Incorporating Temporal and Country Heterogeneity in Growth Accounting - An Application to EU-KLEMS

Transcription

1 ncorporating Temporal and Country Heterogeneity in Growth Accounting - An Application to EU-KLEMS Antonio Peyrache and Alicia N. Rambaldi Fourth World KLEMS Conference

2 Outline ntroduction General Representation of the Production Model Estimation Growth Accounting Empirical Application Data Empirical Results Model Selection Parameter Estimates Growth Accounting Patterns n Progress

3 ntroduction General Representation of the Production Model Estimation Growth Accounting Empirical Application Data Empirical Results Model Selection Parameter Estimates Growth Accounting Patterns n Progress

4 Contribution of this work A general framework that provides a venue to deal with temporal variation in individual heterogeneity, and time variation (trends) of slope coefficients in cross-sections of time series production models. establishes a mapping between parametric deterministic, semi-parametric and stochastic trend specifications. provides practitioners with a simple approach to model selection as criteria such as the AC and BC A growth accounting decomposition based on the estimated production function to separate productivity change from inputs growth effects. allows identification of the main drivers behind observed labour productivity growth. Empirical implementation using the EU-KLEMS to identify the main trends (and biases) in productivity growth in the period OECD countries and 20 industrial sectors of each economy.

5 Relation to previous works Earlier works in stochastic frontiers, panel data stochastic frontiers, and frontier models with deterministic functions of time Schmidt and Sickles (1984), Kumbhakar (1990, 2004), Battese and Coelli (1992), Cornwell et al (1990), Desli et al. (2003) and Tsionas (2006), Tsionas (2002), Karagiannis and Tzouvelekas (2009). Orea (2002), Coelli et al (2003) and Ahn et al (2000) (stochastic but stationary). Recent works closer to ours Jin and Jorgenson (2010) a state-space representation of a cost function where constant time trends (usually used to describe the rate and biases in technical change) are replaced by latent variables. Emvalomatis et al (2011) Their econometric formulation models time varying inefficiency in a non-linear fashion and provides a Kalman filtering procedure to estimate the model. Kneip et al (2012) and Almanidis et al (2015) semi-parametric specifications to accommodate cross-sectional time varying heterogeneity.

6 The production model The production technology is represented via a production function, where i = 1,...,N indexes the number of countries, t = 1,...,T indexes the number of time periods. y it = µ t + g it + X it b t + e it (1) single output yit (log of output) multiple inputs Xit µt,b t are time varying parameters common to all the countries, git is a country specific trend and eit is a normally distributed error term The country specific productivity level is given by a it = µ t + g it ( 1 N Â i a it = µ t )

7 Stochastic Frontier representation Reparameterise using the following transformation: max {a it} = a t, u it = a it a t (this is a measure of technical i=1,..., inefficiency) returns the following stochastic production frontier: y it = a t + X it b t u it + e it (2) The production frontier embedded in (2), and it is time varying (due to the time varying coefficients (at,b t )), and technical inefficiency is time varying.

8 ntroduction General Representation of the Production Model Estimation Growth Accounting Empirical Application Data Empirical Results Model Selection Parameter Estimates Growth Accounting Patterns n Progress

9 The General Econometric Model The full model representation including law of motions for g it (i = 1,...,N), µ t and b kt (k = 1,...,K) with double stochastic trends and drifts Can be represented in a state-space form, There are two advantages y t = g t + 1 N µ t + X t b t + e t (3) y t = Z t a t + e t a t = Da t 1 + h t (4) can show that it nests a number of other models, and can use standard state-space estimation algorithms.

10 Nested Models The following models are nested Fixed Effects (FE) (and FE with deterministic trends) Cornwell Schmidt and Sickles (1990) model (CSS) - and Battese and Coelli (1992) Almanidis, Karagiannis and Sickles (2015) - semi-parametric model Simple stochastic trend model Shown via a set of J linear restrictions on the parameters of the model, and the form of the variances of noise components.

