Panel Fixed effect estimation

[Lubaba Prottoy]

Hello.

I am working on the effect of health shock on household consumption. I have 3 periods of panel data; 2012, 2015, 2018. The health shock data available in each year is the information based on a recall period, that is whether households faced shock since the last survey.

Because I want to observe consumption smoothing behavior, my dependent variable is change in consumption. So that I will be working with 2 periods of data 2015 and 2018 where consumption is differenced over time. This is based on previous literatures and is said to tackle unobserved effects. I want to do panel fixed effect estimation here.

Now my question is,

1.does the differencing of the dependent variable tamper with the fixed effect estimation in anyway? I ask this as even if I regress consumption levels of the 3 periods on health shocks, the fixed effect is said to omit the unobserved time invariant effects. Then what significance does the differencing carry?

2. Should I take log of food consumption before differencing or after? Or I should not take a logged value?

I have looked at a lot of literature but failed to find any satisfactory answer. I hope someone can help. Thanks!

[George Ford]

(1) You can estimate a FE model with first-differenced data, but why? Typically, we think of FE and FD as alternatives, since FE is akin to first differencing.
(2) Some values of the FD will be negative (or could be, theoretically), so log of that is not sensible.
(3) You can take the difference of the logs, and your coefficients will be elasticities. That's a fairly typical approach.

[Lubaba Prottoy]

I am just taking the difference of the consumption data(the dependent variable), so that would be (2015-2012) and (2018-2015), the data for other variables are for 2015 and 2018. So it's not typically first differencing everything, am I correct?

This is the common approach in literature and they argue it omits household unobserved effects. That's where is confuses me because just using fixed effects in the regression of consumption levels on health shocks would also omit unobserved time invariant effects.

Also from what I gather, past consumption can affect present consumption, so taking a lagged value as a control isn't essentially same as taking the difference?

[Carlo Lazzaro]

Lubaba:
1) I'm not clear if you're talking about wealth or health stock (if the latter ever has a techical meaning)
2) be as it may, you may have an endogeneity issue in the form of reverse causation (household consumption can influence the household's wealth stock and, if addtressed to junk-food, alcohol excess and the like, can affect household's healt stock, too).

[Lubaba Prottoy]

No, I am talking about health shocks. This is defined as morbidity or mortality, the variable I am considering is income loss or large medical expenditure due to illness/injury and the death of main earner. These are in effect kind of income shocks and idiosyncratic in nature. I am trying to see whether households can smooth consumption when faced with such shocks. Based on theory they should because such changes are transitory changes in income and should be smoothed out by the means of savings and borrowing.

I am aware of the reverse causation issue. Does fixed effect estimation correct it. Also can you help me regarding my original question?

I am trying to write equations here but can't find the option.

Thanks!

[Andrew Musau]

does the differencing of the dependent variable tamper with the fixed effect estimation in anyway?

Why would it? Your model concerns consumption growth, not consumption. How you create the outcome is irrelevant to the estimation. Other way to ask, do you want to say that there are no time-invariant factors that affect consumption growth just because it represents differences in consumption?

[Lubaba Prottoy]

do you want to say that there are no time-invariant factors that affect consumption growth just because it represents differences in consumption?

Thanks for clearing that out about the model.

Yes I believe the confusion arose from the argument provided for taking consumption growth : "the empirical specification uses the change in consumption rather than the level of consumption as the dependent variable because in this way potential omitted variable biases caused by the unobserved household characteristics can be avoided."

This confused me as to the logic of using fixed effect, which is to omit the time invariant unobserved household characteristics. If consumption growth does that then what will fixed effect do?

Your second question does make me thing about there being time invariant characteristics affecting consumption growth, therefore, giving rationale for using fixed effect estimation for the regression of consumption growth on health shock.

For reference I am attaching the paper here.

[Andrew Musau]

As George mentioned in #2, either FE or FD can be used to wipe out the time-invariant household effect. But you have to difference both the outcome and RHS variables. On the other hand, whether you want to study consumption or consumption growth is a completely different matter. The authors seem to be confounding these two issues, but I have not read their paper and do not intend to do so to give them a fair evaluation. Just equip yourself with the basics and move on, do not hang on every word that you see written in papers. There are quite a few errors present even in published material.

[George Ford]

I’d use FE, with the health shock as a treatment. DID.

[Lubaba Prottoy]

I’d use FE, with the health shock as a treatment. DID.

Thank you for your input George.

Can you please give your opinion regarding using consumption level for each year or consumption changes? I want to make inferences regarding consumption smoothing.The FE model using consumption levels would be

Consumption_it= a_i+ b₀healthshock_it+ b₀X_it+ time fixed effect+ village fixed effect+ village and time interaction+error

Xit is time variant household characteristics.ai is unobserved time invariant household characteristics. The concern here would be the endogeneity of health shock and a possible reverse causality.

I remember having the discussion with you regarding DID in another post. I am considering that as well. Can the below equation be deemed as a DID model? I saw some literatures using this sort of specification for some sort of program evaluation where there is treated in every year.

Consumption_it= a₀+ b₀healthshock+ b₁2015+ b₂2018+ b₃healthshock*2015+ b₄healthshock*2018+ b₅X_it+ u_it

[Jeff Wooldridge]

Andrew's point can't be emphasized enough. Before even thinking about estimation, write down the model, including heterogeneity -- what some call a random effect or fixed effect. Should the equation be in levels? Then that's the starting point. Is it in growth rates? If so, then start with a model in growth rates. In this case, I would expect relatively little serial correlation and I'd used fixed effects. But one could apply FD to the growth equation.

You can't know which variables to difference if you use FD without first writing down the model.

[George Ford]

I'd start here. They use a non-parametric event study.

https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.20161038