Class Presentation

Tuesday, November 12th, 2019

- Which inputs matter?
- Protein vs. no-protein
- Time vs. in-kind
- When do they matter? (Todd and Wolpin 2003)
- $\beta_1^1$: Effects of period one input on period one
- $\beta_1^2$: Does period 1 input have effects in period two?
- $\beta_2^2$: Is the impact of period 2 input on period two the same as $\beta_1^1$
- $y_{t}$ and $y_{t-1}$: can lagged output $y_{t-1}$ summarize the effects of past inputs in a value-added specification?

- Linear
- Inputs are substitutes
- In an optimal choice problem, would only choose one input, even in a dynamic context
- But easier to estimate (Puentes et al. 2016)
- Cobb-Douglas
- Linear in log
- Decreasing returns in single input (Wang et al. 2019a)
- Inputs are complementary if have multiple inputs
- Complementarity of inputs within and across period the same (Wang et al. 2019b)
- Constant Elasticity of Substitution
- Estimate substitutability
- Can allow substitutability to differ by period
- Dynamic complementarity (Cunha, Heckman and Shennech 2010)

- Are parents aware of the production function?
- Can parents choose inputs?
- Are there shocks observable to parents but not to econometrician?
- If no to any of the three questions above: OLS might be able to identify input effects
- OLS allows for the estimation of many inputs concurrently (Wang et al. 2019b)
- In Wang et al. (2019b), we use profiles of height to absorb error term

- With multiple inputs, potential problem with weak instruments
- IVs from prices (Puentes et al. 2016)
- IVs based on differenced moments (Mani et al. 2018)
- LATE, can you extrapolate to production function?
- Difficult to estimate parameters for non-linear and non-separable production functions with multiple inputs

- Ideally, there are different levels of input variations
- Difference in difference to get the treatment effect
- Impose functional form assumptions, extrapolate from differential effects between treatment quantities to production function parameters (Wang et al. 2019a)
- Even single experimental input level might be OK if individuals have existing variations in inputs and the treatment is a subsidy

- Model household choices directly (Wang et al. 2019a)
- There is no endogeneity issue, households in model choose given shocks
- What is the model assumption about the relationship between the unobservable (to econometrician) shock term across periods?
- What is the model assumption about the relationship between the unobservable (to econometrician) shock term with initial conditions?
- Model provides "causal" results, identification in this case is largely a statistical concept. In OLS, statistical identical is trivial given invertibility.

- Know which inputs matter, how much it matters, and how inputs matter jointly
- As a part of a structural model
- How to optimally allocate resources, across children, across periods, and across inputs (Wang 2019)