11 Asimplestochastictrendmodel(TV) The model, y it = g it + X it b t + e t g it = g it 1 + h git (5) b kt = b kt 1 + h bkt where, h git N(0,sg 2 ), h bkt N(0,sb 2 ), k = 1,...,K, and e it is uncorrelated with h git and h bkt.

12 ntroduction General Representation of the Production Model Estimation Growth Accounting Empirical Application Data Empirical Results Model Selection Parameter Estimates Growth Accounting Patterns n Progress

13 Brief on Estimation and Model Selection The vector of levels, g t, (which capture individual country specific trends) and the vector of slopes, b t can be correlated with X t and thus it is an extension of the fixed effects model to the case of time-varying parameters To estimate any of the nested members of the family one can incorporate the corresponding set of restrictions and estimate the corresponding state-space form. However, computation can be approached also by estimating each nested model (ie FE, CSS, TV, etc.) using other consistent estimators. The importance of the result: t is possible to make a systematic statistical comparison among them using the AC and BC measures of fit. AC = log e 0 e NT + NT 2K, BC = log e 0 e log NT NT + K NT.

14 ntroduction General Representation of the Production Model Estimation Growth Accounting Empirical Application Data Empirical Results Model Selection Parameter Estimates Growth Accounting Patterns n Progress

15 Growth Accounting Model (1) is a translog production function at any point in time, but it allows the parameters to move in time in a non-translog way Output growth between two time periods using the reparameterisation of the production model in: y it+1 y it = a it+1 + X it+1 b t+1 a it X it b t (6) Decompose into two effects that are exhaustive and mutually exclusive: y it+1 y it = TFP + FA (7) Then, decompose further TFP = UTC + BTC. The change in the country specific level (UTC = ait+1 a it ) The bias in technical change deriving form the time variation of the input coefficients (BTC)

16 Productivity Growth (TFP) Keeping the level of inputs at the base period level, obtaining the equivalent of the base period Malmquist productivity index: TFP t = a it+1 a it + X it (b t+1 b t ) (8) Keeping the level of inputs at the comparison period value, we obtain the equivalent of the comparison period Malmquist productivity index: TFP t+1 = a it+1 a it + X it+1 (b t+1 b t ) (9) to avoid the arbitrariness of choosing the base, the geometric mean of these two indexes is used as the index of productivity growth: TFP = 1 2 TFPt + TFP t+1 = = a it+1 a it (X it + X it+1 )(b t+1 b t ) (10)

17 Factor Accumulation (FA) The input growth effect or factor accumulation effect (FA) can be computed using the same logic. The base period index is: The comparison period index is: FA t =(X it+1 X it )b t (11) FA t+1 =(X it+1 X it )b t+1 (12) Finally, we use the geometric mean as a measure of the input growth effect: FA = 1 2 FAt + FA t+1 = 1 2 (b t + b t+1 )(X it+1 X it ) (13) FA is the contribution of the increase (decrease) in the inputs endowment. t depends on how much a country is investing and accumulating factors of production.

18 TFP further decomposition The overall growth accounting decomposition is given by: y it+1 y it = TFP + FA = UTC + BTC + FA (14) where TFP = UTC + BTC. The change in the country specific level (a measure of productivity level) UTC = a it+1 The bias in technical change deriving form the time variation of the input coefficients: a it BTC = 1 2 (X it+1 + X it )[b t+1 b t ] (15) BTC measures the extent to which technical change has been biased (for example, capital-using or capital saving). UTC and BTC depend on different coefficients of the model

19 ntroduction General Representation of the Production Model Estimation Growth Accounting Empirical Application Data Empirical Results Model Selection Parameter Estimates Growth Accounting Patterns n Progress

