Big questions in this lecture

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Stockholm Doctoral Course Program in Economics

Development Economics II:

Lecture 4 (1st half)

Firms

Masayuki Kudamatsu IIES, Stockholm University

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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

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Methodology focus in this lecture

• RCT on firms

• Use treatment as IV for estimating production function

• Deal with attrition bias

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1. de Mel, McKenzie, & Woodruff

(2008)

• One of the 1st RCTs on

interventions to firms in LDCs

• Which is usually difficult

• few firms, lots of heterogeneity,

non-persistent outcomes ⇒low power to detect impact (McKenzie 2011) • Estimated parameters used in

subsequent research

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1.1 Research question

• What’s the return to capital for microenterprises in Sri Lanka?

• Important?

• Small firms employ half or more labor force in LDCs

• Microfinance

• Is production function convex?

• Original?

• No credible estimate in the literature

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Empirical challenge

• Observed level of capital stock: reflect (unobservable)

entrepreneurial ability

• Cross-sectional estimation misleading • Those who apply for credit:

selected sample of firms

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1.2 Experimental design

• Sample: 408 microenterprises

(invested capital: ≤100,000 LKR) in Sri Lanka

• 203 in retail sales e.g. grocery stores

• 205 in manufacturing

e.g. sewing clothes, making bamboo products, food processing

• Treatments: grant in cash or in kind

1. 10,000 LKR in cash

2. 20,000 LKR in cash

3. 10,000 LKR equipment of their choice

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• 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

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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)

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1.4 Program evaluation

Yit =

4 �

g=1

T_itg + δt + λi + εit

Yit Outcomes for firm i at time t

Tg indicator of treatment of type g

δt Survey round FE

λi Enterprise FE

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1.4 Program evaluation (cont.)

Results (Table II) • Capital stock ↑ • Profits ↑

• Owner hours worked ↑ for 10,000 LKR treatments

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1.5 Estimating return to capital

πit = βiKit + δt +λi + εit

πit Profit

Kit Capital stock in 100 LKR at time t

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1.5 Estimating return to capital

(cont.)

Results (Table IV) • Return to capital:

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Issues with 2SLS

(i) Exclusion restriction

(ii) Weak instruments

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(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

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Digression: control for outcomes

• Can we avoid this issue by

controlling for owner labor hour? • No. Owner labor hour: correlated

w./ Kit

• In general, when a treatment affects two outcomes A and B, DO NOT regress A on treatment dummy and B

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cf. Angrist & Pischke (2009: 64-66)

By controlling for B, the coefficient on the treatment dummy is

E(A1i|B1i = x)−E(A0i|B0i = x) = E(A1i −A0i|B1i = x)

+{E(A0i|B1i = x)−E(A0i|B0i = x)}

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cf. Angrist & Pischke (2009: 64-66)

By controlling for B, the coefficient on the treatment dummy is

E(A1i|B1i = x)−E(A0i|B0i = x) = E(A1i −A0i|B1i = x)

+{E(A0i|B1i = x)−E(A0i|B0i = x)}

• 2nd term: Selection bias

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(ii) Weak instruments

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(iii) LATE

• Some reasons to believe the IV estimate is ATE, not LATE

• No correlation btw. ∆Kit after

treatment & observables that would correlate with βi

cf. βˆIV: weighted average ofβi w./ weight

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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?

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1.6. Robustness to attrition

• Attrition rate differs across treatment status

• 14.3% (control) vs 9.6% (treated) • If attrition in control is higher for

higher-profit making firms, we overestimate treatment effect • Solution: Lee (2009)

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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)

• Then the bound obtained by

• Identify the excess # of observations missing due to treatment

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• 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

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• Bounds obtained:

• Program effect: 404 to 754 LKR

• Return to capital: 2.6% to 6.7% • Lower profits in baseline increase

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• Bounds obtained:

• Program effect: 404 to 754 LKR

• Return to capital: 2.6% to6.7% • Lower profits in baseline increase

attrition probability

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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

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HH w/ asset A, n working-age members, and ability θ solves:

max

B ≤ B¯ (credit constraint) AK ≤ A

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• 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

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Marginal return to capital:

higher if lower A, lower n, higher θ

f�_(K,_θ

L)

f�₍_K,_θ

H)

r

¯

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• If insurance market is imperfect... • E(marginal utility of capital)

