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Estimating Potential Output for Argentina

María JosefinaRouillet

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

Presentation outline

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

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)

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.

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

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).

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 LtKt1-

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

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.

Production

- GDP at constant 1993 prices (real GDP) comes from Argentina’s 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.

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

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-)+1=[Kt-1/It-1(1+g)](1-)+1,

where g stands for long term rate of growth (3.6%).

Capital stock estimation

- If is the capital/investment ratio, in the steady state we have:

Kt/It=Kt-1/It-1=

Hence, =[/(1+g)](1-)+1 and, rearranging, yields:

=(1+g)/(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.

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

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 INDEC’s recent (and short) series and spliced it with FIEL’s series, but respecting the level of FIEL’s 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.

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.

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.

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.

Total Factor Productivity

- To obtain the gross rate of TFP we apply the lag operator to

Yt = At f(Kt, Lt) = At LtKt1-

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- )

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-

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.

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)

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)

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.

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.

Relative contribution to output

- Despite the positive GDP growth during the first part of the 90’s, 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

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.

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.

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