In the typical poor economy, most of the income gap with the United States is a productivity gap

0.71 The median share of an economy’s gap in output per worker with the United States that is due to TFP, 143 economies, 2023

Not machines, not schooling: the part that capital and workers leave unexplained. Today we measure it, for any economy you choose, with the Penn World Table and a few lines of Python.

Open with the number, then ask: what do you think explains why Nigeria produces less than a tenth of what the United States produces per worker? Most students say capital (machines, roads) or education. The data say those matter, but the residual, total factor productivity, carries most of the gap.

The number is the notebook’s own: the median TFP share of the gap in equation (8), across the 142 economies with a gap, in 2023 (0.706). It comes from Section D.10 of Appendix D.

Everything on today’s charts can be redone for any economy: every chart has a menu, and the notebook has a country picker.

Three questions for today

• Data. What does the Penn World Table measure, and which numbers can we compare across countries and over time?
• Growth accounting. How much of an economy’s GDP growth came from more capital, more workers, and higher productivity?
• Development accounting. How much of the income gap between a poor economy and the United States is due to capital, schooling, and productivity?

These are the three acts of the deck and the three branches of the mind map on the title slide: the Penn World Table and the framework (cyan), growth accounting (lavender), development accounting (green).

Both methods are accounting, not explanation. They say where the differences show up in the production function, not why an economy invested, schooled or innovated more. Chapters 5 and 6 explain the why.

Two methods, one production function

	Growth accounting	Development accounting
Question	Why did this economy grow?	Why is this economy poorer?
Compares	one economy with its own past	economies with each other, in one year
Works with	growth rates of GDP, capital, labour	levels of output per worker, capital, schooling
Result	contributions in percentage points	shares of the gap with the United States
Follows	the Growth Atlas	Caunedo, STEG Lecture 2

In both, total factor productivity is the residual: what the measured inputs leave unexplained.

The table is Section D.1 of the appendix. Point at the last row: the growth accounting follows the method of the Growth Atlas, a study companion that decomposes GDP growth with Penn World Table 11.0; the development accounting translates Julieta Caunedo’s Stata code for the STEG (Structural Transformation and Economic Growth) lectures into Python.

Our growth accounting reproduces the Growth Atlas numbers for all six default economies, 204 country-years, to within 0.012 percentage points (its rounding).

The Penn World Table and the framework

Act I

One production function frames both methods

\[Y = A\,K^{\alpha}\,L^{1-\alpha}, \qquad \alpha = 0.33\]

• \(Y\) output, \(K\) physical capital, \(L\) labour: measured in national accounts
• \(A\) total factor productivity (TFP): not measured, found as the residual
• \(\alpha\) the capital share, the same everywhere: about one third (Hall and Jones 1999)

Measure what you can, and call the rest productivity.

This is equation (1) of the appendix, the Cobb–Douglas production function of Chapters 4 to 6.

The capital share alpha = 0.33 is a classroom standard and the default of both the Growth Atlas and Caunedo’s code. It is not each country’s measured factor share; Section D.11 tests what happens with country labour shares.

Ask: why can’t we measure A directly? Because no statistical office measures “efficiency”. It is defined by the equation itself.

The Penn World Table makes output and inputs comparable across 185 economies

What it provides

• GDP at purchasing power parity: a dollar buys the same basket everywhere
• Capital stocks built from past investment
• Workers, their hours and a human capital index from schooling
• 185 economies, 1950–2023, prices of 2021 (version 11.0)

Two kinds of series

• National prices (rgdpna, rnna): growth over time, within an economy → growth accounting
• PPP (rgdpo, cgdpo, cn): levels across economies in one year → development accounting

Feenstra, Inklaar and Timmer (2015) describe the database; it is maintained at the Groningen Growth and Development Centre.

The distinction in the right column matters and students often miss it. PWT itself recommends the national-price series to compare growth rates over time, and the PPP series to compare levels across countries. That is why the two halves of the appendix use different variables.

Section D.3 of the notebook downloads the official file (pwt110.dta, about 4 MB, from DataverseNL) and checks that the book’s prepared file agrees with it: the largest relative difference in rgdpna is 4.9e-05, which is rounding.

