Driscoll, D. (2020). Do Carbon Prices Limit Economic Growth? Socius.

https://doi.org/10.1177/2378023119898326

/u/LonzosJumpshot originally posted the article here.

RI

The purpose of this paper is to answer the question

...have existing carbon prices limited economic growth?

My RI will primarily be about some of the basic econometric problems this paper has. Regarding the actual effect of carbon prices on growth, it's clear that the long run effect of a carbon tax is positive compared to the counterfactual - a climate disaster. The medium run effect is less clear. The very short run effect would likely be negative due to the capital and labor adjustments needed to switch to producing less carbon-intensive goods. Oh and trade-offs don't exist at the ZLB.

The author approaches his question by looking at GDP per capita for 20 democracies; of these countries, 11 have implemented carbon prices. The sample includes data from before and after carbon price implementation, which the author uses to '''''identify''''' the effect of carbon taxes. This boils down to two pieces of evidence.

Figure 1

The author claims this is evidence that carbon prices have no effect on GDP growth. This is essentially not even wrong, because you cannot just look at panel data, figure out differences in time trends, and average them across countries with your special eyes.

Furthermore, the author is discussing growth rates but his graphs are linear. This is just regular wrong. If GDP goes up linearly, then the growth rate is declining. This additionally makes his 'visual analysis' even dumber, because even simple facts, like changes in the growth rate of gdp/capita, are not clear from just looking at the graphs. In short, the author should log difference gdp/capita in these figures.

"Formal Fixed-Effects Regression Analysis"

Thankfully, he remembered to log the variables this time. But, the author fails to answer the question he's looking to answer: how does the implementation of carbon taxes affect growth?

The author's regression is

reg log(gdpc) time carbon_price_indicator 

where the indicator is "(coded as 0 for years without the policy and 1 for years with the policy..." and gdpc is gdp per capita.

The parameter of interest is the change in growth rate after carbon tax implementation. Note that growth rate is just the average of the log difference in gdpc. Hence, a simple approach is to use OLS with a time trend which the author does. But, the author's mistake is using an indicator variable for the years where a carbon price was implmented.

We can see his mistake clearly by taking his specification and differencing. Suppose t 1 is before implementation. Then, we have

log(gdpc)_{t 1} - log(gdpc)_t = beta    e_{t 1} - e{t}

where beta is the coefficient on the time trend and e is the error term. Suppose s is some period after the carbon tax is implemented. Notice that the log difference is now

log(gdpc)_{s 1} - log(gdpc)_s = beta    e_{s 1} - e{s}

This is the exact same thing. His specification does not capture any changes in the growth rate after the implementation of a carbon tax. A 'correct' specification would be

log(gdpc) = t   carbon_tax_implemented*t   e_t

This actually lets us at least see the average growth rate after carbon tax implementation. We can first difference it and its easy to see that the coefficient on the indicator interaction term will be the change in the growth rate of gdpc after a carbon tax. Just in case you don't believe me, I show how the author's specification is wrong with simulated data in a jupyter notebook linked later on.

What the author had actually estimated with his indicator was average log gdpc after carbon tax implementation. This is basically irrelevant, since the question is about gdp growth. Furthermore, it's also nonsense because the panel is unbalanced and treatment timing varies by country. Specifically, the number of years after implementation differs by country. Countries that implemented a carbon tax at later dates would have higher values for the coefficient on the author's indicator variable due to gdpc growing over time. Hence, it doesn't make sense to use terms that capture average gdp here.

This leads to the next problem - the use of fixed effects before first differencing. The point of using fixed effects here would be to control for differing growth rates across countries. When the author applies fixed effects, he controls for differences in average log gdp. Again, this is irrelevant to the question. Instead, he should have done

reg (log(gdpc)_{i,t 1} - log(gdpc)_{i,t}) carbon_tax_indicator_{i,t}   fixed_effects

To exemplify, suppose in some data Country A is growing at 5% and Country B is growing at 6%. Country A implements a carbon tax and its average growth drops to 3%, while Country B maintains the same growth rate. If we do

reg growth_rate carbon_tax

we don't get the correct result. For instance, if we assume two observations for each country and actually run this regression, we get B_intercept = 4.3, B_carbon_tax = -1.3. Instead, if we do

reg growth_rate carbon_tax fixed_effects

we do get the correct estimate of the effect: 3%. Hence, fixed effects are important in this regression. But, the authors use of them (before differencing) is incorrect.

All of this seems like rookie mistakes that not even an undergrad might make. So, have I done something wrong in interpreting his approach? No.

Replicating the Author's Results

Here is the code for a notebook where I replicate the authors results. In the first section, I show why the regression itself is stupid. In the second section, I do the actual replication.

I follow his methodology exactly as I interpreted it above and get this. To compare,

The R² differs because I used dummies rather than demeaning by group. Otherwise, the results are pretty much identical. So, yes, the author is big dumb.

Just for fun: I ran the regression after first differencing with dummies for the countries. I estimate the effect of carbon taxes on growth to be -0.32% (0.2) which corresponds to a t-stat of -1.285 and a two-sided p-value of 0.199.

This is a stupid estimate for a bunch of other reasons. Here's why:

• The timing of carbon tax implementation likely is related to gdpc. I assume politicians would want to implement carbon taxes when expected future growth is high rather than when it is low, because voters are bad at considering counterfactuals. In other words, treatment is probably endogenous to expected gdpc.

• GDP across countries is probably linked in some causal sense. A carbon tax in one area may affect GDP in another area. This messes up the idea behind diff-and-diff. We want to estimate Y_i(1) - Y_i(0) where Y_i(0) is the counterfactual or untreated countries in this case; this can't be identified if treating one country affects gdp growth in another. A specific potential cause of this problem may be the EU sharing monetary policy which has to accommodate all its members.

• The effect of carbon taxes on growth likely vary by time. With an unbalanced panel, we're missing mixing the short-term and long-term treatment effect together. If they have a negative short-term effect, the estimates could get diluted by including countries that have had carbon taxes for longer periods of time. Again, note that we are looking at average gdpc growth before and after ctaxes in an unblanced panel.