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Estimating the Natural Rate of
Unemployment in Hong Kong
Petra Gerlach-Kristen∗
Hong Kong Institute of Economics and Business Strategy
March 10, 2004
Abstract
This paper uses unobserved components analysis to estimate the natural rate of
unemployment in Hong Kong. We assume that the natural rate follows a random
walk and is a determinant of the Beveridge curve. We find that the natural rate
has increased since the 1990s but nevertheless lies clearly below the actual rate of
unemployment. This indicates that unemployment is likely to decrease in the near
future.
∗HIEBS, University of Hong Kong, 919 KK Leung Building, Pokfulam Road, Hong Kong, ger-
lach@hku.hk. I thank Stefan Gerlach and Alan Siu for useful discussions.
1
1 Introduction
The Hong Kong economy has in recent years been exposed to a series of large negative
shocks. In 1998, the Asian crisis caused a decline of around five percent in real GDP.
While the economy subsequently strengthened considerably in 1999 and 2000, the first
recovery came to an end with the collapse of the global IT bubble and the terrorist attacks
of September 11, 2001. Real GDP declined by one percent in the last quarter of 2001,
but rebounded in 2002. In the spring of 2003, however, SARS stopped a second recovery,
causing another fall in real GDP of roughly half a percent. At the time of writing, the
economy once more seems to rebound.
Figure 1: Time plot of utand vt
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
1985 1990 1995 2000
unemployment rate (%)
vacancy rate (%)
Note: Sample period 1981:4 to 2003:3
Figure 1 shows the rate of unemployment and the vacancy rate over the period 1981:4
to 2003:3.1Unemployment increased over much of the 1990s and up to 2003, while the
vacancy rate declined. In 2003 the vacancy rate was roughly two percentage points below
1The data are from the database of the Census and Statistics Department and have been seasonally
adjusted.
2
its level in 1981, whereas unemployment had risen by four percent. This observation
suggeststhatthenaturalrateofunemployment—therateofunemploymentwhichwould
be observed if the economy were in equilibrium — might have increased. If so, we would
not expect unemployment to fall in the coming years to levels as low as in the 1980s in
spite of the economic recovery. The aim of this paper is to provide an estimate of the
natural rate of unemployment.
Our study is closely related to the Groenewold and Tang [3] who use a structural vector
autoregressive model of the rate of unemployment and real output to estimate over the
period 1982 to 2000 natural unemployment in Hong Kong (as well as in Korea, Singapore
and Taiwan). They focus on the impact of the Asian crisis and present an estimate of the
natural rate of unemployment that increases only slightly in 1998 and thus suggests that
the increase in unemployment at the time mainly was due to transitory factors.
Besides using a longer data sample, our paper complements and extends this analysis
in two important ways. First, while Groenewold and Tang provide estimates of the natural
rate of unemployment using an non-structural time series approach, the results presented
here rely on the Beveridge curve for the theoretical framework. The fact that two such
different approaches yield similar estimates of the evolution over time of the natural rate
of unemployment in Hong Kong provides some grounds for believing the results. Second,
our estimation technique allows us to quantify the uncertainty attached to the estimate of
the natural rate of unemployment. We find that the confidence bands are rather narrow,
which is further evidence suggesting that our estimate of the natural rate is reliable.
The rest of the paper is structured as follows. Section 2 discusses the concept of the
Beveridge curve. Section 3 shows how to use this theoretical framework to estimate the
naturalrateofunemployment. Sincethenaturalrateisavariablewhichisnotmeasured
directly, we apply the unobserved components estimation technique. Section 4 presents
the path of natural unemployment and documents that the estimate seems reasonable in
that it has high explanatory power in a simple Phillips curve and an equation for wage
inflation in Hong Kong. Section 5 concludes.
3
2 The Beveridge curve
The relationship between unemployment and vacancies is commonly studied by means of
the Beveridge curve.2This curve relates the unemployment rate utto the vacancy rate vt.
Figure 2 shows the scatter plot for Hong Kong. The data points describe a hyperbola, so
that the functional form
utvα
t=ct(1)
captures the link between utand vtrather well (α=1would give rise to a rectangular
hyperbola; the larger α, the more curvature has the Beveridge curve). The variable ct
determines how far the hyperbola is from the origin. As illustrated in Figure 3, the higher
ct,thelargerisutfor any given vt.
Figure 2: Scatter plot of utand vt
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
0 1 2 3 4 5
v
u
Note: Sample period 1981:4 to 2003:3
2For an introduction on the Beveridge curve see Blanchard and Diamond [1]. See Shimer [5] for a
recent discussion.
4
Figure 3: The Beveridge curve
v
u(I)
u(II)
increasing c
Note: Rate of unemployment given vtfor different ct.
The natural rate of employment u∗
tis that level of unemployment which results if the
vacancy rate is at its mean, which we denote by v∗. Using equation (1), we define
u∗
t≡ct
(v∗)α.
If we divide both sides of equation (1) by (v∗)α, the Beveridge curve can be written as
ut³vt
v∗´α
=u∗
t
or alternatively
ut¡vt
v∗¢α
u∗
t
=1.
