Technical Resources: Efficiency, Misallocation

Question 1

Please outline 3 sources of productivity (TFP) growth at the firm level.

Answer 1

Within Component (Technology Channel): This source accounts for the productivity growth within firms.
Productivity growth is a result of improvements in how efficiently and effectively the firms use their inputs
- The improvements: managerial skills, labor skills, innovation, and technology adoption capacity.

Between Component (Misallocation Channel):
- Reflects the role of factor reallocation across firms in total productivity growth.
- An increase in the “between” component implies that the most-productive firms command more resources, leading to the largest output and productivity gains.
- However, some distortions can limit the productivity gains.

Selection:
- Refers to the gains in productivity that arise from the dynamic process of firm entry and exit, ie. entry of high-productivity firms (relative to the industry average) and the exit of low-productivity firms.

• It captures the aggregate effect of firm turnover on productivity growth, emphasizing the creative destruction process.
• The creative destruction p. ensures that ressources are continually optimized for long term economic growth.
• Happens though allocating ressources to the most productive firms, and replacing low productive firms with high ones, leading to higher aggregate productivity growth.

Question 2

Please describe what is meant by resource misallocation

• illustrate how relative marginal products of capital can be used to identify whether firms of different employment size are financially constrained.

Answer 2

• Ressource misallocation happens when inputs such as labor, capital or land are allocated inefficiently among production units, leading to inefficient distribution.

Marginal products of firms are used to identify whether firms of different sizes employment sizes are financially constrained.

Question 3

What is relative marginal product of capital (MPK)?

Answer 3

Relative MPK is used to identify whether firms of different sizes of employment are financially constrained.

• If smaller firms have higher MPK relative to the larger firms, it indicates that they are financially constrained as their MPK is not sufficient to equal the MPK size of larger firms
• If large firms have high MPK, it indicates that they face constraints which prevents them from using their capital more efficiently.

Question 4

Please explain what increased variance in TFPQ and TFPR, respectively will do to
sector level TFP (assume elasticity of substitution is larger than 2).

Answer 4

TFPQ:
- If there is increased variance in TFPQ, it increases the sector-level TFP (productivity) of some firms in terms of quantity output, than those with lower TFPQ.

• This is because firms with higher TFPQ have lower marginal costs, enabling them to charge lower prices, and hence capture a larger market share.
• Assuming the elasticity of substitution is larger than 2, the sector-level TFP will increase because firms with higher TFPQ contribute more to overall productivity.

TFPR Assuming elast.sub >2:

• Increased variance in TFPR decreases the sector- level TFP.
• This is because they have higher costs and therefore charge higher prices, which reduce their output due to lower consumer demand.

Question 5

Comment on the magnitude of the correlated distortions

Answer 5

Negative differences:
- negative sign imply that the median firm is larger than the average firm.

• Indicate there is room for improving the ressources, by promoting growth in smaller firms, and reduce the barrier to entry of new firms.
• Indicate there is s skewness to the right, meaning there exist more large firms than small firms in the country. Sign of misallocation.
• concentration on few and large firms, and is not spread out evenly across firms.

Question 6

Please outline the assumptions leading to marginal products of capital (MPK) being
proportional to average product of capital (APK).

Answer 6

• Data on full distribution of formal and informal firms: to analyse the relationship between MPK and APK, data on the complete distribution of firms, including both formal and informal sectors, is required.
• Single Cobb D function: the production function is assumed to follow a CobbD form. What does CD assume on the relationship between inputs and output.

-Zero fixed costs: fixed costs are costs which do no vary with the output, are assumed to be zero and constant.

• Constant factor-intensities and markups: this assumption represent the relative importance of inputs in the production process, remain constant and across firms.
  Similarly, the markups, which capture the difference between price and marginal cost, are assumed to be constant.

Question 7

Please describe what is meant by the “missing middle” and outline two different ways of testing the hypothesis.

Answer 7

• The missing middle refers to the absence of intermediate firm sizes. It describes the gap in countries where there are many small firms, few large, but relatively low medium size firms.
• This pattern suggests that there are barriers for small firms which prevent them into growing to medium sized firms, which can be due to regulation, financial or market constraints.

TESTS

• Firm Size Distribution Analysis

Description: This method involves analyzing detailed and comprehensive datasets on firm sizes to check for the presence of a bimodal distribution. If the distribution shows a clear gap in the middle, it supports the hypothesis of a missing middle.

Regulatory Threshold Analysis:

Description: This method examines whether regulatory obstacles at specific size thresholds create discontinuities in the firm size distribution. For example, if firms face significant regulatory burdens when they exceed a certain size, there might be a concentration of firms just below this threshold and a gap above it.