An improvement in the terms of trade corresponds to an increase in total factor productivity. Both studies show that a change in the terms of trade in the presence of import tariffs has a first-order effect on measured productivity because gross domestic product at the market price (expenditure plus tariff revenue) is used by these authors. Total factor productivity consists of two components: efficiency in the production of gross output and relative prices of trade.
Investment
This measure of total factor productivity in export production is naturally related to production in the sector. On a stationary growth path, the gross growth rate of capital goods is equal to the product of the growth rate of the relative price of imported capital goods and the growth rate of imported capital goods.
Export and import
Investment in machinery and equipment is aggregated from domestic and imported machinery with a Cobb-Douglas production function as follows.
Final consumption good
Household
Competitive equilibrium
The stationary growth path is defined as a stationary equilibrium in which (i) Gross outputs at the sector level grow at constant but varying rates. ii) capital rental rates are constant but different between the two types of capital. iii) The relative prices of products at the sector level change at constant rates. iv) The shares of current price inputs in total inputs are constant. v) Shares of current price gross output at the sector level in total output (or aggregate value added) are constant. The existence of a stationary growth path requires that i) the relative prices of imported goods change at constant rates, which are assumed to hold; and ii) productivity at the sector level increases at a constant rate.
4 Effective aggregation production function
- Gross domestic product at the basic price
- Implicit price of gross output
- Terms of trade and measured productivity
- Gross domestic product at the market price
We also provide the result of using gross domestic product at market price as a measure of aggregate output. The import price does not affect measured aggregate productivity for gross domestic product at basic price, but it does for gross domestic product at market price. To obtain a definition of real gross domestic product at a basic price that is consistent with national accounts, we use the Divisia index that it provides.
Exponentωc is the share of consumption at current price in gross domestic product at base price, and so on. In doing so, real gross domestic product at base price becomes a function of total primary factors. Suppose s=[sj]4×1 is a vector, sjis is the share of value added of sectorj in gross domestic product at the base price.
If the production technology is Cobb-Douglas and trade is balanced at the aggregate level, on the stationery growth path, there exists an efficient production function of real gross domestic product at the base price, given by. If the gross domestic product at market price is used, we can show that both the export price and the import price in relation to domestic market prices affect measured aggregate total factor productivity.
5 Quantitative analysis for Canada
- Recent trends of productivity and relative prices in Canada
- Model calibration
- Domar weights
- Sector-specific total factor productivity
- Growth accounting: data and model
- Accounting for historical aggregate TFP growth
Terms in parentheses reduce to zero under the constant-returns-to-scale technology, and therefore the import price has no effect on total factor productivity. We obtain sector-specific total factor productivity growth rates by matching sector-level gross output growth rates predicted by the model with those in the KLEMS data. Multifactor productivity in the KLEMS data (calculated using gross output deflated by domestic sales prices) grows at rates of 1.001, respectively.
The term in large brackets on the right-hand side is the share of consumption in gross domestic product. In calibrated total factor productivity growth, we have taken into account heterogeneity in labor input growth across sectors. The total increase in factor productivity predicted by the model is mainly driven by the decrease in export costs (reflected in the export-country price ratio), as well as by the total factor productivity in Sector 4, as seen in Table 6.
Faster capital appreciation in the model stems from two differences between the model prediction and the data. In summary, the calibrated model suggests that the export price (relative to domestic price) accounts for approximately half of total factor productivity growth in the Canadian economy. Sector-level total factor productivity in the production of gross output and relative domestic export prices are plotted in Figure B.4 and Figure B.5 respectively.
Empirical evidence seems to suggest that the cost of exporting has increased in the post-2001 period.
6 Productivity growth slowdown across countries
Evidence from WIOD and KLEMS
In the machinery and equipment sector, the significant increase in relative domestic export price offset a sharp decline in total factor productivity, on net, which made a negative contribution to total productivity. So far we have labeled the ratio of export price to domestic price as the export cost, although in the model this ratio may also reflect the total factor productivity of the export sector relative to the domestic sector. Was the fall in the export-domestic price ratio in the 2000s a fall in export costs or an increase in relative productivity in the export sector.