Which data exist, and for how many economies?

Can we measure workers’ hours and schooling for every economy, as we can measure GDP?

Ask the room before showing the chart. Most guess that rich-country data are complete and poor-country data are patchy; the surprise is how few economies have hours before 1990.

Hours exist for far fewer economies than GDP or capital

Data: Penn World Table 11.0 (Feenstra, Inklaar and Timmer 2015); file data/appD/pwt_accounting.csv. Chart inspired by the discussion of the Penn World Table in Chapter 3 of Jones (2024), Macroeconomics, 6th ed.

How to read it: the number of economies (out of 185) with a value for each variable, year by year, from 1970. Hover to read the counts; click a legend entry to hide a line.

Point at: GDP, capital and workers for about 180 economies since 2000; human capital (hc) for 145; hours (avh) for only about 50 before 1990, rising to 130 since 2010; labour shares (labsh) for 140.

Coverage decides which comparisons we can make

• GDP, capital and workers: about 180 economies since 2000
• Hours: about 50 economies before 1990, mostly rich ones; 130 since 2010
• So the default labour input is persons engaged; hours and schooling are options

Look at your data before you analyse it: missing hours would quietly drop most poor economies.

This is why the Growth Atlas, and our appendix, use persons engaged by default. Per-hour development accounting, as in Caunedo’s code, keeps 119 economies in 2023 instead of 143.

A data-science habit to stress: always check coverage before choosing a method, because the sample can change the answer.

Loading the data takes two lines of pandas

PWT_URL = "https://dataverse.nl/api/access/datafile/554030"   # the official pwt110.dta
official = pd.read_stata(PWT_URL)                             # 13,690 rows, 51 columns

pwt = pd.read_csv(DATA_URL + "pwt_accounting.csv")             # the book's prepared file
COUNTRIES = ["USA", "MEX", "CHN", "IND", "KOR", "NGA"]         # your economies: change them!

Open the Appendix D notebook in Colab, replace two codes in COUNTRIES, and choose Runtime → Run all: every chart updates.

The appendix shows both routes: the official Stata file straight from DataverseNL, and the book’s prepared CSV with the nine variables we need from 1970 to 2023. The prepared file is what the rest of the notebook uses, because it is small and fast.

COUNTRIES holds ISO codes. The notebook prints all 185 codes. In Colab, every chart also has a menu of country names.

Growth accounting

Act II

From the production function to the growth accounting equation

Take logs, then the change from one year to the next:

\[\ln Y_t = \ln A_t + \alpha \ln K_t + (1-\alpha)\ln L_t\]

The change in a log is, approximately, the growth rate:

\[g_Y = \underbrace{\alpha\,g_K}_{\text{capital}} + \underbrace{(1-\alpha)\,g_L}_{\text{labour}} + \underbrace{g_A}_{\text{TFP}}\]

\[g_A = g_Y - \alpha\,g_K - (1-\alpha)\,g_L \qquad \text{the Solow residual}\]

Equations (2) and (3) of the appendix. The full derivation is in Section D.4: take logs (a product becomes a sum, a power becomes a coefficient), write the same equation a year earlier, subtract, and use the approximation that a change in a log is a growth rate.

Because TFP growth is computed as the residual, the three contributions add up to GDP growth exactly, even though the log approximation is not exact. Like the Growth Atlas, we use simple yearly growth rates, 100 × (X_t/X_{t−1} − 1).

Intuition with alpha = 0.33: 3 percent more capital adds about 1 point to GDP growth; 3 percent more labour adds about 2 points.

In Python, the whole method is a groupby and a subtraction

growth = d.groupby("iso3")[["rgdpna", "rnna", "L"]].pct_change(fill_method=None) * 100
d["gdp"] = growth["rgdpna"]
d["capital"] = alpha * growth["rnna"]                 # alpha g_K
d["labour"] = (1 - alpha) * growth["L"]               # (1 - alpha) g_L
d["tfp"] = d["gdp"] - d["capital"] - d["labour"]      # g_A, the residual

groupby("iso3") keeps each economy’s growth rates separate, so the first year of one economy is never compared with the last year of another.

