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Econometric Tools for Analyzing Market Outcomes

Focus on Production Functions

Daniel Ackerberg, C. Lanier Benkard,Steven Berry, and Ariel Pakes. (2007)

Handbook of Econometrics

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Production Function• Cobb Douglas production technology

• Taking Log:

• can be interpreted as the mean efficiency level across firms

• is the deviation from that mean for firm j

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OLS?• We have known since Marshak and Andrews

(1944) that direct OLS estimation of production function is problematic

• Simultaneity and selection issues

• Two traditional solutions to these endogeneity problems are instrumental variables and fixed effects

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Instrumental Variables?

• We divide the unobservable into two• Components, and

• Input prices as instrument?

• If input markets are perfectly competitive, then input prices should be uncorrelated with since the firm has no impact on market prices.

• This is the primary assumption necessary to validate input price as instruments.

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Fixed Effects?

• Unobserved productivity is constant over time, strong assumption

• When there is measurement error in inputs, fixed effects can actually generate worse estimates than standard level (OLS) estimators

• Some empirical studies show unreasonably low estimates of capital coefficients

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The Olley and Pakes (1996) Approach• One might also look at Wooldridge (2004), who

presents a concise, one-step, formulation of the OP approach for which standard error derivations are more straightforward.

• This one-step approach may also be more efficient than the standard OP methodology.

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The model• An additional input

• The interest in the age coefficient stems from a desire to separate out cohort from selection effects in determining the impact of age of plant on productivity.

• Unobserved productivity is assumed to follow an exogenous first order Markov process

• Capital is assumed to be accumulated by firms through a deterministic dynamic investment process

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Controlling for Endogeneity of Input Choice• Labor is assumed to be a variable and non-

dynamic input • Assume there are no selection problems due to

exit• Assume that investment levels are always

positive

• Scalar unobservable assumption :the scalar unobservable and monotonicity assumptions essentially allow us to ”observe” the unobserved - this eliminates the input endogeneity problem in estimating the labor coefficient.

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Controlling for Endogenous Selection

• Intuitively, the fact that in the first stage we are able to completely proxy means that we can control for both endogenous input choice and endogenous exit.

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Problems with OP

• Zero Investment Levels. While the OP procedure can accommodate zero

investment levels, this accommodation is not without costs. In particular, there is likely to be an efficiency loss from discarding the subset of data where > 0.

• No Exit.Difference between the balanced sample estimators

and OP estimators on the full sample are truly dramatic

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Levinsohn and Petrin (2003)

• Levinsohn and Petrin (2003) suggest an alternative estimation routine whose primary motivation is to eliminate this efficiency loss.

• In particular LP focus on firms’ choices of intermediate inputs (e.g. electricity, fuels, and/or materials) - these are rarely zero.

• Additional input , assume its non-dynamic input

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LP vs OP• In their application LP find biases that are

generally consistent with those predicted by OP, but some differences in actual magnitudes of coefficients.

• Many datasets, particularly those from developing countries, the set of observations with zero investment can be quite large

• Since is a variable input, it is clearly not orthogonal to the innovation component of . LP address this by using as an instrument for in estimation

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Test of Olley and Pakes’ Assumptions ?• Conditional on capital and age, there is a one to

one mapping between investment and productivity

• There is the direct assumption that the choice of labor has no dynamic implications; i.e. that labor is not a state variable in the dynamic problem

• But assume instead that there are significant hiring or firing costs for labor, or that labor contracts are long term (as in, for example, unionizedindustries), then the labor has dynamic

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Ackerberg, Caves, and Fraser (2004)

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Comparing the models with our data set

OLS FE OP LPAge 0.007*** 0.264*** -0.604* --Capital 0.028*** 0.021*** 0.002 0.008***Materials 0.016*** 0.009*** 0.0015**Unskilled Labour

0.558*** 0.458*** 0.419*** 0.374***

Skilled Labour

0.435*** 0.136*** 0.361*** 0.235***

In our case the estimated TFP values for OP and LP are highly correlated (0.9992)

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TFP• Will try to estimate TFP with GMM soon...!!

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Overview

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Concluding Remark• The appropriateness of different models of how

these decisions are made will undoubtedly depend on the environment being studied.

• There are undoubtedly institutional settings where alternative frameworks might be better to use.

• It is not the precise framework that is important, but rather the fact that productivity studies must take explicit account of the fact that changes in productivity (or, if one prefers, sales for a given amount of inputs) in large part determine how firms respond to the changes being studied, and these must be taken into account in the estimation procedure.