< E(marginal return to capital) • Difference is bigger if

• more risk averse (u��(c))

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So we estimate with FE:

Πit =βiDit +

�

s

γsDit · X_is

δt +

�

s

δ_ts · X_is +λi + εit

Dit Amount of capital grant in 100 LKR

at time t

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• If credit constraint matters, γs < 0 for household asset and household size; γs > 0 for proxies of talent • If insurance constraint matters,

γs > 0 for risk aversion and

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Πit =βiDit +

• In a panel regression, if you

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• Results in Table V: consistent w/ credit market imperfection,

inconsistent w/ insurance market imperfection

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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 &

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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

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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

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2.2 Factor misallocation

• With no distortion in the output price or access to credit, in a given industry s, revenue productivity

TFPRsi ≡ PsiAsi =

PsiYsi

K_siαsL1_si−αs

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Why?

• If not, capital and labor will be reallocated to firms with higher TFPRsi

⇒ Output of such firms ↑

⇒ Output price (Psi) for such firms ↓

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

⇒ Eventually TFPRsi ≡ PsiAsi

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TFPRsi ≡ PsiAsi =

PsiYsi

K_siαsL1_si−αs

• So let’s measure the actual TFPRsi

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

(revenue), Ksi, and Lsi.

• For industry s’s capital share αs,

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• Figure II plots the distribution of ln(TFPRsi/TFPRs) in US, China,

and India

• Normalized by industry average

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

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2.3 What industry characteristics

correlates w/ more variation in

TFPR?

• Run a regression of industry-level variance of ln(TFPRsi) on

industry-level covariates

• Those robustly correlated positively are:

• China: share of state-owned firms

• India: size restriction

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China (Table XII)

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2.4 Monopolistic competition

model

• How much productivity would go up if no distortion in India and China? • To answer this question, Hsieh &

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Digression: Monopolistic competition

• 3 features (according to Matsuyama 1995)

• Each firm in an industry produces 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

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• 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

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2.4.1 Model

• A representative final good

producer combines the outputs of S manufacturing industries by

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• Each firm i in industry s produces differentiated products by

Ysi = AsiK_siαsL1_si−αs

• Their profits:

(1−τY_si)PsiYsi−wLsi −(1+τK_si)RKsi τYsi output distortions

• size restrictions, transportation costs, output subsidies

τKsi capital price distortions

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2.4.2 Analysis

• Profit minimization w.r.t. Ysi by final

good producer implies:

Psi =

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

Lsi =

• The demand curve equation PsiY

s is used to obtain

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2.5 Gains from reallocation

• Industry TFP is expressed as: TFPs ≡

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• Plug in the optimal level of Ksi and

Lsi. Then, lots of tweaks in algebra

• Use the demand curve equation for Psi.

• Treating Asi(1−τYsi)/(1+ τKsi)

α_s

as one term will help

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• Now we need σ and Asi

• Use σ = 3

• Estimates in the literature ranges 3 to 10

• By using the demand curve equation, recoverYsi

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• On the other hand, if no distortion, we have TFPRs = TFPRsi. Which

means

TFP_sefficient = � �

i

Aσ_si−1�σ−11

• Aggregating by Cobb-Douglas with

θs as each industry share, we can

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Equalizing TFPR w/i industries raises TFP by (Table IV):

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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)

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a Field Experiment in Zambia.”

American Economic

Review

100(5): 2383-2413.

Bandiera, Oriana, Iwan Barankay, and Imran Rasul. 2011.

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Journal of Economic

Perspectives

25: 63-82.

Banerjee, Abhijit V., and Esther Duﬂo. 2000. “Reputation

Effects and the Limits of Contracting: A Study of the Indian

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Quarterly Journal of Economics

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Banerjee, Abhijit V., and Esther Duﬂo. 2005. “Growth

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Steven N. Durlauf and Steven N. Durlauf. Elsevier, p.

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Ghatak. 2011. “Incentives and the de Soto Effect.”

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de Mel, Suresh, David J. McKenzie, and Christopher

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we ask how the sausage is made?”

Journal of Development

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88(1): 19-31.

de Mel, Suresh, David McKenzie, and Christopher

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Firm Policies Are Working in Africa? Challenges (and

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