Dynamic Inputs and Resource (Mis)Allocation

John Asker, Allan Collard Wexler and Jan De Loecker NYU, Princeton & NBER

September 23, 2013

CMU

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Research Question:

‘To what extent do dynamic production inputs (e.g. capital) and adjustment shocks shape dispersion of static MRPK (“capital misallocation”) at the industry/country level?’

•  Approach: Build a model, and evaluate the reduced form and structurally estimated predictions on a bunch of different data sets

- ‘Macro-style’ IO

•  Why is this interesting? 1.  Get a sense of what can drive cross-industry and country MRPK

(and productivity) differences 2.  Particularly second moments (Macro/Development literatures)

- e.g. Restuccia & Rogerson (2008), Hsieh & Klenow (2009), Midrigan and Xu (2013)

3.  Persistent challenge in IO: Relate cross sectional patterns to time series behavior

4.  Alternate framework for judging policy responses

Research question

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Think of an industry in which: •  firms face some adjustment cost when changing capital stock, and; •  face an AR(1) process on firms specific productivity.

Punchline:

Model

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Think of an industry in which: •  firms face some adjustment cost when changing capital stock, and; •  face an AR(1) process on firms specific productivity.

Punchline:

Industry Data

(US Census)

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

39% drop

•  Think of an industry in which: •  firms face some adjustment cost when changing capital stock, and; •  face an AR(1) process on firms specific productivity.

Punchline:

Industry Data

(US Census)

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Think of an industry in which: •  firms face some adjustment cost when changing capital stock, and; •  face an AR(1) process on firms specific productivity.

Punchline:

Country Data

(WBES)

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Indonesia

Morocco

47% drop

•  Think of an industry in which: •  firms face some adjustment cost when changing capital stock, and; •  face an AR(1) process on firms specific productivity.

Punchline:

Country Data

(WBES)

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Firm with: •  Cobb-Douglas technology

•  Constant elasticity demand (e = - 4)

•  Sales Generating Function:

(Beta’s sum to 0.75)

•  Which gives the MRPK in a static world as:

Model:

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Firm with: •  Adjustment costs introduce dynamics in capital choice

•  financial cost •  one period time to build

•  very standard AR(1) on log TFP introduces transitions in states

+ a one period time to build

Model:

Dynamics

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Analysis done via computation. •  Parameter values either standard, or from ranges seen in data sets •  Theorem establishes that everything is robust to a firm specific constant in the productivity process

Model:

Comparative Statics

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Lots of data sets •  Each have their issues, which is why we use lots of them •  For presentation, I’ll focus on US and WBES

Data:

Data and Measurement

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Measurement of productivity:

•  Recall that

•  Where beta’s sum to 0.75

•  (log) TFPR is

•  to get coeffs use

•  and use the adding up constraint to get capital coeff

Data:

Data and Measurement

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Measurement of productivity:

•  Recall that

•  Where beta’s sum to 0.75

•  (log) TFPR is

•  to get coeffs use

•  and use the adding up constraint to get capital coeff

•  (and if you hate this, for Slovenia we use OLS estimates from Jan’s earlier work)

Data:

Data and Measurement

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Basic reduced form is that MPRK dispersion should be positively correlated with productivity volatility

•  Hence:

Std(MRPK)

=

Constant +

Std( Δtfpr ) +

Year Dummies

Industry Level Analysis:

Reduced Form

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Industry Level Analysis:

Reduced Form

(same table, just bigger)

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Industry Level Analysis:

Reduced Form

US only

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Industry Level Analysis:

Reduced Form

Robustness

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Industry Level Analysis:

Reduced Form

Robustness

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Industry Level Analysis:

Reduced Form

Robustness

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Why capital?

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Industry Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Objective: to see how much of the differences in dispersion the model is capable of capturing

•  What we need: •  AR(1) on productivity process •  Adjustment Costs •  Sales generating function coeffs •  discount rates, and depreciation rates which we lift from existing literature

•  To get the AR(1) we estimate is from the productivity data, for each industry •  Volatility is the sigma parameter

Industry Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Objective: to see how much of the differences in dispersion the model is capable of capturing

•  What we need: •  AR(1) on productivity process •  Adjustment Costs •  Sales generating function coeffs •  discount rates, and depreciation rates which we lift from existing literature

•  To get the adjustment costs we fit the model to the following moments (using GMM approach)

•  proportion of firms with less than 5% y-o-y change in capital •  proportion of firms with more than 20% y-o-y change in capital •  Std(y-o-y change in log capital)

Industry Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Industry Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

US adj costs X US avg prod. coeffs X Only 1 period TTB 2x US adj costs

Industry Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

US adj costs X US avg prod. coeffs X Only 1 period TTB 2x US adj costs

Industry Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

US adj costs X X US avg prod. coeffs X Only 1 period TTB 2x US adj costs

Industry Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

US adj costs X X US avg prod. coeffs X Only 1 period TTB 2x US adj costs X

Industry Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

US adj costs X X US avg prod. coeffs X Only 1 period TTB X 2x US adj costs X

Country Level Analysis:

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Objective: to see how much of the differences in dispersion the model is capable of capturing at a cross-country level

•  Basically the same analysis, but need a data set with a lot of countries

•  Use the World Bank Enterprise Survey. •  Good coverage of countries (33 we can use, all LDCs) •  Small sample sizes in some countries

•  we throw out anything with less than 25 obs, largest has just over 700 obs (Brazil)

•  Time series created by asking managers “what was it like last year?”

•  First, assess data quality (and model) by making sure it can replicate the reduced form analysis

•  Then, do structural analysis

•  Then look to see if AR(1) is related to anything observable

Country Level Analysis:

Reduced form

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Country Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Estimating the adjustment costs on all countries would be computationally expensive, and previous evidence from industry analysis suggests little or no return

•  Hence we use the US adjustment costs.

Country Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Estimating the adjustment costs on all countries would be computationally expensive, and previous evidence from industry analysis suggests little or no return

•  Hence we use the US adjustment costs.

•  S^2 = .80 for WBES, S^2 = 0.9 for Tier 1

Country Level Analysis:

Structural

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Country Level Analysis:

What might generate productivity shocks?

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

Conclusion

1.  Introduction 2.  Model 3.  Reduced Form 4. Structural 5. Cross-Country 6. Conclusion

Dynamic Inputs

•  Dynamic nature of inputs capable of rationalizing the dispersion in MRPK

•  How to interpret the dispersion differences?

•  Welfare irrelevant? •  if shock process is exogenous then firms acting much as the social planner would like them to

•  Forget about distortions in capital allocations? •  still room for static frictions to mess things up •  IO guy is never going to claim that static frictions are not worthy of a policy intervention •  less clear whether active reallocation is the answer

•  Think carefully about policies that affect the shock process? •  likely some room here for further thinking •  evidence that firms respond to the predictability of their environment •  to the extent that government can influence this, then it seems worth thinking about •  note that the development literature (and others) have made progress here in micro studies