Has COVID-19 Caused a Change in the Dynamics of the Unemployment Rate? — Judit Kapas

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An article by Judit Kapas of the Budapest University of Technology and Economics, Hungary, titled Has COVID-19 caused a change in the dynamics of the unemployment rate? The case of North America and continental Europe. The abstract states that the study asks whether the COVID-19 pandemic will have a long-lasting impact on the dynamics of the unemployment rate, and whether any sign of a structural break is detectable in the time series. It states that the study performs several one-step-ahead forecasts based on the best ARIMA model, using unemployment rate data for five quarters following the pandemic outbreak.

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Has COVID-19 caused a change in the dynamics of
the unemployment rate? The case of North America
and continental Europe

Judit Kapas This study raises the question of whether the
Department of Economics COVID-19 pandemic will have a long-lasting
Faculty of Economic and Social impact on the dynamics of the unemployment
Sciences rate. More specifically, this problem implies an
Budapest University of analysis of whether any sign of a structural
Technology and Economics, break is detectable in the time series of the
Hungary unemployment rate. To obtain some „first-
E-mail: kapas.judit@gtk.bme.hu hand” estimates on whether it is likely that a
structural break will occur in the labour
market, this study performs several one-step-
ahead forecasts based on the best ARIMA
model on the time series of the unemployment
rate, which takes advantage of the availability
of the unemployment rate data for five
quarters following the pandemic outbreak.
Interestingly, the results document practically
no difference in the impact of the pandemic
on the labour market in countries with
different labour market flexibility. Neither
Keywords: North America (United States of America and
pandemic, Canada) with a flexible labour market nor
unemployment, continental Europe (Germany and Austria)
structural break, with a regulated labour market experienced
ARIMA model, any regime change in the unemployment rate
forecast time series.

Introduction
The economic analysis of the COVID-19 pandemic’s various negative impacts on
economies and societies is an ongoing process. The labour market is one of the
most researched economic areas within pandemic related subjects, and a relatively
large body of literature has accumulated in the field, with a wide range of focuses.
Some scholars have analysed how the pandemic increased unemployment in various
countries (e.g., Su et al. 2021, Coibion et al. 2020); findings show that the
unemployment rate has increased significantly, but to different extents in various
countries. Interestingly, the labour market’s recovery has quickly gained popularity

Regional Statistics, Vol. 12. No. 1. 2022, 3–26; DOI: 10.15196/RS120107
4 Judit Kapas

as a research area (e.g., Gregory et al. 2020) not only in terms of the speed of
recovery, but also in terms of possible scenarios (e.g., Petrosky-Nadeau–Valletta
2020). Another crucial issue has centred on a change in unemployment benefits,
exploring various aspects of the problem, such as the optimal unemployment
benefit (Mitman–Rabinovich 2020), lost earnings due to the pandemic (Acs–
Karpman 2020), and how unemployment benefits could compensate for income
loss (Ganong et al. 2020). Of course, many have investigated how shutdown policies
have affected the unemployment rate (e.g., Kong–Prinz 2020a, 2020b), and it has
been shown that, for instance, in Germany, 60% of the inflow into unemployment
in April 2020 was due to shutdown measures (Bauer–Weber 2021). Several studies
focused on how entrepreneurship was affected by the pandemic, an issue indirectly
related to employment (e.g., Nyikos et al. 2021). Besides the economic aspects of
unemployment caused by COVID-19 mentioned above, sociologists and
psychologists, too have been investigating the issue (for an overview of various
psychology-related aspects of unemployment, see Blustein et al. 2020).
However, less attention was paid to the question of whether the „behaviour” of
the labour market is likely to change, a question concerning the topic whether the
labour market will revert to its original pattern. In other words, retaining the same
pattern could mean that COVID-19 has not exercised a long-lasting impact on the
labour market, indicating no regime (structural) change. Of course, we can only
detect a structural change in a time series retrospectively, that is, when we have
sufficient data points after the hypothesised breaking time.1 Since it has been around
a year and a half since the start of the pandemic, we cannot conduct a traditional
structural break analysis on the time series of the unemployment rate, although we
can still be interested in whether the effect on unemployment rate will only be
transitory or long-lasting. Given the shocks arising from past pandemics, this
interest is of crucial importance. As demonstrated by Rodríguez-Caballero–Vera-
Valdés (2020), previous pandemics suggest that without governmental policies
designed to avoid massive job losses, and we should expect a higher unemployment
rate. Accordingly, an implication of an „early” detection of a regime change in the
unemployment rate is that it can advise policy makers in fine-tuning governmental
policy in the field.
The contribution of this study is to propose an analysis able to detect signs of a
possible structural break a couple of periods following the pandemic outbreak,
which can serve as a basis for eventual changes in employment policy. More
specifically, this study proposes to make multiple one-step-ahead forecasts, an
approach taking advantage of the availability of data during the pandemic period. In
terms of econometrics, the procedure is a simple method that can provide some
first-hand „estimates” concerning whether or not it is likely that the labour market

1 On the various econometrics methods to detect a structural break, see Rodríguez-Caballero–Vera-Valdés

(2020).

