Big questions in this lecture

  Stockholm Doctoral Course Program in Economics Development Economics II: Lecture 4 (1st half)

  Firms Masayuki Kudamatsu

  IIES, Stockholm University

23 November, 2011

  

Big questions in this lecture

  1. Is return to capital high for firms in

  LDCs?

  2. Are capital and labor misallocated

  across firms within each industry in LDCs?

  Is return to capital / labor

• heterogeneous across firms within industry? (Banerjee & Duflo 2005)

Methodology focus in this lecture

• Use treatment as IV for estimating

  RCT on firms

• production function Deal with attrition bias
• Estimate eterogeneous impacts
>Monopolistic competi

  

1. de Mel, McKenzie, & Woodruff

(2008)

  One of the 1st RCTs on

• interventions to firms in LDCs
• few firms, lots of heterogeneity,

  Which is usually difficult

  non-persistent outcomes ⇒ low power to detect impact (McKenzie 2011)

  Estimated parameters used in

• subsequent research

  Besley, Burchardi, & Ghatak (2011),

1.1 Research question

  What’s the return to capital for

• microenterprises in Sri Lanka?
• Small firms employ half or more labor

  Important?

  force in LDCs

• Microfinance • Is production function convex?
• No credible estimate in the literature

  Original?

• Feasible?

Empirical challenge

• Observed level of capital stock: reflect (unobservable) entrepreneurial ability
• Cross-sectional estimation misleading
• Those who apply for credit: selected sample of firms
• Exploiting exogenous change in credit access (e.g. Banerjee-Duflo 2004): not the population average return to capital

1.2 Experimental design

  Sample: 408 microenterprises

• (invested capital: ≤100,000 LKR) in Sri Lanka
• e.g. grocery stores

  203 in retail sales

• e.g. sewing clothes, making bamboo

  205 in manufacturing

  

products, food processing

• 1. 10,000 LKR in cash 2. 20,000 LKR in cash 3. 10,000 LKR equipment of their choice

  Treatments: grant in cash or in kind

  The treatments are a big capital

• injection

  55% or 110% of median initial level of

• invested capital

  ⇐ Benefit of RCTs on firms in LDCs:

  you can cheaply create a big shock

  Survey of across-firm RCTs by

• Bandiera et al. (2011) mostly cite studies from LDCs

1.3 Data

  9 waves of quarterly surveys

• (April 2005 to April 2007) Profits: elicited directly
• Better than asking revenues and
• expenditures in detail (de Mel et al. 2009)

  Table I: balancing on covariates

1.4 Program evaluation

  _�

  4 g

  Y it = T + δ t + λ i + ε it

  it g =1

  Y Outcomes for firm i at time t it g

  

T indicator of treatment of type g

δ t Survey round FE λ i Enterprise FE

1.4 Program evaluation (cont.)

  Results (Table II) ↑

  Capital stock

• ↑

  Profits

• Owner hours worked ↑ for 10,000
• LKR treatments Family/hired labor hours: no change
• Robust to outliners (Table III)

1.5 Estimating return to capital

  π = β K + δ + λ + ε

  

it i it t i it

π Profit it

  K Capital stock in 100 LKR at time t it

  ⇐ Instrumented by the amount of capital grant in 100 LKR (0 for control, 100 for treatment group 1 & 3, 200 for the rest)

  

1.5 Estimating return to capital

(cont.)

  Results (Table IV) Return to capital:

• per month

  5.85% Issues with 2SLS

(i) Exclusion restriction

(ii) Weak instruments

  (iii) LATE

  (i) Exclusion restriction

  Instrument can affect labor inputs

• (in quantity or in quality)

  Owner labor hours ↑ indeed (Table

• II(5))

  Deduct from profits the value of

• owner’s labor hours

  ⇒ 4.59% to 5.29% per month Digression: control for outcomes

  Can we avoid this issue by

• controlling for owner labor hour? No. Owner labor hour: correlated
• w./ K it In general, when a treatment affects
• two outcomes A and B, DO NOT regress A on treatment dummy and B

cf. Angrist & Pischke (2009: 64-66) By controlling for B, the coefficient on the treatment dummy is