This is the core of the notebook’s growth_accounting function (Section D.5). The labour input L is persons engaged, or persons × hours, or persons × hours × the human capital index, depending on the labour argument.

The notebook first does the same thing by hand for the United States, column by column, and checks that the largest gap between the sum of contributions and GDP growth is 4e-16, zero up to rounding.

The pandemic year: what happened to U.S. productivity?

In 2020, U.S. employment fell by about 5.5 percent and GDP by 2.2 percent.

Did measured TFP rise or fall in 2020? Write down your guess.

Collect guesses. Most students expect TFP to fall in a recession. The chart answers it on the next slide.

The numbers: GDP growth −2.16 percent; the labour contribution (1 − α) g_L was −3.67 points, so employment fell by about 5.5 percent.

Choose any economy: where did its GDP growth come from?

Data: Penn World Table 11.0 (Feenstra, Inklaar and Timmer 2015), rgdpna, rnna, emp. Method: the Growth Atlas. Chart inspired by the growth accounting of Chapter 6 in Jones (2024), Macroeconomics, 6th ed.

How to read it: stacked bars are the contributions of capital (blue), labour (green) and TFP (orange) to GDP growth, in percentage points, each year from 1990 to 2023; the white line is GDP growth. The bars of each year add up to the line. α = 0.33, labour in persons engaged.

Do live: hover 2020 for the United States (labour −3.67, TFP +0.97). Then open the menu (top right) and pick China, then Mexico, then the economy of a student in the room. The menu lists the 147 economies with complete data from 1990 to 2023.

In 2020, measured TFP rose: a composition effect

• U.S. 1990–2023: GDP 2.49 percent a year = capital 0.73 + labour 0.63 + TFP 1.13 points
• 2020: labour −3.67 points, TFP +0.97: employment fell much more than output, so output per remaining worker rose
• TFP swings far more from year to year than capital, which changes slowly

A one-year residual is not technology: it also absorbs who works, how hard machines run, and measurement error.

Reveal the prediction: TFP rose in 2020. Employment fell sharply while output fell much less, so the residual went up. The job losses were concentrated in lower-paid service work, so the workers who remained were, on average, more productive: a composition effect, not a burst of innovation.

The averages are printed in Section D.5 of the notebook and match the Growth Atlas (2.49, 0.73, 0.63, 1.13).

Which fast growers owe most to productivity?

China, India, Korea, Nigeria, Mexico, the United States: rank them by the share of GDP growth that came from TFP, 1990–2023.

Give students a minute to rank them. The common guess puts China’s growth down to investment alone (“they just built a lot”). The next chart tests it.

Average contributions over a period: move the slider through the decades

Data: Penn World Table 11.0 (Feenstra, Inklaar and Timmer 2015). Method: the Growth Atlas. Chart inspired by the growth accounting of Chapter 6 in Jones (2024), Macroeconomics, 6th ed.

How to read it: for each of the six default economies, the average contribution of capital, labour and TFP over the period on the slider; the diamond is average GDP growth.

Do live: start at 1990–2023, then move the slider to 1990–1999, 2000–2009, 2010–2019 and 2020–2023. Point at Korea’s TFP bar shrinking, and at the pandemic period.

TFP explains more than half of China’s growth and none of Mexico’s

• China: GDP 8.80 percent a year, TFP 4.92 points, capital 3.52
• United States: TFP 1.13 of 2.49, close to half
• India and Nigeria: large labour contributions, 1.39 and 2.18 points: fast-growing workforces
• Mexico: growth came from adding capital and workers; TFP −0.11

Investment alone did not make China grow; productivity did more than half the work.

Reveal the ranking by TFP’s share of GDP growth: China 56 percent, the United States 45, India 41, Nigeria 39, Korea 37, Mexico none. The numbers are the notebook’s averages for 1990–2023 with persons engaged and α = 0.33.

China’s productivity growth includes the reallocation of workers from farms to factories and cities, a classic source of measured TFP in developing economies.