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Has COVID-19 caused a change in the dynamics of the unemployment rate?
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The case of North America and continental Europe

will revert to its original pattern. After modelling the behaviour of the labour
markets in each country of my interest, I will forecast the unemployment rate at
time t+1 by using data from 1 to t, then at time t+2 by using data from 1 to t+1,
etc., where t is time when the pandemic’s impact first appeared. Then, I will
calculate the prediction intervals and check whether the actual COVID-19 period
data actually occurred within the interval. If the actual COVID-19 data are
contained in the corresponding prediction interval a couple of periods after the
pandemic started, I can claim that the overall structure of the unemployment rate
captured by the model has not changed, and the COVID-19 has not caused regime
change. If this is not the case, I will attempt to judge whether there is any sign
indicating that the actual unemployment rates converge to some extent back to the
original pattern, or alternatively, whether a new pattern is emerging, indicating a sign
of a structural break.
In this study, I hypothesise that the capability of a labour market to retain its
original pattern depends not only on policies but also on the characteristics of the
given labour market. Flexible labour markets might translate the pandemic shock
into large increases in the unemployment rate but they probably will quickly return
to the original pattern when the economy returns to normality. However, countries
where the labour market is shaped by governmental regulation and/or the
involvement of social partners in labour bargaining might follow a different path: a
quick return to the original pattern is not very likely, which might indicate either a
regime change in the unemployment rate or a slow reversion. To investigate
whether this difference between the two types of labour markets does indeed exist, I
will take North America as an example of a flexible labour market, and continental
Europe as an example of a regulated labour market. I will analyse two countries in
both regions: the United States of America [USA] and Canada on one hand, and
Germany and Austria on the other. Using two countries for each region for this
analysis offers the advantage of obtaining more solid results, while remaining
feasible within the framework of a single paper.
Interestingly, my results show practically no difference between countries with
different labour market flexibility with regard to the impact of the pandemic on the
labour market: neither North America nor Continental Europe have experienced
regime change in the unemployment rate time series. In Canada, the labour market
has already reverted to the previous pattern; however, in the USA, the actual rates
have been outside the prediction intervals for all periods, but convergence is
apparently taking place. The two continental European countries do not show a
different movement from that observed in North America. Due to rapid and
intense government actions, the German labour market has hardly diverted from its
previous pattern, making Germany very similar to Canada in this respect; in Austria,
the labour market seems to have left its original pattern for a while, although a slow
reversion back to the previous behaviour of the market is already taking place. In

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6 Judit Kapas

summary, multiple one-step-ahead forecasts suggest that the COVID-19 pandemic
has not caused a structural break in the unemployment rate series, irrespective of
the flexibility of the labour market.
In what follows, I will first look at the state of the labour market in the four
countries during the pandemic era. Then, I will model the unemployment rate time
series in the four countries and calculate the one-step-ahead forecasts manually with
prediction intervals. In the last section, I will conclude the paper.

The state of the labour market at the outbreak of the pandemic
in the four countries
The pandemic caused a sharp and unprecedented fall in employment across
countries2, but the extent of the increase in the unemployment rate has been quite
different in the two regions. Table 1 summarises the quarterly unemployment rate
data from 2020Q1 to 2021Q2. For all countries, the economic impact of COVID-
19 manifested in 2020Q2, one quarter after the pandemic broke out.
Table 1
Unemployment rates
2020 2021
Country
Q1 Q2 Q3 Q4 Q1 Q2
USA 3.80 13.07 8.80 6.77 6.17 5.93
Canada 6.40 13.10 10.10 8.80 8.37 8.03
Germany 5.00 6.17 6.33 6.13 6.00 5.97
Austria 8.46 11.86 10.09 9.31 8.78 7.74a)
a) Estimated value for the quarter based on available data for 2 months.
Data source: [1].

Comparing the countries in the first COVID-19 period leads me to the
conclusion that the highest relative increase in the rate occurred in the USA3,
followed by Canada, which is perfectly in line with our expectations based on the
characteristics of their labour markets. The high level of labour freedom and low
level of employment protection implies flexibility, leading to the fact that the
impacts of the pandemic manifest fully on the labour market. In contrast, the
relative increase in the unemployment rate in Germany and Austria was much
lower, suggesting that the immediate intervention of the government on the labour

2 Although we do not have much data from the outbreak of the pandemic, which hinders causality analysis,

Su et al. (2021) performed a Fourier causality test whose results establish that COVID-19 caused unemployment in
selected European economies, including Germany.
3 To illustrate the severity of the situation in the USA, note that initial unemployment insurance claims in the

first month of the pandemic matched the cumulative claims during the worst nine-month period of the 2008
financial crisis (Petrosky-Nadeau–Valletta 2020). For more data on the USA labor market during the pandemic, see
Acs–Karpman 2020.