  (A |B = x) − E(A |B = x) E _{1i 1i 0i 0i} = (A − A |B = x) E _{1i 0i 1i}

• {E(A |B = x) − E(A |B = x)} _{0i 1i 0i 0i} 1st term: Causal effect on A conditional on • B = x for those treated

cf. Angrist & Pischke (2009: 64-66) By controlling for B, the coefficient on the treatment dummy is

  E (A |B = x) − E(A |B = x) _{1i 1i 0i 0i} = E(A − A |B = x) _{1i 0i 1i} {E(A |B + = x) − E(A |B = x)} _{0i 1i 0i 0i}

• 2nd term: Selection bias = x by

  Those induced to have B

• treatment: DIFFERENT from those

  (ii) Weak instruments

  1st stage F-stat on excluded

• instrument: 27.81

  (iii) LATE

  Some reasons to believe the IV

• estimate is ATE, not LATE
_it

  

No correlation btw. ∆K after

• treatment & observables that would correlate with β
_IV

_i

ˆ cf. β : weighted average of β w./ weight _i being the relative size of the change in the regressor due to the instrument (Card 2001: 939)

1.5 Estimating return to capital

  (cont.)

  Implications 5.85% per month ⇒ more than 60%

• per year Market interest rate: 12% to 20%
• per year Why don’t these firms borrow?
>Survey responses: missing mar

1.6. Robustness to attrition

  Attrition rate differs across

• treatment status

  (control) vs (treated)

  14.3% 9.6%

• If attrition in control is higher for
• higher-profit making firms, we overestimate treatment effect Solution: Lee (2009)
• Another example of application in
• development RCT: Ashraf et al. (2010)
Digression: Lee (2009)

  Assume:

  (1) treatment is exogenous both in

• outcome and sample selection

  equations

  (2) treatment induces attrition

• monotonically (ie. either more or less, not in both directions)
• Identify the excess # of observations

  Then the bound obtained by

• missing due to treatment Trim the upper or lower tails of the
Excess # of observations
• non-missing due to treatment = 5.2% of non-missing treated observations

  ⇐

( 0.143 - 0.096 ) / (1 - 0.096)

  Trim 5.2% of the upper or lower tail

• of profit distribution in treated observations
• Program effect: 404 to 754 LKR

  Bounds obtained:

• Return to capital: 2.6% to 6.7%
• Lower profits in baseline increase
• attrition probability
• Program effect: 404 to 754 LKR

  Bounds obtained:

• Return to capital: 2.6% to

  6.7 %

• Lower profits in baseline increase
• attrition probability

  ⇒ Relevant is the upper bound.

1.7 Heterogeneous return to

  capital

  Use a simple model of agricultural

• households (ie. hh that consumes and produces at the same time) to understand

  What individual-level observables

• correlate with bigger return to capital How different theories (credit /
• insurance) predict heterogeneity differently

  We can test which theory is relevant ⇒ HH w/ asset A , n working-age members, and ability θ solves: _{� ��}

  � εf (K , θ) − rK max E u

  K ,B,A ,I +r (A − A ) + (nw − I ) _{K K} K K

  s.t. K ≤ A + I + B

  K K

  B ≤ ¯ B (credit constraint) A K ≤ A

  I K ≤ nw With perfect credit & insurance

• markets, we have

  �

  f (K , θ) = r

  ∗

  Denote this level of capital by K

• If credit market is imperfect so that
• ∗ > ¯ + A + nw...

  K B Marginal return to capital: higher if lower A, lower n, higher θ

  � _� f (K, θ ) _H f (K, θ ) _L r If insurance market is imperfect...

