Estimating Potential Output for Argentina

1
Estimating Potential Output for Argentina
María Josefina Rouillet Economic and Financial
Research Department, Central Bank of Argentina
Strategies for Implementing Monetary Policy
in the Americas The Role of Inflation
Targeting Federal Reserve Bank of Atlanta October
4-5, 2004
2
Presentation outline

• Production function method
• Capital stock and labor estimation
• Total factor productivity estimation
• Potential output estimation
• Gaps and GDP decomposition
• Conclusions

3
Definitions

• The design and implementation of monetary policy
  and inflation control are the principal
  objectives of a Central Bank.
• To achieve these objectives it is desirable for
  the monetary authority to rely on macroeconomic
  models which usually employ equations (i.g. a
  Phillips curve) that include variables such as
  potential output or the output gap
• We present the methodology used by the Research
  Department of the Central Bank for the estimation
  of potential output for Argentina (1980.1-2004.1)

4
Definitions

• Two definitions for potential output
• The equilibrium level of output associated with
  long term aggregate supply
• The level to which GDP converges when the effects
  of transitory shocks vanish and short and medium
  term price and wage rigidities are no longer
  relevant.
• In monetary models, potential output represents
  the level of production that does not encompass
  pressures to increase or reduce the level of
  inflation.

5
Non observable variable indirect estimation

• Statistical techniques
• Hodrick-Prescott filter
• Beveridge-Nelson decomposition
• Kalman filter
• Band-pass filter
• Methods based on economic theory
• Blanchard-Quah decomposition
• Production function methodology

6
The production function methodology
7
The production function methodology

• In the standard neoclassic model the aggregate
  production function relates output, Y, with
  services from capital and labor, sK and sL
  respectively, and a residual factor, A, that,
  among other things, measures technological change
  
• Yt f (sKt, sLt, At)
• The neoclassical production function has
• - constant returns to scale
• - positive and decreasing marginal products for
  each factor that tend to zero
  (infinity) when the respective factors tend to
  infinity (zero).

8
The production function methodology

• The neoclassical model implies that, in the long
  run, productivity depends entirely on
  technological change (which is exogenous) and is
  independent of any other structural parameter
  such as the saving rate.
• Solow (1957) provides an explicit methodology to
  measure a rate of technological change that is
  neutral in Hicks sense (i.e. technological
  change that is not biased towards any factor in
  particular). In symbols
• Yt At f(Kt, Lt) At Lt? Kt1-?  

9
The production function methodology
productivity growth

• Hence, the productivity growth rate is
• ? ln At ? ln Yt - ?K ? ln Kt - ?L ? ln Lt  
• Where
• ? ln Xt is the growth rate of Xt
• ?K ( ?) is output elasticity of capital
• ?L ( 1-?) output elasticity of labor, with ?K
  ?L 1

10
The production function methodology
productivity growth

• The growth rate of total factor productivity is
  obtained as the difference between the output
  growth rate and the rates of growth of capital
  and labor weighed by their respective
  elasticities.
• TFP growth reflects the unexplained part of the
  growth of output and therefore reflects not only
  technological change but also the effects of
  other shocks, such as imperfect competition,
  externalities and production spillovers, omitted
  variables, shocks, cyclical fluctuations, non
  constant returns to scale and the effects of
  factor reallocations.

11
Data used and the estimation of capital, labor
and TFP
12
Production

• GDP at constant 1993 prices (real GDP) comes
  from Argentinas National Accounts.
• The series corresponding to previous base years
  (1980-1992) were spliced backwards to the 1993
  series by using percentage changes.
• The estimation uses quarterly data which were
  seasonally adjusted using the Bureau of the
  Census X12-ARIMA.

13
Capital stock estimation

• The perpetual inventory method links the capital
  stock to gross investment and depreciation
  through an equation of the type
• Kt (1 - ?) Kt-1 It (2)

• While the neoclassical production function
  considers a measure of capital services (flow),
  sKt, the perpetual inventory methodology yields
  the capital stock, Kt
• We used the perpetual inventory method for the
  two main components of investment separately
  construction and durable equipment

14
Capital stock estimation

• The initial stock was estimated using the
  theoretical steady state capital/investment
  ratio
• Dividing both sides of (2) by It we have
• Kt/It(Kt-1/It)(1-?)1Kt-1/It-1(1g)(1-?)1,
• where g stands for long term rate of growth
  (3.6).