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Has COVID-19 caused a change in the dynamics of the unemployment rate?
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The case of North America and continental Europe

market „has come to fruition”. Clearly, two factors contribute to the extent of the
relative increase in the unemployment rate: (1) the flexibility of the labour market
and (2) the volume and character of the stimulus introduced in a particular country.
When it comes to differences in flexibility across the two regions, it is worth
looking at the Employment Protection Index of the Organisation for Economic
Co-operation and Development (OECD) (Figure 1) which measures the procedures
and costs involved in dismissing individuals or groups of workers and the
procedures involved in hiring workers on fixed-term or temporary work agency
contracts. The figure clearly shows that regulation is very strict in both Germany
and Austria, while it is very easy for firms to hire and fire people in the USA and
Canada.
Figure 1
Employment Protection Index, 2019
3.0

2.5

2.0

1.5

1.0

0.5

0.0
USA Canada Germany Austria
Source: [2].

The labour freedom component of the Index of Economic Freedom4 compiled
by the Heritage Foundation (Miller et al. 2021) is another measure used to assess
certain characteristics of the labour market, which explains the differences in the
change in unemployment rates across countries. The data presented in Table 2
highlight that labour freedom is much higher in the USA and Canada, especially
when looking at the average labour freedom in the period from 2005 to 2021.

4 This is a quantitative measure that considers various aspects of the legal and regulatory framework of a

country’s labour market, including the following six quantitative factors, equally weighted: ratio of the minimum
wage to the average value added per worker, hindrance to hiring additional workers, rigidity of hours, difficulty of
firing redundant employees, legally mandated notice period, and mandatory severance pay.

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8 Judit Kapas

Table 2
Labour freedom component of the Index of Economic Freedom
Mean
Country 2021 2020 2019 2018 2017
(2005–2021)
USA 87.1 87.9 89.4 91.4 91.0 93.77
Canada 72.4 72.0 73.7 71.3 73.1 78.53
Germany 53.0 53.0 52.8 53.3 42.8 43.71
Austria 68.4 68.3 68.7 66.7 67.6 73.74
Source: Miller et al. (2021).

In addition to the cross-regional differences in labour market flexibility, as
argued above, we should consider the differences in the policy mix the countries
have applied to cushion the effects of COVID-19.
A very important part of the „stimulus” package introduced in continental
Europe are job retention schemes, namely, short-time work (STW) (see Giupponi–
Landais 2020 for more details) and wage subsidies (Schulten–Müller 2020), which
have been somewhat in short supply in North America. Immediately after the start
of the pandemic, as of May 2020, Germany and Austria introduced these schemes
where the share of approved applications and actual participants as a part of
dependent employees was about 30–40%, while in the USA, this share was
practically 0%, as shown in Figure 2.5
Figure 2
Participation in job retention schemes, May 2020
70
60
50
40
30
20
10
0
New Zealand Austria Germany Canada USA
Approved applications Actual use
Source: [3].

It is worth noting that Austria pioneered the development of SWT to mitigate
the massive increase in unemployment, with the goal of preserving jobs at firms by

5 New Zealand is shown for the sake of comparison as the country whose level of job-retention participation

was the highest.

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Has COVID-19 caused a change in the dynamics of the unemployment rate?
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The case of North America and continental Europe

temporarily reducing firms’ labour costs. The Austrian model has allowed a
temporary reduction in working hours up to 90% while maintaining the
employment relationship and granting almost full public wage compensation. It has
even included the possibility of a temporary reduction to as few as zero hours
(Schnetzer et al. 2020).6 The government has provided remuneration for reduced
hours up to predefined thresholds. In Germany, the regular net replacement rate has
been a little lower (60% for a single individual and 67% for a married person) than
in Austria (Bofinger et al. 2020a, 2020b).
In addition to SWT, the use of wage subsidies is not very important. This
measure is much more in line with labour markets where layoffs are relatively less
costly, which explains why Canada has applied them. Wage subsidies are easier to
implement and more flexible for firms, but less targeted at firms.
In parallel with job retention schemes, many countries have provided liquidity
support for firms, together with central banks’ monetary measures. Moreover, at
EU level, additional measures have been taken to support national efforts. The USA
has focused on reducing the impact of income loss and, accordingly, has expanded
unemployment benefits in various ways: improving access to unemployment
benefits, extending their duration, and increasing their amount ([3], Fang et al. 2020,
Ganong et al. 2020).
In summary, the volume and character of the stimulus packages differed
between the regions. To express these differences, we can rely on an index
developed by Elgin et al. (2020) and updated by the same scholars (update available
at: [4]): the COVID-19 Economic Stimulus combines all adapted fiscal, monetary,
and exchange rate measures. As argued by Elgin et al. (2020), the index may be used
in a cross-country setting because it standardises the measures taken by
governments. Table 3 summarises the components of the index for our countries.
The most important conclusions are as follows.
Table 3
COVID-19 Economic Stimulus Index
Fiscal, %/GDP Rate cut, % Macro-financial, %/GDP
Country
March 2020 May 2021 March 2020 May 2021 March 2020 May 2021
USA 10.50 26.78 100 100 0.00 14.00
Canada 6.00 18.50 57.14 85.70 2.60 18.38
Germany 4.00 20.3 0.00 0.00 12.49 44.74
Austria 17.80 19.50 0.00 0.00 7.31 18.64
Source: Elgin et al. (2020) and [4].