20 Data The EU-KLEMS dataset input and output data on prices and quantities for 26 industrialized countries in the time span (see O Mahony and Timmer (2009)) For each industry value data on gross output, capital compensation, intermediate inputs (materials and energy) along with fixed base price and quantity index numbers (1995=100). We use the amount of total hours worked by persons engaged as a proxy for the quantity of labour We use PPPs to adjust for cross-sectional differential in the general level of prices. PPPs indexes use US as benchmark (US=100, 1995=100), are sector specific (i.e., each sector has different PPPs) and for output, intermediate inputs and capital services. Due to lack of data (missing values) - 13 countries and 20 industrial sectors in the time span

21 Data (cont.) We build a balanced panel dataset Let j = 1,...20 the sector and i = 1,...13 the country, the index of sectoral output for country i at time t Y j it is: Y j it = GOj i1995 PPP j j it (16) i where GO j i1995 is the value of gross output in 1995 for sector j in country i; j it is the fixed base index of sectoral output quantity change between time t and the base period 1995; PPP j i is the purchasing power parity of country i in sector j. Similarly quantity index numbers are built for intermediate output (materials) and capital services.

22 Empirical Model The model we estimate y it = a it + b kt k it + b mt m it + b kk k 2 it + b mmm 2 it + b kmm it k it + e it where y is the log of output per hours worked, k is the log of capital per hours worked and m is the log of materials per hours worked. All the variables obtained with this procedure have been normalized by the sample minimum. We estimate all the models separately for each of the 20 industrial sectors, thus applying them to each sectoral panel dataset individually. Nested models estimated: TV CSS FE (with deterministic trends)

23 Nested Models (Example of Six Sectors) WOOD FUEL R^2 R^2 Adj. BC AC R^2 R^2 Adj. BC AC TV CSS FEDT PLASTCS NON-METALLC MNERAL R^2 R^2 Adj. BC AC R^2 R^2 Adj. BC AC TV CSS FEDT ELECTRCAL AND OPTCAL AGRCULTURE AND FSHNG R^2 R^2 Adj. BC AC R^2 R^2 Adj. BC AC TV CSS FEDT

24 Electrical and Optical Equipment Sector [TFP = UTC + BTC] Level (â it ) UTC = â it+1 â it ESP_A GER_A TA_A JPN_A USA_A ESP_UTC GER_UTC TA_UTC JPN_UTC USA_UTC

25 Electrical and Optical Equipment Sector Capital and Materials Coefficients ( ˆb kt, ˆb mt )

26 Selected Countries in the Chemical Sector [TFP = UTC + BTC] Level (â it ) UTC = â it+1 â it ESP_A GER_A TA_A JPN_A USA_A ESP_UTC GER_UTC TA_UTC JPN_UTC USA_UTC

27 Chemical Sector Capital and Materials Coefficients ( ˆb kt, ˆb mt )

28 Selected Countries in the Postal and Telecommunications Sector [TFP = UTC + BTC] Level (â it ) UTC = â it+1 â it ESP_A GER_A TA_A JPN_A USA_A ESP_UTC GER_UTC TA_UTC JPN_UTC USA_UTC

29 Postal and Telecommunications Sector Capital and Materials Coefficients ( ˆb kt, ˆb mt )

30 Electrical and Optical

31 Chemicals

32 US Growth Accounting

33 Germany Growth Accounting

34 taly Growth Accounting

35 Spain Growth Accounting

36 Afewpatterns T productivity boom in the US - Jin and Jorgenson s findings cannot be generalised to other EU/OECD countries Germany: Stable labour productivity growth Based on a stable flow of investment taly: ndustrial crisis Over 15 years prior to the Global Financial Crises - (growth accounting by sub-periods shown in the paper) Spain: Significant BTC across a number of industries

37 ntroduction General Representation of the Production Model Estimation Growth Accounting Empirical Application Data Empirical Results Model Selection Parameter Estimates Growth Accounting Patterns n Progress

38 Modelling the the joint distribution of outputs and inputs when both are measured with error Rambaldi, A.N, T. H. Y. Tran and A. Peyrache "dentifying Regression Parameters When Variables are Measured with Error"