• E(marginal utility of capital)
• < E(marginal return to capital)
_�� Difference is bigg
• more risk averse (u (c))
>higher variance in output (Var (ε))
So we estimate with FE: _�

  s s

• Π it =β i D it γ D it · X

  i _�

s

s s
• δ δ · X + λ + ε

  t i it t i s

  

D Amount of capital grant in 100 LKR

it

  at time t

  s X i’s s-th characteristics s

  If credit constraint matters, γ < 0

• for household asset and household

  s

  size; γ > 0 for proxies of talent If insurance constraint matters,

• s

  γ > 0 for risk aversion and self-reported uncertainty in profits

  You must have these theoretical predictions before designing the questionnaire

  �

  s s

  Π + it =β i D it γ D it · X

  i _� s s s

• δ δ · X + λ + ε

  t i it t i s

  In a panel regression, if you

• estimate heterogeneous treatment effects by covariate x, never fail to allow time FEs to differ across x

  Results in Table V: consistent w/

• credit market imperfection, inconsistent w/ insurance market imperfection In addition, female owners have
• significantly lower return to capital

  1-8 Taking stock

• At very low capital stock, return to capital is high

  ⇒ Production function is not

  non-convex

• But firms in the sample are those already in operation
• Entry may require a large fixed cost
• Then why don’t they reinvest profits to grow?

• Lack of saving institutions &

2. Hsieh and Klenow (2009)

  Long-standing question in macro

• development: what explains huge differences in TFP across countries Only recently economists start
>looking at inefficient allocations of capital & labor as the source of low TFP in poor countries This paper establishes this as

2.1 Research questions

  Are capital and labor misallocated

• across manufacturing firms in China and India? What industry characteristics
• associate with more misallocation? How much would TFP go up if no
• misallocation?

2.2 Factor misallocation

  With no distortion in the output

• price or access to credit, in a given industry s, revenue productivity

  P Y

  si si

  TFPR si ≡ P si A si =

  1 α −α _{s s}

  K L

  si si

  must be equal for every firm i Why? If not, capital and labor will be

• reallocated to firms with higher TFPR si

  ⇒ Output of such firms ↑

⇒ Output price (P si ) for such firms ↓

Each firm produces differentiated
• product and thus has monopoly power over price

  ⇒ Eventually TFPR ≡ P A si si si

  P si Y si ≡ P =

  TFPR si si A si

  1 α −α _{s s}

  K L

  si si

• si

  So let’s measure the actual TFPR

  in US, China, and India to see if they are equal within each industry For each si, we observe P A

• si si (revenue), K , and L .

  

si si

• s ,

  For industry s’s capital share α

  Figure II plots the distribution of

• ln (TFPR /TFPR ) in US, China,

  si s

  and India

  Normalized by industry average

• TFPR: dispersed a lot more in India
• and China than US

  ⇒ Evidence for distortions in factor

  allocation across firms in India and China

2.3 What industry characteristics

  correlates w/ more variation in TFPR?

  Run a regression of industry-level

• variance of ln (TFPR si ) on industry-level covariates Those robustly correlated positively
• are:

  China: share of state-owned firms

• India: size restriction
• Small firms believed to be

  ⇐

  China (Table XII) India (Table XIII)

  2.4 Monopolistic competition model

  How much productivity would go up

• if no distortion in India and China? To answer this question, Hsieh &
• Klenow set up a monopolistic competition model to derive expressions for industry TFP
Digression: Monopolistic competition (according to Matsuyama 1995)
• Each firm in an industry produces

  3 features

• differentiated product and thus has monopoly power to set their output price With so many firms in each industry,
• each firm takes other firms’ behavior as given

  ie. No strategic interactions as in oligopoly models

  Free entry to each industry & # of • variety endogenously determined Krugman (1980) applies this model

  to intl trade, to explain intra-industry trade Melitz (2003) also applies this

• model.

  

Now the workhorse model of

• international trade Verhoogen (2008) & Bustos (2010) • use this model to analyze plant-level data in Mexico / Argentine (& exploit

  natural experiments: currency

2.4.1 Model

  A representative final good

  producer combines the outputs of S manufacturing industries by technology _�

  θ _s

  Y = Y

  s _� s

  where θ s = 1 and

  s _{� � σ σ −1 � −1 σ} Each firm i in industry s produces

  differentiated products by

  1 α −α _{s s}

  Y = A K L

  si si si si

  Their profits:

• (1 − τ )P Y − wL − (1 + τ )RK

  Y si si si K si _{si si} τ output distortions _{Y si} size restrictions, transportation costs,

