Productivity growth and thetransition to market in China andRussia
Yasushi NAKAMURAGSISS, Yokohama National University
March 28, 2015
At SERC, Hokkaido University, Sapporo

Motivation
 Different ways to market economy in China andRussia.
 How the difference influenced their productivitygrowth?
 New developments in theory and application ofthe normalized CES function and the Bayesianstatistical method.

+ Decomposition of the technology progress is possible.
+ Consideration of the elasticity of substitution (ES) ispossible.
+ Easy to model structural breaks (time-varyingparameters: TVP).
+ Fundamental difficulty to estimate.
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Structure of the presentation
 New methods to estimate TFP Normalized CES(NCES) function
 Extended Solow residuals method
 Bayesian TVP-NCES and Malkov Chain Monte Carlo(MCMC) simulation

 Data Results
 Discussion

3New methods to estimate TFP-Normalized CES production functionYt
 Kt t 
Y0 π 0 GK   K0
σ −1σ Lt t + (1 − π 0 )  GL  L0

σσ −1 σ −1σ

 Looks not very different from the ordinary CESfunction.

Ytσ −1σ Lt Kt+ (1 − π 0 )  
AtY0 π 0   K0 L0 
σσ −1 σ −1σ

4New methods to estimate TFP-Normalized CES production function

 The normalization is necessary: to properly measure the ES. The elasticity is defined as apoint elasticity; thus, we need to fix the point (thenormalization benchmark) to measure the elasticity.
 to fix a share parameter which serves as the benchmark
to determine the type of technology progress.

 The normalized CES production function includes alltypes of technical progress: Hicks, Solow, andHarrod.
 The relation between ES and the economic growth:a low ES may slow economic growth. If a production
factor increases faster than the others and the ES islow, the output grows less because the low ES
accelerates decrease in marginal productivity.

5New methods to estimate TFP-Normalized CES production function

 NCES tends to give very low ESs.

 OECD average = 0.34 (Mallick, Lab.Eco., 2012), Japan andFinland=around 0.2 (Not particularly low. Nakamura andKorhonen, 2013)

 Intuitive explanation for the low ES.

 K can grow faster than L and, sometime, than Y. As NCES

is to take a weighted average of K and L which fits to Y. It
needs to smash the faster K growth.
 A low ES is good to discount the faster growth of K: K^s(s<1). Otherwise, we should have very small (may bedecreasing) GK.

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New methods to estimate TFP-Normalized CES production function

 A fundamental difficulty of NCESsstt

Yt

π K ( GK Kt ) + (π L ) ( GL Lt )s

Assuming Git=Yt/it (i=K,L),

Yt = π K (Yt / K t ⋅ K t ) + (π L ) (Yt / Lt ⋅ Lt )sss

= π KYt + π LYt = Yt .
sssThus, Y/K and Y/L are, argibically, perfect solutions
with any s. It’s OK, but s is unidentifiable without
additional information.
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New methods to estimate TFP-Extended Solow residual method

 Use NCES anyway! TFP can be calculated:

π K (Yt −1 / Kt −1 ⋅ Kt ) + (π L ) (Yt −1 / Lt −1 ⋅ Lt )ssˆ
TFPt Yt / Yt − 1=sˆYtss If s=1, this method is just the Slow residulas

method [TFPt(1)]. We can calculate TFPt(σ) for aplausible range of σ, although we do not know thetrue σ.
 This may be called ’extended Solow residuals
method.’8

New methods to estimate TFP-Bayesian TVP-NCES and MCMC

 The best way to estimate NCES seems to be ‘thesystem method’ to use dY/di=wi (i=K and L).
 However, it is often difficult to obtain data on wifor economies such as Russia and China.
 In this study, NCESs are estimated under some
soft additional constraints:
 Gi follows random walk: smoothing Truncation of the Gi random walk distributions

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New methods to estimate TFP-Bayesian TVP-NCES and MCMC

Yt =π K ( G K t ) + (π L ) ( G L ) + eY
sst
Kln ( G ) ln ( G=tit −1istL t)+eGis  N ( s ,τ s )T( LB, −0.1)
eY  N (0,τ Y )eGi  N (0,τ Gi )T( LB, +∞ )
 R and JAGS were used for the Bayesian MCMC

simulation.

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Data-China

 Period: 1952-2011 annual.

 Y, K, L for 1952-2008: Wu(RIETI DP, 2011-E-003)

 Y and L are extended to 2011 with the official data.
 K for 2009-2011 are extended with the perpetualinventory method. The depreciation ratio follows
Wu’s. GFCF: UNSD, National Accounts Estimates ofMain Aggregates. The deflator for GFCF is theproperty price index for investment in fixed assets.
 The share parameter: 2011 Regional accountingdata.
 The normalisation base is 2011.
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Data-Russia Period: 1961-2012, annual.

 Y: GDP for 1961-2005 estimated by Kuboniwa andPonmomalenko. 2005 and after: Official GDP.
 L: Official head count data.
 K: 1961-90: Official. 1990 and after: Official. Simplylinked.
 Share parameter: 2011. Official nationalaccoounting data. The Labor share=(Compensationof employees - indirect tax)/(GDP - indirect tax) The normlisation base is 2012.
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Data

-The Benchmark year Russia 2012, China 2011.
 See Maddison’s GDP per capita in the 1990 USD.

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Data: The normalized time series of Y, K, and L

 The quality of data seems low for both China and Russia:

the headcount of L, questionable K.
 Small fluctuations in China, big changes in Russia.

Data: Annual growth in Y, K, and L

 China: Y/L increases relatively steadily after 1978, while Y/K

increases only recently.
 Russia: The decreasing trend in Y/K was remarkable before 1991. Alarge drop both in Y/K and Y/L in 1990. The turning point was 1995.

Results-Productivity level (ESR & NCES)

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Results-Annual growth rates (ExSR & NCES)

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Results-Comment on TVP-NCES results The estimates by TVP-NCES method fall in themiddle of partial productivities (Y/K and Y/L) or theestimates by extended Slow residuals method.
 In this sense, the estimates by TVP-NCES seemreasonable. However, it is far from an accurateestimation. In particular, Russian TFP before 1991.

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Results-China and Russia compared (NCES estimation)

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Wrap-up about the methods
 Extended Solow residuals method is easy to use.
 Estimation of TVP-NCES production function withtime-varying parameters is easy. But, the accuracy
is not guaranteed. This study showed not
fundamentally different results between Extended
Solow and TVP-NCES.
 Elasticity of substitution is low in both China (0.2)
and Russia (0.16). However, it is not clear how
significantly low they are.

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Wrap-up about the productivity
 China has been increasing TFP steadily since theopen-door in 1978. The problem of low capital
productivity lingers. However, we see the sign ofimproving capital productivity in the latter half ofthe 2000s.
 Russia’s decreasing trend in TFP was outstanding
before 1991 (actually before 1995). The transitionto market changed it. Both capital and laborproductivities, and, thus, TFP turned to increase.
However, the improvement seems vulnerable tothe external (oil price) shock.
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