Decade by decade, for any economy

Data: Penn World Table 11.0 (Feenstra, Inklaar and Timmer 2015). Method: the Growth Atlas. Chart inspired by the growth accounting of Chapter 6 in Jones (2024), Macroeconomics, 6th ed.

How to read it: average contributions in each decade (the 2020s are 2020–2023), for the economy chosen in the menu. It starts on China.

Do live: China’s TFP contribution was 5.84 points in the 1990s and 5.91 in the 2000s, then 3.99 and 2.48. Switch to Republic of Korea: 2.88, 2.00, 1.25, 0.13. Then Mexico: negative TFP in the 2000s (−1.06) and the 2020s (−0.64).

As economies mature, their TFP contributions shrink

• Korea: TFP 2.88 points a year in the 1990s, 0.13 in the 2020s
• China: about 5.9 in the 1990s and 2000s, 2.5 in the 2020s
• Catch-up growth borrows ideas from the frontier: the closer to it, the less there is to borrow

Fast TFP growth is a feature of catching up, not a permanent state.

Link to Chapter 6: in the combined Solow–Romer view, economies far below the frontier can grow fast by adopting existing ideas; as they converge, growth slows toward the frontier’s rate. The decade table in Section D.7 of the notebook holds the numbers.

The answer depends on two choices: α and the labour measure

Choice	Economy	Labour	TFP
Persons, α = 0.33 (default)	Korea	0.95	1.82
Total hours, α = 0.33	Korea	0.26	2.52
Persons, α = 0.33 (default)	China	0.36	4.92
Persons, α = 0.40	China	0.32	4.21

Average contributions, percentage points a year, 1990–2023.

Hours per Korean worker fell, so counting hours moves growth from labour to TFP; a higher α moves China’s growth from TFP to capital.

In the notebook, the Fig. 4 widget has a slider for α and a menu for the labour measure: persons engaged, total hours (emp × avh), quality-adjusted hours (emp × avh × hc).

Quality-adjusted hours move growth from TFP to labour in economies where schooling rose fast. Ask students to try Nigeria with hours: its hours data start only in 2005, so its hours-based accounting starts in 2006.

“TFP growth measures technological progress”

TFP growth is the rate of technological progress.

TFP growth is a residual. Over decades it reflects ideas, organization and reallocation; in any one year it also absorbs changes in hours, skills, capacity use, commodity prices and measurement error, as 2020 showed.

Solow (1957) called it technical change, and Abramovitz (1956) called the residual “a measure of our ignorance”. Both views are useful: the long-run average is informative; single years are not.

Mexico’s growth puzzle: lots of investment, no productivity growth

Mexico opened to trade, stabilized prices and invested, yet TFP contributed nothing to its growth since 1990. What should policy target?

What the accounting says

• Capital 0.83 and labour 1.57 points a year: all of the 2.29 percent growth
• TFP −0.11: the same inputs did not become more productive
• So more investment alone would not have closed the gap

What it leaves out

• Why TFP stagnated: Levy (2018) points to misallocation, as informality and tax and social insurance rules keep resources in low-productivity firms
• Whether better measurement (informal output, hours) would change the residual

Evidence: Santiago Levy (2018), Under-Rewarded Efforts: The Elusive Quest for Prosperity in Mexico, Inter-American Development Bank, argues that the allocation of capital and labour toward small, informal, low-productivity firms explains the stagnation of Mexican productivity. This is one influential reading, not a settled consensus; others stress credit, rule of law or the China shock to Mexican manufacturing.

The accounting itself only says where the growth came from: inputs, not productivity.

Development accounting

Act III

Why is Nigeria so much poorer than the United States?

Nigeria’s output per worker is 8.5 percent of the U.S. level. How much of that gap is machines, how much is schooling, and how much is productivity?

Ask students to split the gap themselves first, in three percentages. Keep their answers on the board; the next slides compute them.

