Firm Distribution and Misallocation Flashcards
(12 cards)
Consider the model from Restuccia and Rogerson, 2008. The production function for an individual firm is given by:
y = sk^αn^γ
What do each of these variables/parameters represent?
s denotes firm level productivity (firm-level TFP), k denotes capital, α denotes the capital share of output, and γ denotes the labour share of output.
If we solve the firms problem for the optimal levels of k and n, what conclusion do we draw about how firm size and profits depend on productivity?
More productive firms (higher s) use more capital and hire more labour, therefore firm size positively depends on productivity. We can also observe from the firm profit function that larger firms earn greater profits.
With firm entry and exit (Restuccia and Rogerson, 2008) what is the free entry condition and why is it needed?
The free entry condition says that W(e)=0. That is that the value of a potential entrant firm (PV of future profits) must be zero in the steady-state equilibrium, otherwise additional firms would enter the market.
Consider the model from Restuccia and Rogerson, 2008, when we add policy distortions via taxes, where firms have heterogenous tax rates, into the firms problem, how do taxes impact firm size?
We see that tax rates directly impact firm size. A high tax rate reduces the size a firm. Tax rates essentially decrease a firms productivity.
Consider the quantitative analysis of the model by Restuccia and Rogerson, 2008. What two step strategy do they use to implement the model?
- calibrate the model with no distortions to fir US data.
- Simulate the calibrated model with different distortions to study the impact of distortions. They study uncorrelated idiosyncratic distortions, and correlated idiosyncratic distortions.
In Restuccia and Rogerson, 2008, what is meant by uncorrelated idiosyncratic distortions?
Distortions (i.e. taxes) are uncorrelated with firm-level productivity (s) and examine the effects on TFP.
In Restuccia and Rogerson, 2008, what is meant by correlated idiosyncratic distortions?
This is a case where firms with low TFP receive a subsidy and firms with high TFP are taxed.
What are the key findings in Restuccia and Rogerson, 2008?
- When looking at uncorrelated idiosyncratic distortions they find that as tax rates rise, TFP falls, and as the fraction of firms in the economy who are taxed rises TFP falls.
- When When looking at correlated idiosyncratic distortions they find that as tax rates rise TFP falls. The falls in TFP in this case are far bigger relative to the falls in TFP with uncorrelated distortions. Changing the fraction of firms taxed also has a bigger impact on TFP in this case.
In Hsieh and Klenlow, 2009, consider the capital-labour ratio, labour allocation, and output. How do distortions on output and capital impact these variables on the firm-level?
Distortions on capital decrease the capital-labour ratio as these distortions cause firms to use capital relatively less than labour.
Labour allocation is decreasing in distortions to both output and capital. Note that distortions on capital decrease the marginal product of labour as firms use less capital, thus both labour allocation and the capital-labour ratio fall.
Distortions on output and capital both decrease output.
In Hsieh and Klenlow, 2009, What are TFPQ and TFPR and what is the key difference?
TFPQ denotes total factor productivity quantity and TFPR denotes total factor productivity of revenue. TFPR is TFPQ*price. The key difference is thatTFPQ differs across firms, whereas in the absence of distortions TFPR is identical across firms in an industry. This makes TFPR useful for the analysis of the impacts of distortions.
In Hsieh and Klenlow, 2009, What are the implications of capital and output distortions for the labour-capital compensation ratio and labour share?
A distortion on capital increases the compensation to labour relative to the compensation to capital.
In Hsieh and Klenlow, 2009, what are the results of their quantitative analysis?
The distribution of firm level TFPR (firm size) is more dispersed in China and India than the US. In fact, the US distribution is tighter than the efficient distribution, suggesting there should be fewer mid-sized firms and more small and large firms.
