Review questions L8 Flashcards
- Please outline 3 sources of productivity (TFP) growth at the firm level
One source of productivity (TFP) growth is the within component, which accounts for productivity growth within firms. It depends on change in the efficiency or intensity of the components in the production. Increasing efficiency yields higher productivity due to increased capabilities through better labor skills, innovation, technology and more. This is also referred to as the technology channel.
Another source of TFP growth is the between component, which is reflected in the role of factor reallocation across firms in aggregate productivity growth. This refers to the idea that the most productive firms would need more resources, and thus rendering the largest output and productivity gains. So, resources should be reallocated from smaller, more unproductive firms, to larger, more productive firms.
Another source of growth in Total Factor Productivity (TFP) is the process of selection, where more productive firms succeed and less productive ones fail and exit the market. This continual process of high-productivity firms growing and low-productivity firms leaving results in an overall increase in the average productivity of the industry. This concept is often referred to as “creative destruction,” highlighting the dynamics of economic progress.
- Please describe what is meant by resource misallocation and illustrate how relative marginal products of capital can be used to identify whether firms of different
employment size are financially constrained
Resource misallocation refers to a inefficient distribution of inputs, fx. labor, capital or land, across production firms (varying in size) within an industry. The misallocation lead to significant productivity losses, entailing lower marginal products of capital, as resources are not used by the most productive firms. In an optimally efficient economy, the inputs (capital and labor) should be allocated such that the marginal products of capital (MPK) and labor (MPL) are equalized across the firms within an industry.
In order to identify whether firms are financially constrained we use the relative MPKs of firms of varying size within the same industry. We assume the firms produce with a Cobb-Douglas production function Y=AK^α L^(1-α) and derive the marginal product of capital from this: MPK=δY/δK=α*Y/K, for each firm. Now, the MPKs should be the same for all firms, within an industry, regardless of employment size. If this is not the case, then some firms are financially constrained.
- High MPK in Small Firms: If smaller firms have a significantly higher MPK compared to larger firms, it suggests that small firms are financially constrained. They have high returns to additional capital, indicating they could produce more if they had better access to capital.
- Low MPK in Large Firms: If larger firms have a lower MPK, it implies they have more capital than they can use productively, possibly due to better access to financial resources or market power.
- Please explain what increased variance in TFPQ and TFPR, respectively will do to
sector level TFP (assume elasticity of substitution is larger than 2)
Assuming that the elasticity of substitution, σ, >2, then an increased variance in TFPQ will increase TFP, because firms with higher physical productivity (higher A or TFPQ) will have lower marginal costs, which leads to these firms charging proportionately lower prices. Thus, their output will be higher and they will get more weight in the overall TFP calculation than the firms with lower A (TFPQ).
Given the same assumption in regard to the elasticity, an increased variance in TFPR will decrease TFP, as these firms will have higher marginal costs, inducing them to charge proportionately higher prices. Thus, they will produce less and their output will be lower.
If TFPR and TFPQ are positively correlated, it indicates that firms with higher TFPQ also face higher TFPR. Due to market distortions, these firms experience higher marginal costs and thus charge higher prices (proportionately), leading them to produce less than their optimal capacity. Consequently, these highly productive firms do not grow as much as they should, reducing their contribution to the overall TFP of the economy. Hence, the positive correlation between TFPR and TFPQ results in a less efficient allocation of resources, hurting aggregate TFP. So, the correlation between TFPR and TFPQ matters.
- From the Table, please calculate the relative firm size difference between the 75 percentile and the 25 percentile for the 4 African countries. Moreover, comment on
the magnitude of the correlated distortions
See table 3.3 in notes.
The relative firm size difference between the 75 percentile and the 25 percentile is calculated by taking the exponential of TFPR in each country:
For example with Kenya; eksp(1,99) = 7,32. This means that the 75th percentile firms in Kenya are 7,3 times larger than the 25th percentile firms in years 2003-2012.
In an economy with no distortions the TFPR will be the same for all firms. An economy with large distortions of TFPR has a great deal of distortions, which is the case in Kenya, based on these calculations.
From table 3.3 we see that all four countries have relatively high correlated distortion (from the ‘reg. coeff.’), for comparison this in 0,09 in the US. This means that there is a higher rate of distortion in Sub Saharan Africa, and that they could gain quite a lot from adjusting the misallocation, by reallocating the resources more efficiently – that is by giving more resources to (larger) more productive firms.
The stronger the correlation between TFPQ and TFPR, suggests that the more-productive firms are relatively more restricted from using more resources and using them more efficiently, which in the end worsens aggregate productivity (TFP).
- Please outline the assumptions leading to marginal products of capital (MPK) being
proportional to average product of capital (APK).
These assumptions are used by Hsieh and Olken (2014), where they compare marginal returns. As alternative to measuring the marginal returns, they measure the average returns to inputs. For the marginal product of capital MPK to be proportional to the average product of capital APK the following assumptions are needed:
- Revenue is generated by a cobb-douglas production function. This assures sub-elasticity between labor and capital.
- Factor intensities and markups are constant. This implies that the relation between labor and capital remains the same, regardless of much revenue is up-scaled.
- The fixed costs are zero (i.e. constant), which is necessary for the costs not to decline with quantities.
These three assumptions assures the approach of using APK as MPK is valid.
- Please describe what is meant by the “missing middle” and outline two different
ways of testing the hypothesis.
The missing middle refers to the hypothesis that there is a large number of small firms, some large firms, and very few middle-sized firms in developing countries, therefore a “missing middle”. There are different possible reasonings for this. Either small firms are constrained (or disfavored) by lacking access to finance or not benefitting from policy interventions (the institutional environment discriminate against smaller firms and favor larger firms). Thus the small firms are limited in growing larger. Another explanation is based on the theory of “dual economy”, where middle-sized or large firms face substantial fixed costs or regulatory burdens, preventing establishment and growth.
The first possible reason of constrained small firms is tested with a “C-test”, where the marginal returns should be higher in smaller/constrained firms, compared to larger/unconstrained firms.
The second theory of constrained medium and larger firms is tested with a “D-test”, where the marginal returns will be lower in smaller/unconstrained firms compared to their larger/constrained counterparts.