The decline in the export-to-domestic price ratio is then likely attributed to an increase in relative productivity in the exporting sector. The charts suggest that regardless of the decline in the contribution of the domestic-export price ratio, four European countries (Finland, France, Germany and Sweden) have experienced positive growth in total factor productivity. For Spain and Italy, overall total factor productivity showed negative growth in the 2000s, largely due to the negative contribution of the domestic export price ratio, and sector specific productivity was actually increasing.
For Korea, overall productivity declined in the 2000s, dragged down by the declining contribution of the domestic export price ratio. It is clear that the relative export price has played an important role in the slowdown in overall productivity for some countries.
Aggregate TFP and aggregate relative price across countries
This difference is most likely due to the relative export price trends in our data being different from those in the PWT data. In Japan, total total factor productivity tracks closely with sector-specific productivity, indicating a small contribution of the domestic to export price ratio. For the three countries (Italy, Korea and Spain) where the relative export price was important for the slowdown, ESCAP-World Bank cost of trade data show that the cost of trade with their main trading partners did not increase.
This suggests that the decline in the domestic export price may be due to the declining relative productivity of the export sector in these countries. On the basis of this information, we calculate the contribution of the ratio between domestic and export prices to aggregate productivity growth, i.e. we also conclude on the contribution of productivity (again, production of gross output). An import price in one country may be an export price in another, so we allowed the error terms to be stratified by region, allowing for within-region correlation.
In the last two columns, the independent variable is the growth rate of the exchange rate. The coefficient estimates for domestic-export price ratio are positive and statistically significant for both sub-samples as expected.
7 Conclusions
The second set of estimates suggests that the correlation between measured total factor productivity and the terms of trade is weak and negative for a broad set of countries. An improvement in the terms of trade may slightly reduce measured productivity rather than increase it, although for some individual countries this correlation may be strong and positive. These assumptions are commonly held by statistical agencies to measure productivity, which may explain the insignificant estimates of the import price coefficients in the cross-country data.
Relaxing these assumptions can allow for a role played by import pricing in productivity growth, for example, as in Gopinath and Neiman (2014). In Canada's case, the improved terms of trade in the 2000s increased the purchasing power of the domestic economy, leading to increased consumption despite a poor productivity record.
Jones, Charles I., "Misallocation, Economic Growth and Input - Output Economics," in Daron Acemoglu, Manuel Arellano, and Eddie Dekel, eds., Advances in Economics and Econometrics, Vol. Tesar, "Effective Tax Rates in Macroeconomics: Country Estimates of Tax Rates on Factor Income and Consumption," Journal of Monetary Economics, December. Samaniego, “Mapping prices into productivity in multisector growth models,” Journal of Economic Growth, September.
Statistics Canada, "Guide to the Income and Expenditure Accounts," Systems of National Accounts Catalog No. Wang, Weimin og Karim Moussaly, "The Impact of Leased and Rented Assets on Industry Productivity Measurement," The Canadian Productivity Review 2014036e, Statistics Canada, økonomisk analyse juli 2014.
A Data sources
- Growth accounting data
- Definition of sectors
- Factor shares
- Shares of sector outputs
- Cross-country data
Capital costs as a percentage of production in construction are small, probably due to measurement errors (for example, related to the way labor and capital costs are allocated to this sector in the input-output table for certain construction activities). In calibration, we impose the constant returns to scale in the production of each sector, and calculate the capital share as the total share after subtracting the labor share and the intermediate input share. In the WIOD data, the average shares of intermediate inputs in gross output are from 1995 to 2012, respectively.
From the WIOD we also obtain the uses of sector outputs as a part of sector outputs, as well as the uses of sector imports as a part of sector imports. Sector Intermediate input Final consumption Investment Export Total Uses of domestic goods, as part of sector-level outputs. Using the similar calculation, we obtain imported sector-4 goods for final consumption as a share of total non-housing consumption, 0.089.24 This value is close to the WIOD data 0.09 in Table A.2.
We use KLEMS data to calculate both the share of sector-level output in aggregate gross output and Domar aggregation weights (sectoral-level gross output divided by gross domestic product). Note that Sector 2 (construction) in Table A.5 includes both residential buildings, non-residential buildings, non-residential engineering, and building repairs.
B Figures
Price of investment M and V / price of non-investment GDP Price of gross output of M and V / price of remaining gross output. The solid line represents aggregate TFP, the dashed line represents the contribution of sector-level TFP to aggregate TFP, and the dotted line represents the contribution of relative domestic export price to aggregate TFP.
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