6 The first version of this model was used during the 2008 financial crisis (Hijzen–Venn 2011). For an analysis

of the rationale for STW benefits and their effects on labour adjustment during the 2008 recession, see Boeri–
Bruecker 2011.

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10 Judit Kapas

In Europe, an interest rate cut was not used, unlike in the USA and Canada. The
volume of the fiscal measures as a percentage of gross domestic product (GDP) was
more or less the same in the four countries, but the magnitude of macro-financial
measures was extremely large in Germany. In addition, macro-financial measures
came later in North America, while Austria and Germany had already introduced
them by March 2020 ([3]).
Based on the above, it is clear that the labour markets have not been cushioned in
the USA and Canada, implying that whether the labour market will revert back to its
original behaviour depends mainly on the speed of the recovery of the economy: in
case of quick recovery – and seemingly, this is what happens – we should expect a
reversion. However, in Germany and Austria, the rigidity of the labour markets might
hinder the reversion unless „good” governmental policies „overcompensate” it.

Modelling the unemployment rate series and multiple one-step-
ahead forecasting
In what follows, I model the unemployment rate time series in the four countries
and make several one-step-ahead forecasts, which allow me to conduct preliminary
investigations regarding a possible structural break. When it comes to modelling, I
select the best ARIMA model based on the Bayesian Information Criterion (BIC),
and then, to validate the model, I thoroughly check the residuals to see whether they
follow a white noise process.7 To check the stationarity of the series on which I fit
ARIMA models: besides the traditional Augmented Dickey-Fuller (ADF) test of
non-stationarity, I also perform the Kapetanios test (Kapetanios 2005).8 The reason
for this is a well-known weakness of the ADF unit root test: it does not allow for
the possibility of structural breaks for a stationary time series. In other words, the
ADF test may fail to reject the unit root (non-stationarity) hypothesis if the series
have structural breaks. By performing the Kapetanios test9, in which the null
hypothesis is that the series has a unit root with m structural breaks, while the
alternative hypothesis is that it is stationary with m breaks, one can avoid this risk.
Forecasting is performed manually, as follows. I forecast 𝑌𝑡+1 (the
unemployment rate at time t+1) by using data from 1 to t, then 𝑌𝑡+2 by using data
from 1 to t+1, etc. To calculate the prediction interval, we need the standard
deviation of the forecast distribution. We know that for a one-step-ahead forecast,
the standard deviation of the forecast distribution is equal to the standard deviation
of the residuals. Since I make a one-step-ahead forecast, but carry it out several

7 I use R for all analyses.
8 The use of this test has been suggested by one of my reviewers, for which I am very thankful.
9 The Kapetanios tests will be performed in Gretl in the following setting: maximum number of breaks: 5,

maximum number of lags: 5, type of break: level and trend.

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Has COVID-19 caused a change in the dynamics of the unemployment rate?
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The case of North America and continental Europe

times, I can take the standard deviation as the same for each forecast. Since the first
COVID-19 period is 2020Q2 (see Table 1), forecasts can be made for five periods.
Data were taken from the Federal Reserve Economic Data (FRED). I use
quarterly seasonally adjusted data. The chosen period is from 1970Q1 to 2021Q1
for the USA and Germany, and from 1980Q1 to 2021Q1 for Canada and Austria.

The United States of America
Figure 3 shows the time series of the unemployment rate for the entire period, and
the first difference of the time series together with ACF and PACF for the training
dataset.
Figure 3
Unemployment rate, ACF and PACF, USA
Unemployment rate, USA, Differenced unemployment rate, USA
Q1 1970–Q1 2021 Q1 1970–Q1 2021
% %
14 2.0
12 1.5
10
1.0
8
0.5
6
0.0
4
2 –0.5
0 –1.0
1970 1980 1990 2000 2010 2020 1970 1980 1990 2000 2010 2020
ACF for differenced PACF for differenced
unemployment rate, USA unemployment rate, USA
0.8 0.8

0.6 0.6
0.4
0.4
0.2
0.2
0.0
0.0 –0.2
–0.2 –0.4
0 4 8 12 16 20 0 4 8 12 16 20
lag lag
Data source: [1].

