Here are a couple of slides showing the relationship between CO2 and annual temperature anomalies from 1980 thru 2022 conditioned by the type of year (viz., el Nino, la Nina or neutral) as defined by NOAA.  I used an ANCOVA analysis in the "R" package "HH".  The first slide shows the summary results.  The key takeaway is that the relationship is statistically significant (F-test).  The second slide graphs temperature anomalies and CO2 levels with the type of year set as a "factor" in the ANCOVA analysis.  The key takeaway is that the slopes showing the underlying rise in temperature anomalies as CO2 levels rise are consistent.  What does change are the intercepts.  El Nino years see a jump in the intercept while la Nina years see a drop in the intercept relative to the neutral years.  In other words, the type of year (whether it's an el Nino or la Nina or neutral year) shifts the temperature anomaly up or down, but does not affect the slope.  The underlying slope of the temperature rise is a function of CO2 levels.

 Another hot July, so it's time for another post on climate change.  We've all heard how el Nino and la Nina events affect temperature data in any given year, but we rarely see those events included in any kind of time series.  Usually it's just a linear time trend or some kind of smoothed trend.  So let's take a look at how those events have influenced annual temperatures per NOAA data.  I selected annual temperature data from 1980 thru 2022 along with NOAA's assessment as to whether each corresponding year was an el Nino year, a la Nina year or a neutral year.  The model is an ARMAX(1,0) type with three exogenous variables.  The dependent variable is temperature anomaly (in Celsius).  Along with a constant (which captures a "neutral" year) I've included a dummy variable for el Nino, a dummy variable for la Nina and a linear time trend.  Without further ado, here are the results:

The "phi_1" parameter is the AR(1) component of the ARMAX model.  Basically it shows that about 40% of each year's temperature persists into the next year.  Including this parameter ensures that any autocorrelation between years is scrubbed out and thereby ensuring statistical independence.  All of the coefficients have the expected sign and all are statistically significant.  A Chi-square test cannot reject the null of a normal distribution for the residuals.  And this graph shows no evidence of remaining autocorrelation in the residuals:

This graph plots actual temperatures and predicted temperatures:

Overall the fit is pretty good, which shouldn't be a surprise given that the Adjusted R-square is 0.91 (see summary output in the first slide).  

Time to play a "what if" game.  What if 2023 turns out to be a neutral?  In that case the point estimate would be an anomaly of 0.99 degrees with a 95% confidence band between 0.86 and 1.13 degrees, as shown here:

This would make 2023 the second hottest year on record, falling just short of 2016's record of 1.03 degrees.  Now, what if 2023 turns out to be an el Nino year, which seems likely?  In that case the point estimate would be an anomaly of 1.05 degrees with a 95% confidence interval between 0.92 and 1.19:

BTW, the jigsaw pattern in these graphs is due to the effects of el Nino, la Nina and neutral years.

 Graphs showing relationship between CO2 and temperature anomalies (HADCRU5) using annual data from 1959 thru 2021.

Basic OLS output:

No evidence of positive autocorrelation.  R-sq is very high.  All coefficients are significant.

Further ACF graph shows no evidence of autocorrelation in the residuals:

What about normality of the residuals.  Cannot reject normality:

Here is a graph showing fitted versus actual:

I am not particularly recommending this model.  It has lots of problems.  My only point here is to show that the results of the regression depend on the start date.  Including a lot of very early CO2 data convolutes things because of various regime changes.  Using later data better captures what's going on in more recent times when CO2 emissions have become a much bigger problem for lots of different reasons.

 This post takes an historical look at the difference between the unemployment rate as calculated using the civilian labor force at the peak of the business cycle and the headline unemployment rate.  If the economy was in a recession (NBER dates), then I calculated the unemployment rate as:

1 - (employment / civilian labor force at the last peak)

As a general rule going back to 1948, the difference between the above calculation and the headline unemployment rate tended to be negative, although there were a couple of short-lived minor recessions where this pattern did not occur.  In the figure below the green rectangles indicate NBER recessions (USRECM) and the orange/brown line (diffurate) indicates the difference between the calculation shown above and the headline unemployment rate.  Obviously the brown line shows no difference (beyond rounding, hence the squiggles) when the economy is not in recession.  

It's obvious from this figure that something is radically different in the relationship between the unemployment rate and the civilian labor force.  Even when the economy suffered large employment shocks, as happened during the 1970s, the pattern showed a negative difference between the unemployment rate calculated using the cyclical peak civilian labor force and the headline unemployment rate.  This is the only major recession in which that pattern does not hold.  Why?