Add schooling, then write capital relative to output

Output with physical and human capital, \(H = hL\), divided by workers:

\[y = A\,k^{\alpha}\,h^{1-\alpha}\]

Substitute \(k = (K/Y)\,y\), collect \(y\), and raise to \(1/(1-\alpha)\):

\[y = \underbrace{A^{\frac{1}{1-\alpha}}}_{\text{TFP term}} \times \underbrace{\left(\frac{K}{Y}\right)^{\frac{\alpha}{1-\alpha}}}_{\text{capital term}} \times \underbrace{h}_{\text{human capital}}\]

Each term is then divided by its U.S. value: a ratio of 0.5 means half the U.S. level.

Equation (5) of the appendix; the derivation is in Section D.8: write k = (K/Y) y, so y = A (K/Y)^α y^α h^(1−α); divide by y^α, so y^(1−α) = A (K/Y)^α h^(1−α); raise both sides to 1/(1−α).

h is PWT’s human capital index (hc), built from years of schooling and the returns to schooling. Output per worker is rgdpo/emp, and K/Y is cn/cgdpo, both at PPPs.

Why the capital–output ratio, and not capital per worker?

• A more productive economy produces more, saves more, and builds more capital: part of its high \(k\) is caused by TFP
• In the Solow model, \(K/Y = s/(\bar{n} + \bar{d})\) in steady state: it does not depend on \(A\)
• So the capital term measures only the capital that TFP does not explain

Credit TFP for the capital it induces, and capital for the rest.

This is the choice of Hall and Jones (1999) and of Caunedo’s code. Chapter 4’s development accounting, y = A k^(1/3), credits capital for all capital. Section D.10 shows how much the choice matters: the success of the inputs doubles in the capital-per-worker form.

Splitting the gap into three shares

\[\frac{y_{US}}{y_i} = \underbrace{T_i}_{\text{TFP gap}} \times \underbrace{K_i}_{\text{capital gap}} \times \underbrace{H_i}_{\text{schooling gap}}\]

\[s^{TFP}_i = \frac{T_i}{T_i + K_i H_i}\]

\[s^{K}_i = \frac{K_i}{K_i + H_i}\,(1 - s^{TFP}_i), \qquad s^{H}_i = \frac{H_i}{K_i + H_i}\,(1 - s^{TFP}_i)\]

If the TFP gap equals the gap the two inputs create together, TFP’s share is one half; if it is three times as large, three quarters.

Equation (8). Each gap factor is the U.S. level divided by economy i’s level. This is the split in Caunedo’s code (share_due_to_TFP, then the rest divided between human and physical capital in proportion to their gap factors). The three shares add up to one; the notebook checks it (largest error 1e-16).

The method in Python: three columns and a division

d["y"] = d["rgdpo"] / d["emp"]                                # output per worker
d["ky"] = (d["cn"] / d["cgdpo"]) ** (alpha / (1 - alpha))      # capital term
d["h"] = d["hc"]                                               # human capital
d["tfp"] = d["y"] / (d["ky"] * d["h"])                         # TFP term, the residual
for col in ["y", "ky", "h", "tfp"]:
    d[col + "_rel"] = d[col] / us[col]                         # United States = 1

Per hour instead of per worker? Divide by emp * avh. That is the only change.

The core of dev_levels and relative_to_us in Section D.9. The notebook also drops Venezuela, whose PWT output after 2017 is not plausible because hyperinflation broke its price data, and checks that the three ratios multiply to the output ratio (equation (7)).

Nigeria: which term is furthest from the U.S. level?

Output per worker is 0.085 of the U.S. level. Guess each term: the capital term, human capital, and the TFP term.

Most students guess capital is the lowest. Keep the guesses for the reveal.

Choose any economy: its three terms relative to the United States

Data: Penn World Table 11.0 (Feenstra, Inklaar and Timmer 2015), rgdpo, cgdpo, cn, emp, hc. Method: Caunedo, STEG Lecture 2. Chart inspired by the development accounting of Chapter 4 in Jones (2024), Macroeconomics, 6th ed.

How to read it: four bars for the economy in the menu, each relative to the United States (the dashed line at 1), per worker, 2023: output per worker, the capital term, human capital and the TFP term. The output bar is the product of the other three.

Do live: Nigeria first. Then India, China, Mexico, Korea, and a student’s choice. The menu lists the 142 economies with data in 2023 (the United States excluded).