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12 Judit Kapas

The data do not show any trend; instead, it seems that there is a constant long-
run mean (about 6–7%). The spread of the data also seems to be within the same
boundary, except for the COVID-19 starting period when the spike was very large.
The time-constant mean, time-constant variance, and time-reversibility of the data
suggest that the USA unemployment rate is stationary. I use more sophisticated
tools to check this. The formal test of non-stationarity (ADF test) indicates that the
series is stationary, since the p-value of the test statistic is 0.05, at lag 1, suggesting
that we are at the border, at a 5% significance level, of rejecting the null hypothesis
that the series is not stationary. However, the Kapetanios test suggests otherwise; I
cannot reject the null hypothesis because the test statistic is –7.308, while the critical
value at a 10% significance level is –7.426.
Taking the first difference of the USA unemployment rate time series makes me
conclude that the series is stationary, based on both tests (the p-value in the ADF
test is 0.01 at lag 1, and the test statistic in the Kapetanios test is -9.449 which is
significant at the 1% level). The ACF and PACF for the first difference of the series
in Figure 3 show that the data are autocorrelated, which is further corroborated by
the Box-Ljung test up to lag 6 (p-value<2.2e–16). The slow decay of the ACF
indicates a typical AR process.
Therefore, since the first difference of the time series of the unemployment rate
is stationary, I can fit ARIMA models on the training data set (1970Q1–2020Q1),
and determine the best model relying on BIC as the model selection criterion.
(I prefer BIC to the Akaike information criterion because it selects a simpler model.)
ARIMA(1,1,0) is selected as the best model, the equation for which is as follows:
𝑌𝑡 − 𝑌𝑡−1 = 𝜙1 (𝑌𝑡−1 − 𝑌𝑡−2 ) + 𝑢𝑡
where 𝑢𝑡 ∼ 𝑁(0, 𝜎𝑢2 ).
After rearranging the equation:
𝑌𝑡 = (1 + 𝜙1 )𝑌𝑡−1 − 𝜙1 𝑌𝑡−2 + 𝑢𝑡
where 𝑢𝑡 ∼ 𝑁(0, 𝜎𝑢2 ).
In the above equations and in all that follow, 𝑌𝑡 is the unemployment rate at
time t, and 𝑢𝑡 is the error term at time t. Table 4 presents the estimation results.
Table 4
Estimations for ARIMA(1,1,0), USA
ar1
Estimate 0.668***
Standard error 0.0529
*** Significance at 0%.

Now, I check whether the residuals of this model follow a white noise process
(Figure 4).

Regional Statistics, Vol. 12. No. 1. 2022, 3–26; DOI: 10.15196/RS120107
Has COVID-19 caused a change in the dynamics of the unemployment rate?
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The case of North America and continental Europe

ACF seems to be appropriate, with only one bar being slightly outside the
boundary at lag 8; the same can be said for PACF with two bars outside at high lags.
Overall, we can accept that there is no autocorrelation at least up to lag 6 because
the Box-Ljung test statistic is not significant (p-value=0.4653). The p-value of the
test statistic (0.01) in the ADF test indicates high significance, meaning that we can
reject the hypothesis that the residuals are not stationary. Based on the above, I can
conclude that the residuals of the model follow a white noise process, meaning that
the model can be used for forecasting.
Figure 4
Residual diagnostics for ARIMA(1,1,0), USA
Residuals of ARIMA(1,1,0), USA ACF for ARIMA(1,1,0), USA
1.5 0.2

1.0
0.1
0.5
0.0
0.0
0.1
–0.5

–1.0 –0.2
1970 1980 1990 2000 2010 2020 0 4 8 12 16 20
lag
PACF for ARIMA(1,1,0), USA Fitted values for ARIMA(1,1,0), USA
%
0.2 12

0.1 10
8
0.0
6
0.1
4
–0.2 2
–0.3 0
0 4 8 12 16 20 1970 1980 1990 2000 2010 2020
lag

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14 Judit Kapas

Based on the above estimations, I use the following equation for forecasting:
𝑌𝑡 = 1.668𝑌𝑡−1 − 0.668𝑌𝑡−2
Table 5 shows the forecasts, together with the 95% prediction intervals.
Table 5
Forecasted unemployment rates and prediction intervals for the USA
One-step-ahead forecasts Actual
Period
forecast low upper unemployment rate
2020Q2 3.93 3.44 4.42 13.07
2020Q3 19.26 18.77 19.75 8.80
2020Q4 5.95 5.46 6.47 6.77
2021Q1 5.41 4.92 5.90 6.17
2021Q2 5.05 4.56 5.54 5.93

Forecasts based on previous patterns have been very far from the actual values
in the first two periods10, while in the second half of the pandemic period, these two
have been much closer to one another, which might indicate that the
unemployment rate reverts to the original pattern. Overall, the USA labour market
behaved as expected: the increase in the rate was extremely high in the beginning
because the government let the market work, which then started to recover quite
quickly when the USA economy started stabilising and returning to normal. In
2021Q2, the upper limit of the prediction interval was 5.54, while the actual rate was
5.93; it seems that these two values not very far from one another.

Canada
The time series of the unemployment rate for Canada for the period between
1980Q1 and 2020Q1 has proven to be stationary based on the ADF test (the
p-value is 0.03 at lag 1), but non-stationary based on the Kapetanios test (the test
statistic is –6.42, while the critical value at a 10% significance level is –6.686).
Accordingly, I take the differenced time series, which can be considered stationary
based on both tests (the p-value in the ADF test is 0.01 at lag 1, and the test statistic
in the Kapetanios test is –6.968). Figure 5 shows the time series for Canada.

10 As mentioned earlier, unemployment insurance became more generous immediately after the pandemic

started. Fang et al. (2020) have shown in their calibrated model that unemployment insurance policies in the USA
led to a 3.7 percentage point increase in the unemployment rate between April and December of 2020. This
negative association between the unemployment rate and the generosity of unemployment insurance in the USA
has been corroborated by Finamor–Scott (2021), too.