Cullen and Frey graph shows the observation (large blue dot to the left) and 1,000 bootstrapped data points (yellow) using the 1968Q4 thru 2013Q3 changes in quarterly GDP.  You can compare the actual observation and the bootstrapped observations alongside with other theoretical distributions; e.g., normal, beta, gamma, etc.

Did Reagan's "Supply Side" Tax Cuts Perform as Advertised?

Defenders of President Reagan's 1981 tax cut like to argue that his "supply side" approach resulted in an exceptional surge in economic growth.  In support of this claim defenders of the "supply side" approach point to growth rates that were higher than growth rates observed since the onset of the Great Recession.  Of course, no one disputes that GDP growth rates were higher during the Reagan years than growth rates since the Great Recession.  But does that mean Reagan style tax cuts in the immediate wake of the 2007/2008 financial collapse would have resulted in growth rates similar to those observed in the 1980s?

In attempting to answer this question we have to ask what distinguishes a "supply side" growth approach from a garden variety business cycle macro approach to managing aggregate demand (AD)?  Notice that you cannot answer this question simply by noting that Reagan's tax cuts are associated with an increase in the GDP growth rate.  Why?  Several reasons, but one among many is that tax cuts don't just operate on the supply side; they also stimulate AD, so this presents an identification problem.  What we observe with actual GDP is best thought of as the equilibrium point where AD and aggregate supply (AS) intersect.  In the econometric literature this is called "simultaneous equations bias."  This is a serious but not insurmountable problem.  It's also one that I'm not going to discuss further because I want to move things along.  For now just note that "simultaneous equations bias" is one of many problems a researcher is likely to come across if that researcher is only looking at observed GDP.

There are a lot of cartoon versions of what supply side economics is supposed to accomplish.  One of the more famous (or infamous) of these cartoon versions is the familiar one that non-technical readers would find on the op-ed pages of the Wall Street Journal.  But there was a more serious set of claims and predictions made by serious economists (i.e., economists not named Art Laffer).  There were three major claims, all of which are testable.  The first claim is that cutting the top marginal tax rate would encourage greater labor effort.  Leisure is a normal good, so people demand more leisure as incomes go up.  But with tax cuts the cost of leisure also goes up because workers are giving up a greater increment in after tax earnings with each additional hour of leisure.  This second effect is called the substitution effect.  Proponents of the Reagan supply side tax cuts argued that the substitution effect would dominate the income effect, and this would lead to an increase in labor effort.  This would predict an increase in average hours worked.  But when we look at the FRED data we find that average hours worked do not appear to have increased at all.  In fact, there has been a steady decline going back for decades.

The second claim is that Reagan's supply side structured tax cuts would encourage greater personal saving, which would then be available for private domestic investment.  Again, let's go to the FRED data showing saving as a percent of GDP:

Clearly the personal saving rate fell throughout the 1980s and 1990s.  A fall in personal saving would be associated with an increase in AD because it would signal an increase in consumption; but it would not suggest greater saving that could be applied to investment.  So it doesn't appear that this prediction panned out either.

The third prediction was that the tax cuts would pay for themselves.  If that were true, then we should have observed a shrinking of publicly held debt as a percent of GDP.  Clearly, that did not happen:

Finally, if the Reagan tax cuts actually affected the supply side of the macro economy in a way that was a unique historical event, then we should have observed an unparalleled increase in the growth rate of real potential GDP.  Looking at year-over-year seasonally adjusted annual rates (SAAR), there does not appear to be anything particularly special about the effect of Reagan's supply side tax cuts on the growth rate of real potential GDP.  Yes, real potential GDP did grow at a pretty good clip immediately after the Reagan recession, but it quickly faded and was nothing special by mid-decade.  In fact, even at its peak it was only barely above the growth rates during the Nixon, Ford and Carter years and well below the real potential GDP growth rates enjoyed during the LBJ and Clinton years.

So there doesn't appear to be anything especially unique or spectacular about economic growth during the Reagan years.  It was good, but not great.  And none of the three principal and testable claims made by supporters of the Reagan supply side approach seem to have panned out.

A far more interesting question is why the growth rate of real potential GDP started to fall after the 2001 recession and never really recovered to the historical growth rates going back at least 50 years.  Something has clearly happened to the growth rate of potential GDP.  And there is no evidence that Reagan style "supply side" tax cuts would have done anything to change the post-2001 trajectory.  The Reagan tax cuts did not accelerate the growth rate of real potential GDP during the 1980s, so why would we expect a different result in the 2010s?