Taking logarithms we obtain
ln hut³vt
v∗´αi−ln(u∗
t)=0.(2)
Expression (2) can be thought of as an equilibrium condition that holds on average over
time but which can be disturbed by temporary shocks. We define deviations from equi-
librium as
xt=lnhut³vt
v∗´αi−ln(u∗
t)+ex
t(3)
5
and assume that ex
tis white noise.
3 Estimation
We use the time series process of the actual rate of unemployment to estimate the path of
the natural rate. In particular, we assume that the rate of unemployment adjusts so as to
offset past deviations from the Beveridge curve. Allowing, moreover, for autocorrelation
in the changes of unemployment, we consider
∆ln(ut)=β∆ln(ut−1)−γxt−1+eu
t,(4)
where eu
tis white noise.3Equation (4) states that the rate of unemployment tends to rise
when it increased last period and if xt−1waslow. Notethatweuseln(ut)rather than ut
to account for the fact that the unemployment rate cannot turn negative. Replacing xt−1
with equation (3), we then estimate
∆ln(ut)=β∆ln(ut−1)−γnln hut−1³vt−1
v∗´αi−ln(u∗
t−1)o+et,(5)
where et=eu
t−γex
tis distributed as N(0,σ2
e). Equation (5) thus implies that unem-
ployment tends to decrease if either ut−1or vt−1were high relative to the natural rate
of unemployment. In terms of Kalman filtering, equation (5) constitutes an observation
equation.4
The state equation is given by
ln(u∗
t)=ln(u∗
t−1)+e∗
t,(6)
where e∗
t∼N(0,σ2
∗). Thus, we assume that the logarithm of the natural rate of unem-
ployment follows a random walk. We estimate the parameters of equations (5) and (6)
using Kalman filtering. Table 1 shows the regression output.
We find that αis below unity, which implies that the Beveridge curve in Hong Kong
appears to have less curvature than a rectangular hyperbola.5The AR coefficient βis
3We exclude the constant since it was insignificant in preliminary estimations.
4For a discussion of Kalman filtering, see e.g. Harvey [4].
5However, a Wald test does not reject the hypothesis that αequals unity (p-value =0.17).
6
Table 1: Unemployment model
α0.728∗∗
(0.201)
β0.229∗
(0.102)
γ0.403∗∗
(0.123)
σ2
e0.009
σ2
∗0.005
log likelihood 50.328
Note: Maximum likelihood estimates, 1982:2-2003:3. Standard errors in
parentheses. ∗/∗∗ denotes significance at the five / one percent level.
estimated as 0.23 and the adjustment coefficient γas 0.40. Correspondingly, the median
lag, which is given by ln(0.5)/ln(1 −γ), equals 1.34. This indicates that, if condition
(2)wasnotmetinthelastperiod,theunemploymentratemovessuchthathalfofthe
misalignment is corrected after roughly four months. The estimate of the natural rate of
unemployment at the end of the sample is 2.99%. With 95% probability, u∗
tlay in the
third quarter of 2003 between 2.11% and 4.25%.
Figure4showstheestimateoftheBeveridgecurveattheendofthesampleperiod.
The actual data for 2003:3 lie within the 95% confidence interval. However, the vacancy
rate of 0.59% is much below its equilibrium value, which is estimated to be 1.90%, while
utis with 8.30% above the estimate of u∗
t=2.99%.
4 The natural rate of unemployment
Next we construct an estimate of the natural rate of unemployment. Figure 5 shows the
smoothed u∗
ttogether with the actual rate of unemployment. Natural unemployment is
estimated as around 3.5 percent in the first half of the 1980s. It then declines to two
7
Figure 4: Beveridge curve for 2003:3
0
4
8
12
16
20
0
4
8
12
16
20
0.5 1.0 1.5 2.0 2.5 3.0
v
estimated Beveridge curve
95% confidence band
actual data 2003:3
equilibrium
u
Note: Based on estimates in Table 1.
percent at the beginning of the 1990s. Thereafter, it rises over time and approaches three
percent in 2003.
Actual unemployment was slightly above trend from 1983 to 1986, but fell below the
estimated natural rate in 1987.6During the economic expansion at the beginning of the
1990s, utremained significantly below u∗
t, but rose sharply during the Asian crisis. From
then onwards, unemployment in Hong Kong seems to have clearly exceeded its natural
rate. It thus appears likely that in the absence of further negative shocks, unemployment
in Hong Kong will return to a level of around three percent in the near future.
As noted in the introduction, our estimate of the natural rate is closely related to that
presented in Groenewold and Tang [3]. Their estimate also suggests that unemployment
was above its natural level during most of the 1980s, below it from the end of the 1980s
6For a detailed discussion of economic developments in Hong Kong over the period 1982 to 2000, the
interested reader is referred to Groenewold and Tang [3].
8
Figure 5: Actual and natural unemployment
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
1985 1990 1995 2000
u
u*
95% confidence band
Note: Sample period 1982:1 to 2003:3
to the onset of the Asian crisis and again above it from 1998 onwards. In contrast to our
estimate, the path of u∗
tin their paper displays slightly more time variation and is a little
higher throughout the sample.