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Has COVID-19 caused a change in the dynamics of the unemployment rate?
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The case of North America and continental Europe

Figure 5
Unemployment rate, ACF and PACF for Canada
Unemployment rate, Canada, Differenced unemployment rate, Canada,
Q1 1980–Q1 2021 Q1 1980–Q1 2021
% %
14 2.0
12 1.5
10
1.0
8
0.5
6
0.0
4
2 –0.5
0 –1.0
1980 1990 2000 2010 2020 1980 1990 2000 2010 2020
ACF for differenced unemployment rate, PACF for differenced unemployment rate,
Canada Canada
0.6 0.6

0.4 0.4

0.2 0.2

0.0 0.0

–0.2 –0.2

–0.4 –0.4
0 4 8 12 16 20 0 4 8 12 16 20
lag lag
Data source: [1].

Proceeding in the same way as before, the best ARIMA model is (1,1,0), as in the
case of the USA, whose equation is as follows:
𝑌𝑡 = (1 + 𝜙1 )𝑌𝑡−1 − 𝜙1 𝑌𝑡−2 + 𝑢𝑡
where 𝑢𝑡 ∼ 𝑁(0, 𝜎𝑢2 ).

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Estimation results are shown in Table 6.
Table 6
Estimations for ARIMA(1,1,0), Canada
ar1
Estimate 0.5530***
Standard error 0.0664
*** Significance at 0%.

Residual diagnostics validate the model, since the residuals are proven to follow a
white noise process: the p-value of the test statistic in the ADF test is 0.01 at lag 1, it is
0.4702 in the Box-Ljung, and as shown in Figure 6, ACF and PACF suggest that there
is no autocorrelation in the residuals, and the model fit is seemingly very good.
Figure 6
Residual diagnostics for ARIMA(1,1,0), Canada
Residuals of ARIMA(1,1,0), Canada ACF for ARIMA(1,1,0), Canada
1.5 0.2

1.0
0.1
0.5
0.0
0.0
0.1
–0.5

–1.0 –0.2
1980 1990 2000 2010 2020 0 4 8 12 16 20
lag
PACF for ARIMA(1,1,0), Fitted values for ARIMA(1,10),
Canada Canada
0.2 %
14
0.1 12
10
0.0 8
6
0.1
4
2
–0.2
0 4 8 12 16 20 0
lag 1980 1990 2000 2010 2020

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The case of North America and continental Europe

One-step-ahead forecasts for the COVID-19 period are given in Table 7 based
on the following equation:
𝑌𝑡 = 1.553𝑌𝑡−1 − 0.553𝑌𝑡−2
Table 7
Forecasted unemployment rates and prediction intervals for Canada
One-step-ahead forecasts Actual
Period
forecast low upper unemployment rate
2020Q2 6.77 6.19 7.35 13.10
2020Q3 16.81 16.23 17.38 10.10
2020Q4 8.44 7.86 9.02 8.80
2021Q1 8.08 7.50 8.66 8.37
2021Q2 7.88 7.30 8.46 8.03

The pandemic’s first impact was enormous in Canada, as in the USA, but
starting from 2020Q4 the market reverted remarkably to its original pattern: the
actual unemployment rate happens to be in the prediction intervals in 2020Q4,
2021Q1, and 2021Q2. Briefly, it is very likely that the pandemic has not exercised
long-lasting effects on the dynamics of the Canadian labour market.

Germany
Figure 7 includes four panels for Germany, starting with the one showing the time
series of the unemployment rate. There are ups and downs in the rate, with a
positive trend until about 2008, after which the trend is decreasing. Looking at the
difference in the unemployment rate might suggest stationarity, which I formally
test with the ADF test (the p-value is 0.01 at lag 1) and the Kapetanios test (the test
statistic is –9.3421, while the critical value at a 1% significance level is –8.243), both
confirming stationarity. ACF indicates an autoregressive process of the differenced
unemployment rate.
The best model, based on BIC, which describes the process in Germany is an
ARIMA(2,1,0) model, whose estimations are shown in Table 8, and the equation is
as follows:
𝑌𝑡 − 𝑌𝑡−1 = 𝜙1 (𝑌𝑡−1 − 𝑌𝑡−2 ) + 𝜙2 (𝑌𝑡−2 − 𝑌𝑡−3 ) + 𝑢𝑡
2
where .
𝑢𝑡 ∼ 𝑁(0, 𝜎𝑢 )
After rearrangement, the equation becomes:
𝑌𝑡 = (1 + 𝜙1 )𝑌𝑡−1 + (𝜙2 − 𝜙1 )𝑌𝑡−2 − 𝜙2 𝑌𝑡−3 + 𝑢𝑡
2
where 𝑢𝑡 ∼ 𝑁(0, 𝜎𝑢 ).