Capital is not the problem; productivity is

• Nigeria’s capital term is 1.73, above the U.S. level: its capital is high relative to its output
• Human capital: 0.56 of the U.S. level
• TFP term: 0.088, so TFP accounts for 92 percent of the gap
• India, China, Mexico and Korea: TFP shares of 0.70 to 0.78

Poor economies have little capital per worker because they produce little, not the other way round.

Reveal the prediction. Numbers from Section D.9: Nigeria’s y_rel 0.085, ky_rel 1.729, h_rel 0.557, tfp_rel 0.088, share_tfp 0.916. India 0.775, China 0.761, Mexico 0.709, Korea 0.702.

Korea’s human capital is slightly above the U.S. level (1.011): its whole gap is capital-light productivity.

Across all economies, the poorer the economy, the larger the TFP share

Data: Penn World Table 11.0 (Feenstra, Inklaar and Timmer 2015). Method: Caunedo, STEG Lecture 2. Chart inspired by the development accounting of Chapter 4 in Jones (2024), Macroeconomics, 6th ed.

How to read it: each dot is an economy; horizontal, output per worker relative to the United States on a ratio scale; vertical, the share of its gap due to TFP. The six default economies are orange and labelled. It opens on 2023.

Do live: hover the far left (Burundi, D.R. Congo, Madagascar). Then press play to run 1990 to 2023: the cloud drifts up.

TFP carries most of the gap, and more so where the gap is largest

• The 31 economies below a tenth of U.S. output per worker: TFP share 0.70 to 0.88 in most cases, median 0.81
• Richer than the United States (Ireland, Norway, Switzerland, Singapore, Qatar, Brunei): the shares measure their lead
• Over time the cloud drifts up: TFP explains a larger share in 2023 than in 1990

The income gaps of the poorest economies are, above all, productivity gaps.

Interquartile range of the TFP share among the 31 poorest economies: 0.705 to 0.878, median 0.809 (the notebook’s 2023 data).

Data hygiene: oil economies (Qatar, Brunei, Norway) look rich partly because of resource rents, which Section D.11 removes.

The typical economy’s TFP share has risen since 1970

Data: Penn World Table 11.0 (Feenstra, Inklaar and Timmer 2015). Method: Caunedo, STEG Lecture 2. Chart inspired by the development accounting of Chapter 4 in Jones (2024), Macroeconomics, 6th ed.

How to read it: the three solid lines are the medians, across economies, of the TFP share, the physical capital share and the human capital share of the gap with the United States, each year since 1970. The dotted amber line is the TFP share of the economy in the menu (starting with Nigeria).

Do live: switch the menu to China, India, Mexico, Korea.

Schooling has spread faster than productivity

• Median TFP share: 0.44 in 1970 → 0.71 in 2023
• The sample grows from 107 economies in 1970 to 142 from 1990 on, but the rise continues with the sample fixed
• Human capital gaps narrowed: poor economies schooled their workers faster than they raised productivity

As schooling gaps close, what remains of the income gap is ever more a productivity gap.

Numbers: the median TFP share 0.438 in 1970, 0.551 in 1990, 0.626 in 2010, 0.706 in 2023; physical capital 0.243 → 0.110; human capital 0.309 → 0.172 (Section D.10).

Inputs explain only 16 percent of the spread of incomes

\[\text{success} = \frac{\operatorname{var}\left[\ln y^{KH}\right]}{\operatorname{var}\left[\ln y\right]}, \qquad y^{KH} = (K/Y)^{\alpha/(1-\alpha)}\,h\]

Form of the factor-only model	Success, 143 economies, 2023
capital–output form (this appendix, Caunedo)	0.157
capital-per-worker form (Chapter 4, Caselli 2005)	0.301

If every economy had U.S. TFP, the spread of log output per worker would shrink by 84 percent; how much “inputs” explain depends on who gets credit for TFP-induced capital.

Equation (9), the success measure of Caselli (2005): the share of the cross-country variance of log output per worker that a factor-only model, with the same TFP everywhere, would reproduce.

Physical capital alone 0.053, human capital alone 0.068 (the two do not add up, because they are correlated).

