(hours[['GDPC1','HOANBS','PRS85006023','PRS85006013']]).dropna())
Compare cyclical components of total hours worked vs its components: hours per employee and number of employees
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hp_cycle.columns = ['Output','Total Hours','Hours per Employee','Employment']
cf_cycle.columns = ['Output','Total Hours','Hours per Employee','Employment']
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))
cf_cycle[['Total Hours','Employment']].to_period('D').plot(ax=ax1, style=['k-','r-'], lw=2)
ylim = ax1.get_ylim()
ax1.hlines(0, cf_cycle.index[0], cf_cycle.index[-1], linewidth=0.5)
ax1.fill_between(fred.index, ylim[0], ylim[1], fred['USREC'], facecolor='lightgrey', edgecolor='lightgrey')
l = ax1.legend(loc='upper right')
l.get_frame().set_linewidth(0)
l.get_frame().set_alpha(1)
cf_cycle[['Total Hours','Hours per Employee']].to_period('D').plot(ax=ax2, style=['k-','r-'], lw=2)
ylim = ax2.get_ylim()
ax2.hlines(0, cf_cycle.index[0], cf_cycle.index[-1], linewidth=0.5)
ax2.fill_between(fred.index, ylim[0], ylim[1], fred['USREC'], facecolor='lightgrey', edgecolor='lightgrey')
l = ax2.legend(loc='upper right')
l.get_frame().set_linewidth(0)
l.get_frame().set_alpha(1)
# plt.savefig('Hours_CF.pdf', bbox_inches='tight', pad_inches=0.05)
plt.show()
Calculate the variance-covariance matrix of total hours worked and its components
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hp_cycle[['Total Hours','Employment','Hours per Employee']].cov()
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Constructing the vacancy rate time series¶
The statistics on job openings (vacancies) from the JOLTS program are available only starting from December 2000. However, there are data on Help Wanted Index, which were gathered by private companies. Thanks to the work of Regis Barnichon, we can use them.
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dta = fred.copy()
dta.tail()
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dta[['JTSJOR','UNRATE']]['2000-12':].plot()
plt.legend(frameon=False)
plt.show()
Read in Regis Barnichon's Composite Help Wanted Index and join the two datasets
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hwi = pd.read_csv('data/HWI_index_old.txt', delimiter='\t', skiprows=5)
# Manage dates
dates = []
for date in hwi['Date ']:
dates.append(date[-2:]+'-01-'+date[0:4])
hwi.index = pd.to_datetime(dates)
hwi.index.rename('DATE', inplace=True)
# Cleanup
hwi = hwi.drop('Date ', 1)
hwi.columns = ['HWI']
hwi.tail()
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# Join datasets
df = dta.join(hwi)
df.tail()
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Adjust the index to observed levels and splice the data from two sources
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df['Vacancies'] = df['JTSJOL']['2014-01-01'] * df['HWI'] / df['HWI']['2014-01-01']
df['Vacancies']['2005-01-01':] = df['JTSJOL']['2005-01-01':]
df[['Vacancies','JTSJOL']].plot()
plt.legend(frameon=False)
plt.show()
Construct time series for unemployment and vacancy rates
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df['Unemployment rate'] = 100 * df['UNEMPLOY'] / df['CLF16OV']
df['Vacancy rate'] = 100 * df['Vacancies'] / df['CLF16OV']
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fig, ax = plt.subplots()
df['Vacancy rate'].to_period('D').plot(ax=ax, style='k', lw=2)
df['Unemployment rate'].to_period('D').plot(ax=ax, style='r', lw=2)
ylim = ax.get_ylim()
ax.fill_between(fred.index, ylim[0], ylim[1], fred['USREC'], facecolor='lightgrey', edgecolor='lightgrey')
l = ax.legend(loc='upper left')
l.get_frame().set_linewidth(0)
l.get_frame().set_alpha(1)
plt.title('US vacancy and unemployment rates (%)')
# plt.savefig('VU.pdf')
plt.show()
Behavior of unemployment and vacancy rates in the United States¶
Below I plot the scatterplot of unemployment and vacancy rates, with colors reflecting different decades.
