As the new semester begins, a set of cautionary notes for my students. [Ec435] [PA854]

Forgetting whether nominal or real magnitudes are more important

Often we hear of records being broken. But there are records and there are records. For instance, consider this headline: Nasdaq and S&P 500 Climb to Records. The statement is correct, but it’s lacking in context to the extent that the real, or inflation adjusted, price is more relevant (given that share prices represent valuations of a claim to capital).





Figure 1: Nasdaq (blue), and CPI-deflated (red), in 2009$. Source: NASDAQ via FRED, BLS, and author’s calculations.

Now, some people evidence wariness about deflation, particularly in terms of the accuracy of the deflators. However, it is usually better to account for price level effects and note the concerns, rather than rely on people to keep their preferred deflators in their head to calculate the real magnitudes (see this post).

Adding up chain weighted quantities

While in many cases, real magnitudes are the relevant ones, working with real magnitudes is not always straightforward. For instance, in principle, if one had data on real consumption by households in Wisconsin and household in Minnesota, and one wanted to add them up to find real consumption in Wisconsin and Minnesota, one could do that by deflating each state’s consumption by the CPI and adding. That’s true because the CPI is essentially a fixed base year weighted index (in this case, a Laspeyres index, using the initial weights).

This is not true for the series in the national income and product accounts, such as the components of GDP. The real measures – consumption, investment, government, net exports — are obtained using chain weighted deflators, i.e., deflators where the weights vary over time.

Can one make a mistake this way? Certainly. Consider this recent case at Political Calculations, wherein the commentator added up the state level real GDPs and because it didn’t match the national level GDP, the commentator inferred a massive impending downward revision in GDP.





Source: Political Calculations.

Needless to say, the massive downward revision did not occur. Overall, real GDP was revised slightly upward. Figure 2 depicts what actually transpired.





Figure 2: Real GDP pre-benchmark revision (green), post-benchmark revision (red), and arithmetic sum of state level GDP (black), all in Ch.2009$ SAAR. Source: BEA 2016Q1 3rd release, 2016Q2 advance release, BEA state level quarterly GDP, revision of 27 July 2016, and author’s calculations.

More discussion in this post. Now, sometimes one wants to express ratios of real magnitudes. This post discusses one way at getting at something like that.

Forgetting what “SAAR” means

SAAR is short for Seasonally Adjusted, at Annual Rates. Most US government statistics are reported using this convention, even when the data are at a monthly or quarterly frequency. (In contrast, European quarter-on-quarter GDP figures are often reported on a non-annualized basis.) Most prominently, quarterly GDP is reported at annual rates, so when one sees 18,000 Ch.09$ in 2016Q2, that doesn’t mean the flow of GDP was 18,000 Ch.09$ in that quarter; rather that if the flow that occurred in 2016Q2 continued for a whole year, then GDP would be recorded at 18,000 Ch.09$.

Now, this does not matter if one is calculating percentage growth rates (as long as one also remembers to annualize the growth rate if one is calculating quarter-on-quarter changes). It does matter if one is calculating a “multiplier”, the increase in GDP for a given increase in government spending. That’s because the government spending increase (or stimulus) is sometimes reported in absolute (non-annualized) rates, and GDP in SAAR terms. Obviously, if one did the mathematical calculation forgetting this point, one’s multipliers would look four times as large as they should. If compounded with failing to take into account annualizing growth rates, then they would look sixteen times as large as they should. Even professional economists make this mistake – consider the case of this University of Chicago economist, who thought “…the multiplier is 20 or 50 or something like that” because he was essentially dividing a quarterly stimulus figure by an annualized figure, and forgetting that growth rates are typically reported at annualized rates.

What about the “SA” part of the SAAR? Most of the time, one wants to use seasonally adjusted series; in fact, this is almost always what is reported in the newspapers. The reason is that there is a big seasonal component to many economic variables; retail sales jump in December because of the Christmas holidays, for instance.

Occasionally, people (usually noneconomists) get into trouble when they mix and match seasonal and non-seasonal data. For instance, Wisconsin Governor Walker’s campaign got into trouble when they touted job creation numbers obtained by adding together seasonally unadjusted jobs figures (from what is called the Quarterly Census of Employment and Wages) with seasonally adjusted jobs figures (from the establishment survey) to get a cumulative change in employment. (They did this because QCEW figures lag by many months, while the establishment survey data are more timely). This is shown in Figure 3.





Figure 3: Wisconsin nonfarm private employment from Quarterly Census of Employment and Wages, not seasonally adjusted (blue), private nonfarm private employment from establishment survey, seasonally adjusted (red). Black arrows denote changes over QCEW and establishment survey figures; teal arrows over establishment survey. Source: BLS.

Notice that one can calculate the changes from December 2010 (just before Walker takes office) to March 2012 (the latest QCEW figures available as of December 12, 2012), and then add to the change from March 2012 to October 2012 (the latest establishment figure available as of December 12, 2012). That is, add 89.1 to 6.4 to get 95.5 thousand, close to the 100 thousand figure cited by Governor Walker’s campaign. You can see why Governor Walker’s campaign officials did so – the correct calculation using the change in the establishment survey from December 2010 to October 2012 was only 61.1 thousand.

Log aversion

Oftentimes, we depict economic statistics in log terms. The reason for this is that when plotted over time, a variable growing at a constant rate will look like it is accelerating if the Y-axis is expressed in level terms. However, it will look like a line with constant slope if the Y-axis is in log terms.

Figure 4: Real consumption, normalized to 1967Q1=1 (blue), and log real consumption, normalized to 1967Q1=0 (red). Source: BEA, 2016Q2 second release, and author’s calculations.

Solely examining the level series, consumption appears to be accelerating, particularly in the 2000’s. That illusory acceleration disappears in the log series.

For more on log transformations, see [1], [2], [3], [4], and [5]. And here’s Jim Hamilton’s post on logs. Here is an example of where the use of logs has driven someone to ranting and raving.

Shadowstats and other data conspiracies

It is not uncommon for commentators to allege conspiracies to manipulate government economic statistics. Take this FoxNews article:

What a coincidence. Just as momentum was building towards an interest rate hike by the Fed, along comes a dismal jobs report that takes any increase off the table. Contrary to the general perception, this is a lucky break for Democrats. … Given all that is stake, it is surprising that no one has questioned whether the jobs report might have been massaged by the Labor Department.

In modern times, these types of allegations are unfounded. The data series might not be particularly accurate, but deliberate manipulation to distort the economic picture does not occur for standard series released by the BEA, BLS, and Census.

One particularly egregious form of conspiracy-mongering is Shadowstats, a money-making enterprise that purports to provide a more accurate set of price measurement. Instead of going into detail, I will turn the case over to Jim Hamilton, who thoroughly debunks the Shadowstats approach. Anybody who cites Shadowstats should immediately lose all credibility. So … don’t do it!

More data conspiracies, see here.