15
Capital stock estimation

• If ? is the capital/investment ratio, in the
  steady state we have
• Kt/ItKt-1/It-1?
• Hence, ??/(1g)(1-?)1 and, rearranging,
  yields
• ?(1g)/(g?).
• Then, 1950 capital stock is the gross internal
  fixed investment of 1950 multiplied by 16.045 in
  the case of construction and by 8.684 in the
  case of durable equipment.

16
Capital stock estimation

• We applied constant rates of depreciation
• 2.86 per annum for construction (useful life of
  35)
• 8.33 for durable equipment (useful life of 12)

• Investment data were seasonally adjusted for
  each component using X12-ARIMA.
• Finally, the two series were added to obtain the
  series for total capital stock

17
Capital stock estimation
18
Capital stock estimation controlling for degree
o capacity utilization

• Total capital stock is adjusted for
  underutilized capacity.
• The only data available in Argentina for
  capacity utilization is for the manufacturing
  sector.
• We used INDECs recent (and short) series and
  spliced it with FIELs series, but respecting the
  level of FIELs series
• Both series have a monthly frequency, so we
  converted them to a quarterly frequency by simple
  averages and then seasonally adjusted them with
  X12-ARIMA.

19
Capital stock estimation controlling for degree
of capacity utilization
20
Labor estimation

• As information on hours worked is not available,
  labor is measured by the number of employees.
• The only comprehensive data available for the
  labor market are published by INDEC and comes
  from its household survey (EPH), which includes
  data from 28 main urban areas. We used the rates
  of labor participation and employment for the 28
  urban areas and applied them to the total
  population (including rural).
• Data frequency conversion to quarterly
  frequency of data before 2003.

21
Labor estimation adjustment forinvoluntary
unemployment

• Data obtained for employment were adjusted for
  the involuntary underemployment of those
  employed.
• On average, underemployed workers (those that
  work less than 35 hours a week but would like to
  work more hours) are unemployed 51.8 of their
  time.
• So we added 51.8 of the underemployment rate to
  the unemployment rate and used this hourly
  employment rate to obtain and hourly equivalent
  employment series.

22
Labor estimation adjustment forinvoluntary
unemployment
23
Labor and capital shares

• The labor share was estimated from the average
  share of labor income in current GDP during the
  period 1980-2003, resulting in a labor share of
  0.4384 and a capital share of 0.5616.
• Collins and Bosworth (1996), suggest the share
  of capital could fluctuate between 0.3 and 0.4,
  being higher in developing economies.
• Englander and Gurney (1994) study factor shares
  for OECD countries and find that capital shares
  range from 0.3 to 0.4
• Kim and Lau (1994) find that the output
  elasticity of capital for recently industrialized
  countries in Southeast Asia is around 0.4.

24
Total Factor Productivity

• To obtain the gross rate of TFP we apply the lag
  operator to
• Yt At f(Kt, Lt) At Lt? Kt1-?
• and divide, obtaining
• Yt/Yt-1 (At/At-1) (Lt/Lt-1)a (Kt/Kt-1)1-a
• Rearranging and using lower case letters for
  factors of variation
• (e.g. kt Kt/Kt-1 1 D Kt/Kt-1) yields
• at yt / (lt? kt1- ?)

25
Potential output estimation

• If factors are used at potential levels and the
  TFP series is smoothened then the level of
  potential output is given by
• Yt At (Lt)? (Kt)1-?
• For factors potential level is given by the
  natural level of utilization (taking as given
  the existing structural distortions).
• Dividing by the same equation lagged one period,
  we obtain the expression in terms of factors of
  variation
• yt at (lt)? (kt)1-?

26
Potential output estimation factor natural
levels

• We obtain lt by constructing a potential
  employment series, Lt, that is derived from a
  posited underemployment adjusted NAIRU by
• Lt FLt (1 Unt)
  
• We construct kt as the gross rate of variation
  of the potential capital stock, Kt, which is
  obtained by adjusting by the historic average
  degree of utilization
• In the case of TFP, we smoothen the series of at
  to obtain at as the 19 quarters geometric
  moving average of changes in TFP.