The resulting negative relationship is known as the Beveridge curve
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dfq = df.resample('QS').mean()
plt.plot(dfq['Unemployment rate']['1950-01-01':'1959-12-01'],
dfq['Vacancy rate']['1950-01-01':'1959-12-01'], 'o-', label='1950s')
plt.plot(dfq['Unemployment rate']['1960-01-01':'1969-12-01'],
dfq['Vacancy rate']['1960-01-01':'1969-12-01'], 'o-', label='1960s')
plt.plot(dfq['Unemployment rate']['1970-01-01':'1979-12-01'],
dfq['Vacancy rate']['1970-01-01':'1979-12-01'], 'o-', label='1970s')
plt.plot(dfq['Unemployment rate']['1980-01-01':'1989-12-01'],
dfq['Vacancy rate']['1980-01-01':'1989-12-01'], 'o-', label='1980s')
plt.plot(dfq['Unemployment rate']['1990-01-01':'1999-12-01'],
dfq['Vacancy rate']['1990-01-01':'1999-12-01'], 'o-', label='1990s')
plt.plot(dfq['Unemployment rate']['2000-01-01':'2009-12-01'],
dfq['Vacancy rate']['2000-01-01':'2009-12-01'], 'o-', label='2000s')
plt.plot(dfq['Unemployment rate']['2010-01-01':'2019-12-01'],
dfq['Vacancy rate']['2010-01-01':'2019-12-01'], 'ko-', label='2010s')
plt.legend(frameon=False)
plt.xlim(2, 12)
plt.ylim(1, 5)
plt.yticks(np.arange(1, 6))
plt.xlabel('Unemployment rate (%)')
plt.ylabel('Vacancy rate (%)')
plt.title('Shifts in the US Beveridge curve')
# plt.savefig('BC.pdf')
plt.show()
Separate trend from cycle to eliminate structural shifts to the Beveridge curve, note the adjustment of filtering options to monthly frequency
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hp_cycle_uv, hp_trend_uv = sm.tsa.filters.hpfilter(100*np.log(df[['Vacancy rate','Unemployment rate']]).dropna(),
lamb=1600*3**4)
cf_cycle_uv, cf_trend_uv = sm.tsa.filters.cffilter(100*np.log(df[['Vacancy rate','Unemployment rate']]).dropna(),
low=1.5*12, high=8*12)
Plot cyclical components of unemployment and vacancy rates vs cyclical component of output
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fig, ax = plt.subplots()
cf_cycle_uv.resample('QS').mean().to_period('D').plot(ax=ax, style=['k','r'], lw=2)
cf_cycle['Output'].plot(ax=ax, style=['b'], lw=2)
ax.set_ylim(-45, 45)
ylim = ax.get_ylim()
ax.hlines(0, hours.index[0], hours.index[-1], linewidth=0.5)
ax.fill_between(fred.index, ylim[0], ylim[1], fred['USREC'], facecolor='lightgrey', edgecolor='lightgrey')
ax.set_xlim('1950-01', hours.index[-1])
l = ax.legend(loc='upper right')
l.get_frame().set_linewidth(0)
l.get_frame().set_alpha(1)
plt.title('Deviations from Christiano-Fitzgerald trend (%)')
# plt.savefig('VU_CF.pdf')
plt.show()
Run a (very simplified) linear regression on cyclical components of unemployment and vacancy rates, the slope is very close to -1
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x = hp_cycle_uv['Unemployment rate']
y = hp_cycle_uv['Vacancy rate']
slope, intercept = np.polyfit(x, y, 1)
print(slope)
print(intercept)
plt.scatter(x, y, facecolor='none', edgecolor='C0')
plt.plot(x, intercept + slope*x, 'r-', lw=2)
plt.xlim(-45, 45)
plt.ylim(-45, 45)
plt.hlines(0, -45, 45, linewidth=0.5)
plt.vlines(0, -45, 45, linewidth=0.5)
plt.title('Deviations from Hodrick-Prescott trend (%)')
plt.xlabel('Unemployment rate')
plt.ylabel('Vacancy rate')
# plt.savefig('BC_HP.pdf')
plt.show()
Generate the 'estimated' Beveridge curve without structural shifts
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u = np.mean(dfq['Unemployment rate'])
v = np.mean(dfq['Vacancy rate'])
print(u, v)
scale = np.linspace(-40, 60, 101)
plt.plot(u*np.exp(scale/100), v*np.exp(intercept+slope*scale/100), 'r', lw=2)
plt.plot(u, v, 'ko')
plt.xlim(2, 12)
plt.ylim(1, 5)
plt.yticks(np.arange(1, 6))
plt.xlabel('Unemployment rate (%)')
plt.ylabel('Vacancy rate (%)')
plt.title('US Beveridge curve without structural shifts')
# plt.savefig('BC_est.pdf')
plt.show()
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u = np.mean(dfq['Unemployment rate'])
v = np.mean(dfq['Vacancy rate'])
print(u, v)
scale = np.linspace(-40, 60, 101)
plt.plot(u*np.exp(scale/100), v*np.exp(intercept+slope*scale/100), 'r', lw=2)
plt.scatter(u*np.exp(x/100), v*np.exp(y/100), marker='.')
plt.xlim(2, 12)
plt.ylim(1, 5)
plt.yticks(np.arange(1, 6))
plt.hlines(v, 2, 12, linewidth=0.5)
plt.vlines(u, 1, 5, linewidth=0.5)
plt.xlabel('Unemployment rate (%)')
plt.ylabel('Vacancy rate (%)')
plt.title('US Beveridge curve without structural shifts')
# plt.savefig('BC_est_2.pdf')
plt.show()