As a last step of the analysis, we study the plausibility of the estimated natural rate
of unemployment. In particular, we assess whether the deviation of actual unemployment
from its natural rate is useful in explaining CPI and nominal wage inflationinHong
Kong.7A plausible estimate of u∗
tshould make the unemployment gap, defined as u∗
t−ut,
impact both on πtand wt.
Figure 6 plots the unemployment gap, annual CPI inflation and the output gap yt,
which is estimated using a Hodrick-Prescott filter. A clear link between the unemployment
gap and πtis evident. Using the data in the figure, we estimate two simple Phillips curves
for Hong Kong. We first fit
πt=a+bπt−1+cyt+εt.(7)
7See Genberg and Pauwels [2] for a study on price formation in Hong Kong.
9
To account for potential simultaneity, we estimate all equations with GMM, using the
first and second lag of the right-hand side variables as instruments. Table 2 holds the
regression output and shows that we do not reject the hypothesis that bequals unity,
which suggests that inflation returns only slowly to equilibrium after a shock. Moreover,
the constant ais insignificantly different from zero, implying that the long-run mean of
inflation is zero.
Figure 6: Phillips curve data
-10
-5
0
5
10
-10
-5
0
5
10
1985 1990 1995 2000
unemployment gap
output gap
CPI inflation
Note: Sample period 1982:1 to 2003:3
We next include the unemployment gap and estimate
πt=a+bπt−1+cyt+d(u∗
t−ut)+εt.(8)
The impact of the unemployment gap is estimated as 0.58. Thus, when unemployment is
one percentage point below its natural level, CPI inflation tends to increase by roughly
half a percentage point. The autoregressive coefficient on inflation is significantly smaller
than unity, suggesting a comparatively fast return of inflation to equilibrium. More im-
portantly, ais significantly larger than zero. The long-run mean of inflation is estimated
as a/(1 −b)=6.75%. Thus, once the unemployment gap starts to close, we expect to
10
Table 2: Assessment of the plausibility of u∗
t
Phillips curves Wage equation
Equation (7) (8) (9)
a-0.142
(0.128)
1.148∗∗∗
(0.288)
1.050∗∗∗
(0.520)
b0.982∗∗∗
(0.020)
0.830∗∗∗
(0.042)
0.866∗∗∗
(0.060)
c0.263∗∗∗
(0.053)
0.061∗
(0.036)
d0.581∗∗∗
(0.190)
0.359∗∗
(0.169)
R20.959 0.970 0.970
Note: GMM estimates, instruments are two lags of the right-hand side variables. Sample
period 1982:4-2003:1 for equations (7) and (8) and 1983:3-2001:3 for equation (9). Standard
errors in parentheses. ∗/∗∗ /∗∗∗ denotes significance at the ten / five / one percent level.
observe the emergence of a positive rate of CPI inflation in Hong Kong.
To mo d el wage i nflation, we consider the annual increase in nominal wages and the
unemployment gap. Figure 7 plots the data and suggests a close relationship between the
two variables. This is confirmed by a regression of the form
wt=a+bwt−1+d(u∗
t−ut)+εt.(9)
The last column of Table 2 shows that the impact of the unemployment gap is significant.8
If unemployment is low relative to its natural level, nominal wages tend to increase.
8Including CPI inflation in equation (9) did not yield a significant coefficient.
11
Figure 7: Wage equation data
-8
-4
0
4
8
12
16
-8
-4
0
4
8
12
16
1985 1990 1995 2000
unemployment gap
nominal wage inflation
Note: Sample period 1982:1 to 2003:3
5Conclusions
We use the Beveridge curve as analytical framework to estimate the natural rate of unem-
ployment in Hong Kong. We find that the natural rate declined in the 1980s and increased
from the beginning of the 1990s onwards. For the third quarter of 2003, when our data
end, the natural rate is estimated as three percent and thus lies clearly below the actual
unemployment rate of 8.3 percent. This suggests that unemployment is likely to decrease
in the near future.
To assess the plausibility of our estimate of the natural rate of unemployment, we fit
equations for CPI and wage inflation. We find that the unemployment gap, defined as
the difference between the natural and the actual rate of unemployment, is an important
explanatory variable.
12
References
[1] Blanchard, Olivier Jean and Peter Diamond (1989), The Beveridge curve, Brookings
papers on economic activity 1989:1, 1-60.
[2] Genberg, Hans and Laurent Pauwels (2003), Price formation and deflation in Hong
Kong, mimeo, Graduate Institute of International Studies Geneva.
[3] Groenewold, Nicolaas and Sam Hak Kan Tang (2004), The Asian financial crisis and
the natural rate of unemployment: Estimates from a structural VAR for the newly
industrializing economies of Asia, Pacific Economic Review 9(1), 45-64.
[4] Harvey, Andrew C. (1989), Forecasting, structural time series models and the Kalman
filter, Cambridge University Press, Cambridge.
[5] Shimer, Robert (2003), The cyclical behavior of equilibrium unemployment and va-
cancies: Evidence and theory, NBER working paper 9536.
13