Analysis: TFP projections

Data

• Procedures and Definitions
• Financial Years
• Adjusting Expenditures for Inflation
• Purchasing Power Parity Exchange Rates
• Cost Categories
• Funding Sources
• Full-Time Equivalents (FTEs)
  

Analysis

• ASTI intensity index
• R&D investment and knowledge stocks
• TFP projections

Practitioner's guide

Practitioner's guide for national and regional focal points (PDF)

Sample surveys

ASTI’s primary data surveys differ according to the type of agencies being surveyed. The following are downloadable examples of ASTI’s surveys in Excel format:

• Government and nonprofit agencies
• Higher education agencies
• Private, for-profit companies

TFP projections

To link knowledge stock and production we use the neo-classical production function as in Griliches (1995), where output (Y) is a function of inputs (X) and the technological stock (SK):

\(Y=F(X,SK)\) (C.1)

For simplicity, we assume that the production function in (C.1) is represented by the Cobb-Douglas function with constant returns to scale on conventional inputs and where α and γ are parameters:

\(Y= \prod\limits^{n}_{j=1} X^{βj}_{j} SK^γ \) (C.2)

From equation (C.2) we define TFP as follows:²

\(TFP= {Y\over\prod\limits^{n}_{j=1} X^{βj}_{j}} = SK^γ \) (C.3)

As a result, TFP growth is a function of changes in the knowledge stock:

\( {{dTFP}\over{TFP}} = {γ {{dSK}\over{SK}}} \) (C.4)

Equation (C.4) represents the relationship between the benefits and costs of R&D investment, where the benefits are given by the growth of TFP, and the costs result from R&D expenditure in previous periods that contribute to a change in total knowledge stock in the year of analysis. The change in SK (dSK/SK) represents a change in the capacity of a country to produce “new ideas,” while the impact of “new ideas” on productivity is given by the parameter γ.

For this study, knowledge stocks by crop and livestock activity were calculated using ASTI research focus data showing the proportion of total time researchers spend in activity-specific programs. As there is no information of TFP at the crop level, TFP growth by crop was calculated as follows:

1. A regression of ln(TFP) against year was ran for each country to determine annual TFP growth (the coefficient of the year
independent variable) for the period 1981-2016
2. Yields were calculated for each crop (y_c=output/harvested area) and livestock activity (y_lvsk=output/animal stock) and as with TFP, the ln(yield) was ran against year to obtain the average annual growth rate of yield for the period 1981-2016 by activity and country.
3. Using the share of each activity in total output (s_m) we calculated a measure of total yield growth (GY) as the sum of each individual yield weighted by its share in output:
   

   \( GY = \sum\limits^{M}_{m=1} S_{m}gy_{m} \) (C.5)

4. We then used GY to calculate the contribution of each activity’s yield growth to aggregated yield:
   

   \( C_{m}=s_{m}gy_{m}/GY \) (C.6)

   Where \( \sum\limits^{M}_{m=1} C_{m} = 1 \) for each country.

5. C_m allows us to allocate TFP growth at the country level across activities:
   

   \( gTFP_{m}= gTFP_{m} \times C_{m} \) (C.7)

6. Using changes in TFP by crop (gTFP_m) as defined above and changes in country’s i knowledge stock, we obtain an overall knowledge stock-TFP elasticity for each crop and country:
   

   \( γ_{im} = {{{dTFP_{im}}\over{TFP_{im}}}\over{({{dSK_{im}}\over{SK_{im}}})} } \) (C.8)

Elasticity values used in the analysis for Southeast Asia are shown in the table below.

Source: Elaborated by ASTI.

² TFP used in ASTI’s analysis is obtained from ERS (2019) available at: https://www.ers.usda.gov/data-products/international-agricultural-productivity/

Table—Elasticities determining changes in TFP that result from changes in own-country’s knowledge stocks