Additive Growth

Thomas Philippon, "Additive Growth,"National Bureau Of Economic Research, April 2022, https://www.nber.org/papers/w29950

“…Model D, unlike model G, appears to have only one break over the period 1890-2019. We can formally test this idea following Bai and Perron (2003). The unconstrained test finds one break in the series around 1930 (the point estimate is 1933). We cantest H0: no breaks versus H1: break in 1933. The W statistic is 21.72 and the p-value is 0.0. I emphasize, however, that while the existence of a break is clear, the date is really an interval between the late 1920s and WW2. The date of the break is consistent with Field (2003)’s argument that “the years 1929- 1941 were, in the aggregate, the most technologically progressive of any comparable period in U.S. economic history.” This period corresponds to the large scale implementation of the discoveries of the second industrial revolution: electric light, electric power, and the internal combustion engine, as discussed in Jovanovic and Rousseau (2005). Gordon (2016) points out that it is somewhat surprising that “much of the progress occurred between 1928 and 1950,” several decades after the discoveries were made. Following David (1990), he explains the paradox by showing that the 1930s were a period of follow-on inventions, such as the perfection of the piston power-powered aircraft and television, and the increasing quality of machinery made possible by the large increases in available horsepowers and kilowatt-hours of electricity. Following these historical insights, figure 5 proposes an interpretation of US TFP from 1890 to 2019, using linear growth with one structural break in 1933 after the electrification revolution. We can summarize this idea in the following remark, keeping in mind that we normalize US TFP to 1 in 1890. Fact 5. From 1890 to 1933, TFP increases by.017 each year until it reaches a level around 1.75 in the early 1930s. From 1933 to 2019 TFP increases by.057 each year (3.3 p.p. of its level in 1933) to reach a level around 8 at the end of the sample….”

The outlier

Core Finding:"....There is no TFP slowdown, or, to put it differently, the perceived TFP slowdown is the result of using a misspecified model as a benchmark. Initial trend growth is around 2.5%. After 40 year, TFP doubles, and since increments are constant, the trend growth rate is half of what it used to be. After 60 years later, it is only one percent...."

Evidence from the United States, "...Figure 1 reveals a new fact and makes an important empirical point. The new fact is that there is no TFP slowdown in the US according to model D. The important empirical point is that, with realistic values for TFP growth rates, the distinction between models D and G requires at least 10 years of out-of-sample forecasts....US growth is better described as additive rather than multiplicative. Instead of stating that the average growth rate of TFP is 1.45%, which is correct but not particularly useful, it is more relevant to say that TFP increases by 0.0245 points each year starting from a normalized value of 1 in 1947. For labor productivity, both the additive growth model and the multiplicative growth model predict an increasing size of productivity increments, but at different speeds. The additive model D predicts that labor productivity increments increase with the square of the time horizon, while the geometric model G predicts exponentially increasing increments. Model G does not describe the data with a constant growth rate. Model D describes the data relatively well with year-on-year increments of about $1560 per full time worker ($0.87 per hour, assuming 1800 hours worked in a year) around 2010…”

"...Figure 3 shows the raw and smoothed series....The data is from Bergeaud et al. (2016) and winsorized in the first and last percentiles to remove limit extreme outliers during WW2. The model is initiated over the first 10 observations, 1891 to 1900. As expected the trend growth of the economy changes over this long sample.....Table 1 shows that the volatility of TFP growth rates declines significantly over time...."

TFP growth is not exponential. New ideas add to our stock of knowledge; they do not multiply it. TFP has been growing linearly over the past 90 years in the US and the additive model beats the exponential model for every single country, developed or catching up, where TFP data is available. The TFP frontier appears to grow linearly within broad historical periods: 1650 to 1830, 1830 to 1930, and 1930 until today. Additive TFP growth predicts increasing growth of labor productivity and GDP per capita thanks to capital accumulation. This prediction also appears to be empirically accurate... The additive growth model explains the observed TFP slowdown as a simple side effect of model misspecification. We should not have expected growth rates to be constant in the first place. The additive model does not necessarily solve the research productivity puzzle....... since this puzzle is not about the stochastic process for TFP but rather about the specification of the production function for ideas.Models where ideas are non-rival often imply a tight connection between growth and the quantity of research. These models predict accelerating growth - whether of the linear kind or not - from an increasing number of researchers....I start my investigation with post-war US data. The empirical justification is that this is the most widely used and reliable data. The theoretical justification is that one might expect different TFP dynamics between countries at the frontier and countries catching up to the frontier. The main advantage of post-war US data, then, is that one can reasonably argue that the US was at the technological frontier during the entire period....My primary sources for TFP are Fernald (2012) (Fernald)and Bergeaud et al. (2016) (BCL).... Fernald’s series cover only the US business sector, while BCL include households and the government....The simplest way to start comparing model D and model G is to consider the following experiment. Suppose that two agents, George and Daniela, are asked in the middle of the sample (1983) to predict the level of TFP in the second half of the sample (1984- 2019). The agents have access to data from the end of World War 2 until 1983. The two agents have dogmatic beliefs regarding the correct model of economic growth. George believes in model G from equation (2) while Daniela believes in model D from equation (3). George therefore fits a log linear model over the years 1947: 1983 and predicts future (log) TFP as log Aˆ (G) t = ˆag + ˆgt for t = 1984: 2019. Daniela instead fits a linear model and predicts future TFP as Aˆ (D) t = ˆa + ˆbt. Figure 1 shows that Daniela would have made a much better forecast than George. George is puzzled by the TFP slowdown while Daniela does not perceive an obvious long term break in her model (although there are some meaningful medium term deviations).....Figure 1 reveals a new fact and makes an important empirical point. The new fact is that there is no TFP slowdown in the US according to model D. The important empirical point is that, with realistic values for TFP growth rates, the distinction between models D and G requires at least 10 years of out-of-sample forecasts...Fact 1. There is no TFP slowdown in the US according to model D....US growth is better described as additive rather than multiplicative. Instead of stating that the average growth rate of TFP is 1.45%, which is correct but not particularly useful, it is more relevant to say that TFP increases by 0.0245 points each year starting from a normalized value of 1 in 1947. For labor productivity, both the additive growth model and the multiplicative growth model predict an increasing size of productivity increments, but at different speeds. The additive model D predicts that labor productivity increments increase with the square of the time horizon, while the geometric model G predicts exponentially increasing increments. Model G does not describe the data with a constant growth rate. Model D describes the data relatively well with year-on-year increments of about $1560 per full time worker ($0.87 per hour, assuming 1800 hours worked in a year) around 2010...Fact 2. Postwar US TFP growth is well described by Model D with increments of ∆ = 0.0245 points each year starting from a normalized value of 1 in 1947. Model D also predicts the correct non-linear evolution of labor productivity.