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Figure 7
Unemployment rate, ACF and PACF, Germany
Unemployment rate, Germany, Differenced unemployment rate, Germany,
Q1 1970–Q1 2021 Q1 1970–Q1 2021
% %
12 2.0
10 1.5
8 1.0
6 0.5
4 0.0
2 –0.5
0 –1.0
1970 1980 1990 2000 2010 2020 1970 1980 1990 2000 2010 2020
ACF for differenced unemployment rate, PACF for differenced unemployment rate,
Germany Germany
0.6 0.6

0.4 0.4

0.2 0.2

0.0 0.0

–0.2 –0.2
0 4 8 12 16 20 0 4 8 12 16 20
lag lag
Data source: [1].
Table 8
Estimations for ARIMA(2,1,0), Germany
ar1 ar2
Estimate 0.4583*** 0.1947**
Standard error 0.0690 0.0690
*** Significance at 0%; ** Significance at 1%.

After performing residual diagnostics, I can conclude that the residuals are the
realisation of a white noise process because the ADF test shows the stationarity of
the residuals (p-value=0.01 at lag 1), as indicated by Figure 8; there is no

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The case of North America and continental Europe

autocorrelation in the residuals (ACF and PACF are perfect), which is further
corroborated by the Box-Ljung test (p-value=0.97).
Now, I use this model for forecasting. The specific equation I can apply based
on my estimation is the following:
𝑌𝑡 = 1.4583𝑌𝑡−1 − 0.2636𝑌𝑡−2 − 0.1947𝑌𝑡−3
Forecasts, together with the prediction intervals, are shown in Table 9.
Figure 8
Residual diagnostics for ARIMA(2,1,0), Germany
Residuals of ARIMA(2,1,0), Germany ACF for ARIMA(2,1,0), Germany
2.0 0.2
1.5
0.1
1.0
0.5 0.0
0.0
0.1
–0.5
–1.0 –0.2
1970 1980 1990 2000 2010 2020 0 4 8 12 16 20
lag
PACF for ARIMA(2,1,0), Fitted values for ARIMA(2,1,0),
Germany Germany
%
0.2 14
12
0.1 10
8
0.0
6

0.1 4
2
–0.2 0
0 4 8 12 16 20 1970 1980 1990 2000 2010 2020
lag

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Table 9
Forecasted unemployment rates and prediction intervals for Germany
One-step-ahead forecasts Actual
Period
forecast low upper unemployment rate
2020Q2 5.00 4.57 5.43 6.17
2020Q3 6.70 6.28 7.13 6.33
2020Q4 6.64 6.21 7.02 6.13
2021Q1 6.07 5.65 6.50 6.00
2021Q2 5.90 5.47 6.33 5.97

As seen from the above table, Germany is unique in terms of how the labour
market has behaved; in the first pandemic period, the actual unemployment rate was
only about 25% above the forecasted one, and then, starting from the second
period, the actual rates are practically within the prediction intervals, meaning that
the market is behaving in the same way as before the pandemic.11 This suggests that,
despite the rigidity of the labour market, governmental intervention has been so
rapid and important in terms of magnitude that the actual unemployment rate has
been „disciplined”; it seems that the labour market was not very disturbed by
COVID-19. This dynamics of the labour market is the opposite of what I have
hypothesised based on the character of the labour market (see introduction).
Despite the heavy governmental regulation, the labour market has surprisingly
reverted, and behaved similarly to the very flexible Canadian labour market.

Austria
As shown in Figure 9, the time series of the unemployment rate for Austria has a
positive trend, but differencing the unemployment rate leaves me with a stationary
but autocorrelated series. The p-value of the test statistic in the ADF test is 0.02 at
lag 1, and the corroboration of stationarity with the Kapetanios test (the test statistic
is –5.1362) makes me reject the null hypothesis that there is a unit root at a 5%
significance level (the critical value is –5.081).

11 The only exception is the third period in which the actual rate is a little outside the interval. However, I do

not consider this deviation crucial since one period before and after the actual rate is contained in the interval.

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The case of North America and continental Europe

Figure 9
Unemployment rates, ACF and PACF, Austria
Unemployment rate, Austria, Differenced unemployment rate, Austria,
Q1 1980–Q1 2021 Q1 1980–Q1 2021
% %
10 1.5

8
1.0
6
0.5
4
0.0
2

0 –0.5
1980 1990 2000 2010 2020 1980 1990 2000 2010 2020
ACF for differenced unemployment rate, PACF for differenced unemployment rate,
Austria Austria
0.5 0.5
0.4 0.4
0.3 0.3
0.2 0.2
0.1 0.1
0.0 0.0
0.1 0.1
–0.2 –0.2
0 4 8 12 16 20 0 4 8 12 16 20
lag lag
Data source: [1].

After fitting the ARIMA models, the best one based on BIC is ARIMA(1,1,2),
the equation of which is as follows:
𝑌𝑡 − 𝑌𝑡−1 = 𝜙1 (𝑌𝑡−1 − 𝑌𝑡−2 ) + 𝜃1 𝑢𝑡−1 + 𝜃2 𝑢𝑡−2 + 𝑢𝑡
where 𝑢𝑡 ∼ 𝑁(0, 𝜎𝑢2 ).
After rearrangement, the equation becomes:
𝑌𝑡 = (1 + 𝜙1 )𝑌𝑡−1 − 𝜙1 𝑌𝑡−2 + 𝜃1 𝑢𝑡−1 + 𝜃2 𝑢𝑡−2 + 𝑢𝑡
where 𝑢𝑡 ∼ 𝑁(0, 𝜎𝑢2 ).
Estimation results are shown in Table 10.

