Positive effect in cross-sectional analysis, negative effect in panel analysis

[Wolfgang Schoenramer]

Dear all,

I am trying to analyze the effect of communication technology on offshoring for manufacturing firms, first in a cross-sectional analysis for the years 2006, 2010 and 2014 and then in a time-series analysis over the same time period. In the cross-sectional part, I find a positive effect of communication technology on offshoring in every single year. However, this relationship vanishes once I use panel data and fixed effects estimation to get rid of unobservable, time-constant firm heterogeneity.

Here's what I type in stata and the results that I get:

1. Cross-sectional: 2006, 2010 and 2014

For example baseline regression 2014 in (1): areg offshoring14 tech14 sales14 wage14 border14 sea14 nport14 , a(industry14) cluster(industry14)

2. Time-series analysis

Baseline regression in (1): xtreg offshoring tech sales _Iyear*, fe vce(cluster industry)

Transition matrix for offshoring and communication technology:

xttrans offshoring
xttrans tech

How can I possibly explain that the positive relationship between communication technology (first row in all tables) and offshoring in the single years 2006, 2010 and 2014 turns mostly negative in the panel analysis? Is it possible that there is just not enough variation over time in the two variables offshoring and technology?

I'm very thankful for any answer!

Best,
Wolfgang

[Clyde Schechter]

The two models are very different. Each contains variables that are not present in the other. Why do you expect the results to even resemble each other vaguely?

[Wolfgang Schoenramer]

The control variables in the first model are all regional variables: regional wage by industry, international border in a region, access to sea in a region and number of ports in a region. I excluded those variables from the panel analysis because they are subsumed in the fixed effects (xtreg, fe). I was expecting at least the same sign of the tech coefficient.

[Clyde Schechter]

Whenever you change the variables in the model, you are redefining the effects that the other variables are estimating. They can change in any way imaginable. This is sometimes referred to as Simpson's paradox, when continuous variables are involved it is sometimes called Lord's paradox. Wikipedia has a good page on Simpson's paradox.

There is something else going on here as well that you should look into. Your N's are very different. So apparently when you add the region variables, there are observations with missing values on these variables that then drop out of the estimation sample. So it is also possible that some or all of what you are seeing is due to estimating on a biased subsample. Try re-running these, doing the model with the extra variables first, and then run the model excluding those variables with -if e(sample)- restriction. You may (or may not) find that the results of those analyses are more similar to each other. If the difference between the results of the two models persists then this is a Simpson's paradox issue, and your task is to figure out which model is the one that actually answers your research questions. If the difference goes away, then you have to decide what you want to do about all that missing data.

[Phil Bromiley]

To add my personal preference to Clyde's answer, it is questionable to run all your interactions separately. You show in one set of results that the other results suffer from omitted variables bias (assuming your iv's are not orthogonal). It is also standard practice to include the main effects in any analysis including interactions.

While Simpson's paradox holds, you might get more similar parameters from what you call the time series analysis if you allow the years to interact with all the variables in an ols. When you run year-by-year you're letting all the parameters vary each year. Your xtreg will still differ from reg since xtreg controls for things (the fixed effects) that are not controlled for in the reg.

You'll increase your chances of a helpful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

[Wolfgang Schoenramer]

Thanks to both of you for your answers!
Clyde Schechter I just performed the cross-sectional analysis for each year 2006, 2010 and 2014 only for the subset of firms that are included in the panel data set. The relationship between tech and offshoring is still positive and significant. So it seems to be a Simpson's paradox issue here. And just for my personal understanding: The low variation over years in offshoring status and technology status has nothing to do with the results from the panel analysis? For example, more than 80% of firms that did not offshore in one period did not offshore either in the next period. My first thought was that this variation is just not sufficient for a proper panel analysis over time.

Phil Bromiley I'm not sure if I understand you correctly. What columns are you referring to and what would you suggest to change? So you would include all interactions in one regression together with the main effects, i.e.

Tech CAD LAN Robots TechxCAD TechxLAN TechxRobots

instead of each interaction separately?

[Clyde Schechter]

Well, when you have reduced variation in a variable, you have reduced ability to detect associations with that variable. But the extent of variation you describe seems sufficient, in sample sizes like the ones you have, to support a meaningful longitudinal analysis.

[Wolfgang Schoenramer]

Alright then I don't have to worry much about that. Interestingly a pooled OLS regression on the panel data set, i.e.

areg off tech sales border sea nport _Iyear* , a(ind) cluster(ind)

also shows a positive and significant relationship between technology and offshoring. So for the same data set, xtreg, fe produces negative coefficients while areg gives very significant positive estimates for communication technology. So it seems like there is some time-constant, unobserved firm heterogeneity at work and communication technology is actually not a significant determinant in offshoring decisions.