Estimating Pure Country and Industry Effects with Weighted Regressions

Summary

The document describes a cross-sectional method for decomposing stock returns into world, country, and industry components. Monthly weighted least squares regressions relate individual stock returns to country and sector indicators, using market capitalization as the weight. The regression intercept represents the global return, while the country and sector coefficients represent effects after accounting for the other dimensions.

To identify “pure” country and industry effects, the method constrains each group’s market-weighted factor effects to sum to zero in each period. These restrictions prevent the group effects from absorbing the overall market component. The document defines how the constraints should be interpreted but presents no implementation or empirical results; its motivating question asks how to impose them in R. It therefore explains the model structure rather than demonstrating a complete estimation procedure.

Key ideas

• The decomposition separates stock returns into world, country, and industry components.
• The method uses cross-sectional weighted least squares at each time period.
• Market capitalization provides the regression weights in the example.
• Country and sector effects are constrained to have zero market-weighted means.
• The intercept is interpreted as the world return, and the document does not supply an R implementation.

Tags

# How to set up Heston and Rouwenhorst regression?


# How to set up Heston and Rouwenhorst regression?












Heston and Rouwenhorst (1994) devised an empirical estimation strategy to decompose stock returns into three components: a pure industry effect, a pure country effect, and a world-factor return. Essentially, they perform monthly cross-sectional weighted least squares regressions on individual stock returns to determine "pure" country and sector effects. To estimate "pure" effects, they add constraints to the regression so that the country and sector factors have a weighted mean of zero for each period. Note the intercept in this equation would be interpreted as the global world return.

The sector constraint would be interpreted as the product of each sector's market weight and its sector factor coefficient summed over each sector. Same for country.

As an example, I've built country and sector factors and set up the following regression for one time period but don't know how to add the constraints...

```
lm(Return ~ Country + Sector, data = data, weights = MktCapUsd)
```

Are there packages available to easily add in these types of constraints?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.