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Table 10

Estimations for ARIMA(1,1,2), Austria
ar1 ma1 ma2
Estimate 0.4676** –0.1739** 0.6680**
Standard error 0.1466 0.0664 0.2078
** Significance at 1%.

The residual diagnostics shown in Figure 10 lead me to conclude that the
residuals follow a white noise process because the ADF test indicates the
stationarity of the residuals (the p-value=0.01 at lag 1) and, as indicated by ACF and
PACF, there is no autocorrelation in the residuals, which is further corroborated by
the Box-Ljung test (p-value=0.5976).
Figure 10
Residuals diagnostics for ARIMA(1,1,2), Austria
Residuals of ARIMA(1,1,2), Austria ACF for ARIMA(1,1,2), Austria
1.5 0.2

1.0 0.1

0.5 0.0

0.0 0.1

–0.5 –0.2
1980 1990 2000 2010 2020 0 4 8 12 16 20
lag
PACF for ARIMA(1,1,2), Fitted values for ARIMA(1,1,12),
Austria Austria
0.2 %
10
0.1
8

0.0 6

4
0.1
2
–0.2
0 4 8 12 16 20 0
lag 1980 1990 2000 2010 2020

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The case of North America and continental Europe

Now, I make several one-step-ahead forecasts based on the following equation
and show the results in Table 11.
𝑌𝑡 = 1.4676𝑌𝑡−1 − 0.4676𝑌𝑡−2 − 0.1739𝑢𝑡−1 + 0.668𝑢𝑡−2
Table 11
Forecasted unemployment rates and prediction intervals for Austria, regression
One-step-ahead forecasts Actual
Period
forecast low upper unemployment rate
2020Q2 8.63 8.33 8.94 11.86
2020Q3 13.65 13.34 13.95 10.09
2020Q4 12.04 11.74 12.35 9.31
2021Q1 7.04 6.74 7.35 8.78
2021Q2 6.40 6.09 6.70 7.74a)
a) Estimated value for the quarter based on available data for 2 months.

The Austrian case is different from the German one. In the first pandemic
period, the relative increase in the unemployment rate was higher in Austria than in
Germany, and in the second half of the period, the market is converging to its
previous dynamics. This means that it is not very likely that a regime change will
occur in Austria; instead, one can argue that the Austrian government has managed
to cushion the impact of COVID-19 on the labour market almost as well as the
German government.

Conclusions
This study raises the question of whether the COVID-19 pandemic has changed the
dynamics of the labour market, a problem that has not received much attention so
far. A traditional analysis of a possible structural break in the unemployment time
series is not yet feasible because the pandemic is still present and we do not have
data for a sufficiently long period after the potential break. However, as I have
suggested, making several one-step-ahead forecasts by taking advantage of the
availability of data for the pandemic periods allows us to make some „first-hand”
estimates about a possible regime change in unemployment rates.
I hypothesised that the degree of flexibility of the labour market might have an
impact on whether a regime change due to COVID-19 is likely to occur. In this
regard, I have taken two countries from two regions where the labour markets differ
considerably in terms of flexibility, namely, North America (United States of
America and Canada), where the market is flexible, and continental Europe
(Germany and Austria), where it is regulated. My one-step-ahead forecasts for five
periods during the pandemic do not indicate differences between the two regions
with regard to the question if the labour market is going to revert to the original
pattern. Somewhat surprisingly, irrespective of the character of the labour market,
no sign of a structural break has been detected in any of the countries. More

Regional Statistics, Vol. 12. No. 1. 2022, 3–26; DOI: 10.15196/RS120107
24 Judit Kapas

precisely, the labour markets in Canada (a flexible market) and Germany (a regulated
market) quickly reverted to previous dynamics. However, the labour markets in the
USA and Austria have behaved somewhat differently. After an important spike in
2020Q2, it seems that a kind of convergence is taking place, but not a full reversion.
Overall, what we can conclude is basically the same in all four countries, and it is
very likely that the COVID-19 pandemic has not caused a structural break in the
unemployment rate time series.12 This result, in the case of continental Europe,
confirms the findings of Rodríguez-Caballero–Vera-Valdés (2020) in the sense that
a careful design and implementation of policies aimed at minimising the incidence
of companies firing workers during the pandemic have contributed to the fact that
the COVID-19’s impact on unemployment rate seems to be transitory. In North
America, however, the flexibility of the labour market has been a key factor in the
quick reversion back to the original dynamics of the market, at least in Canada. In
the USA, due to some special features (see Footnotes 3 and 11), it takes more time
for the market to gain the original dynamics back.
The above suggests that the flexible labour market is not superior to the
regulated one during the pandemic: well-designed governmental policies can
substitute the „virtues” of a free labour market.

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