• output subsidies

  τ capital price distortions _{K si}

2.4.2 Analysis

• si

  Profit minimization w.r.t. Y by final

  good producer implies: _{σ −1 σ} θ YY

  s s

  P =

  si _{σ 1} Y si

  This is the demand curve faced by

• each monopolistic firm i in industry

  Firm i’s profit maximization problem

• thus becomes: _{σ −1 σ σ −1 σ} max �(1 − τ Y )θ s YY Y

  s _si si K _{si si} ,L _�

  − wL − (1 + τ )RK

  si K si _si

  si

  si

  Y

  si

  ) P

  K _si

  ) (1 − τ

  Y _si

  σ (1 − τ

  R (σ − 1)

  = α s

  K

  si

  Y

  si

  )P

  Y _si

  (1 − τ

  (σ − 1) σ

  = (1 − α s ) w

  si

  L

  FOCs for profit maximization of firm i give us the optimal level of inputs

• The demand curve equation P _si

  Y ^{1 σ} _si = θ _s YY ^{σ σ−1} _s is used to obtain

2.5 Gains from reallocation

• Industry TFP is expressed as:

  TFP

  α _s si

  1 −α _s

  L si ^�

  α _{s � �} i

  K si ^�

  i

  ) ^{� σ σ −1} _{� �}

  1 −α _s si

  L

  K

  s

  (A

  

i

  = ^{� �}

  

1

−α _s

s

  L

  α _s s

  K

  ≡ Y s

  si

• (by model assumptions for the
• si

  Plug in the optimal level of K and

  L si . Then, lots of tweaks in algebra

  Use the demand curve equation for

• P . _{si α} ^s Treating A (1 − τ )/(1 + τ ) as _{si Y K si si}
• one term will help

  obtains _{� � σ � � σ−1 � 1} TFPR −1

  s

  TFP = A

  s si

  TFPR si

  i Now we need σ and A

  si Use σ = 3

• Estimates in the literature ranges 3 to

  10

• As gains

  ↑ more w/ higher σ, take lower bound _{si σ−1 σ} A is obtained by

• (P ) _{si si}

  Y κ _{s α s s 1 −α} K L _{si si}

• Only P Y observed, not Y _{si si si}

  By using the demand curve equation,

• recover Y _si
On the other hand, if no distortion,

  we have TFPR s = TFPR si . Which means _{� � � 1}

  efficient σ−1 σ ₋₁

  TFP = A

  s si i

  Aggregating by Cobb-Douglas with

• θ s as each industry share, we can compare aggregate TFP gains by
Equalizing TFPR w/i industries raises TFP by (Table IV):
• China: 86.6 - 115.1%
• India: 100.4 - 127.5 %
• US: 30.7 - 42.9%

3. Other topics on firms in LDCs

• Contract enforcement

• McMillan & Woodruff (1999)

• Banerjee & Duflo (2000)
• Macchiavello & Morjaria (2010)
• Impact of export
• Verhoogen (2008a)
• Bustos (2011)

  

cf. See Eric Verhoogen’s lecture notes

  (2008b, 2008c) for these topics and

  Ashraf, Nava, James Berry, and Jesse M Shapiro. 2010.

“Can Higher Prices Stimulate Product Use? Evidence from

a Field Experiment in Zambia.” American Economic Review 100(5): 2383-2413.

  Bandiera, Oriana, Iwan Barankay, and Imran Rasul. 2011. “Field Experiments with Firms.” Journal of Economic

  

we ask how the sausage is made?” Journal of Development

Economics 88(1): 19-31. de Mel, Suresh, David McKenzie, and Christopher Woodruff. 2010. “Returns to Capital in Microenterprises: Evidence from a Field Experiment.” Quarterly Journal of Economics 123(4): 1329-1372.

  McMillan, John, and Christopher Woodruff. 1999.

“Interfirm Relationships and Informal Credit in Vietnam.”

Quarterly Journal of Economics 114: 1285-1320.

  Melitz, Marc J. 2003. “The Impact of Trade on Intra- Industry Reallocations and Aggregate Industry