27
Potential output estimation

• To obtain the level of potential output, we set
  the starting level so as to make the simple
  average of the output gaps during the resulting
  five complete cycles (in the period1981.1-1998.4)
  equal to zero.
• In order to deal with the end-point problem,
  we made projections for all the relevant
  variables for the periods included in the last
  observation average (that is, for the nine
  quarters following the last observation)

28
Potential output estimation
29
The resulting gaps

• Since we have potential levels for the component
  series, we are able to construct not only the
  output gap but also the gaps for labor, capital
  and productivity as follows
• Yg (output gap) Y/Y
• Lg (employment gap) L/L
• Kg (capital gap) K/K
• PTFg (productivity gap) Y/Y / ((L/L)a. (
  K/K)(1-a)

30
The resulting gaps
31
The resulting gaps
32
The resulting gaps
33
The resulting gaps
34
GDP decomposition
Growth in (qoq)
Contributions
(geometric averages)
Period
Degree of
Degree of
Real GDP
Employment
Capital
TFP
Employment
Capital
TFP
Stock
capacity
Stock
capacity
utilization
utilization
1980.2-1990.2
-0.23
0.15
-0.43
0.16
-0.60
-0.06
0.06
-0.24
0.09
-0.33
-0.06
1990.3-1998.2
1.47
0.29
1.26
0.35
0.90
0.63
0.13
0.71
0.20
0.51
0.64
1998.3-2002.2
-1.38
-0.89
-1.77
0.23
-2.00
0.01
-0.39
-0.99
0.13
-1.12
0.00
2002.3-2004.1
2.12
2.59
3.68
-0.07
3.75
-1.05
1.14
2.07
-0.04
2.11
-1.08
1980.2-2004.1
0.31
0.20
0.20
0.22
-0.02
0.11
0.09
0.11
0.12
-0.01
0.11
Growth in (qoq)
Contributions
(geometric averages)
Period
Degree of
Degree of
Real GDP
Employment
Capital
TFP
Employment
Capital
TFP
Stock
capacity
Stock
capacity
utilization
utilization
1980.2-1991.1
-0.09
0.24
-0.44
0.14
-0.58
0.05
0.10
-0.25
0.08
-0.33
0.05
1991.2-1998.2
1.42
0.17
1.45
0.41
1.04
0.54
0.07
0.81
0.23
0.58
0.54
1998.3-2001.4
-1.21
-0.47
-2.13
0.31
-2.43
0.20
-0.20
-1.20
0.18
-1.37
0.19
2001.4-2004.1
1.06
1.13
3.03
-0.12
3.15
-1.11
0.50
1.70
-0.07
1.77
-1.14
1980.2-2004.1
0.31
0.20
0.20
0.22
-0.02
0.11
0.09
0.11
0.12
-0.01
0.11
Note
GDP
is
real
GDP
at
1993
prices,
employment
includes
rural
areas
and
is
adjusted
for
involuntary
underemployment,
capital
stock
is
adjusted
for
the
degree
of
capacity utilization. Contributions are
calculated by multiplying growth rates by their
respective shares.

35
GDP decomposition

• In two of the sub-periods GDP growth is
  positive on average (the second and fourth), and
  in two it is negative (the first and the third).
• Over the whole sample, capital growth and
  particularly the degree of capacity utilization
  growth, has the same sign as GDP growth, whereas
  employment shows positive rates of growth in all
  sub-periods except during the third.
• The last sub-period shows rates of factor growth
  that on average are quite higher than GDP growth.
  Hence, TFP declines by more than 1 on average.

36
Relative contribution to output

• Despite the positive GDP growth during the
  first part of the 90s, the economy actually
  experienced in this sub-period an extensive
  pattern of growth, with a higher factoral than
  TFP contribution to growth.
• In fact, it is basically the contribution of
  capital that accounts for this, since the
  contribution of labor was very low.
• In both parts of the table the second sub-period
  shows a higher contribution of capital than TFP
  to GDP growth

37
Conclusions

• We use a methodology based on a neoclassical
  aggregate production function
• GDP is real GDP at 1993 prices
• Employment is that of rural and urban areas and
  is adjusted for involuntary hourly
  underemployment
• The capital stock is estimated through the
  perpetual inventory methodology for construction
  and durable equipment separately and is adjusted
  for the degree of capacity utilization.

38
Conclusions (cont.)

• Total factor productivity is derived as a
  residual and is smoothened in order to estimate
  potential output.
• Potential capital is constructed by multiplying
  the capital stock by the historic average degree
  of capacity utilization
• Potential employment by positing an hourly
  underemployment adjusted NAIRU.