The success fell from about 0.21 in 1990 to 0.14 in 2010 and was 0.16 in 2023.

The result survives hours and resource rents, but not country labour shares

Variant	Economies	Success of inputs	Median TFP share
per worker (baseline)	143	0.157	0.706
per hour (Caunedo)	119	0.151	0.713
net of resource rents	140	0.150	0.734
country labour shares	119	1.944	0.846

A success above 1 is impossible: where the labour share is tiny (Qatar 0.18), the capital exponent \((1-0.18)/0.18 \approx 4.6\) explodes.

Section D.11. Net of rents: GDP is scaled by (1 − rents/100), with the World Bank’s total natural resource rents, and Ireland and Macao are dropped, as in Caunedo’s code. Labour shares: PWT’s labsh, which counts resource rents and the income of the self-employed as capital income in many economies; Gollin (2002) shows that adjusting for self-employment makes labour shares much more similar across countries. That is why development accounting keeps one common α.

The rising TFP share holds per hour and net of resource rents

Data: Penn World Table 11.0 (Feenstra, Inklaar and Timmer 2015); World Bank WDI, total natural resources rents. Method: Caunedo, STEG Lecture 2.

How to read it: the median TFP share of the gap, 1990–2023, under the four variants. The three variants with a common α stay close together and rise; the labour-share line lies above them for the reason on the previous slide. Click a legend entry to hide a line.

“Poor countries are poor because they lack machines”

Poor countries are poor mainly because they have too little capital.

Relative to their output, poor economies have as much capital as the United States: Nigeria’s capital term is 1.73, India’s 1.12. Capital per worker is low because output is low, and output is low mainly because TFP is low.

This is the central lesson of development accounting since Hall and Jones (1999) and Caselli (2005). It does not mean capital is unimportant: TFP-induced capital is real capital; the accounting credits it to TFP because TFP caused it.

If productivity is the gap, what should policy target?

A finance ministry wants to close the gap with richer economies. Subsidize investment, expand schooling, or remove what keeps productivity low?

What the accounting suggests

• Investment alone raises \(K/Y\), which is already near the U.S. level
• Schooling closes part of the gap (Nigeria’s \(h\) is 0.56)
• Most of the gap is TFP: how well inputs are used

What it leaves out

• What TFP is: institutions and “social infrastructure” (Hall and Jones 1999), misallocation across firms (Hsieh and Klenow 2009), technology adoption
• Whether hc measures skills well: Hendricks and Schoellman (2023) find a larger role for human capital

Hsieh and Klenow (2009) estimate that reallocating capital and labour across manufacturing plants to U.S. levels of efficiency would raise manufacturing TFP by 30–50 percent in China and 40–60 percent in India. Hall and Jones (1999) relate output per worker to institutions and government policies. Both are influential; the size of the effects is debated.

Development accounting itself prescribes nothing; it tells policymakers where the gap is.

A skeptic: “TFP is just a measure of our ignorance”

A skeptic says: “You call the residual productivity, but it is simply everything you failed to measure. Saying it explains 70 percent of the gap says nothing.”

Reply: the skeptic is half right, which is the point. Abramovitz (1956) called the residual “a measure of our ignorance”. Accounting shows how big that ignorance is, and robustness checks (hours, rents, schooling) show it does not go away when we measure more. That is why growth theory, from Solow to Romer, is about TFP.

Use this to motivate Chapters 5 and 6 and the research on institutions and misallocation. The residual is large and robust; explaining it is the open question.

What to remember from this appendix

• I. The Penn World Table gives comparable output and inputs for 185 economies: national-price series for growth, PPP series for levels
• II. Growth accounting splits GDP growth into capital, labour and TFP: since 1990, TFP did more than half of China’s growth, close to half of U.S. growth, and nothing in Mexico
• III. Development accounting puts most of the income gap on TFP: the median TFP share is 0.71 in 2023, and inputs explain only 16 percent of the spread of incomes
• Both are accounting: they say where the differences are, not why

One takeaway per act, in the order of the mind map’s branches. Ask students which number surprised them most.

Walk the three branches in a minute each: the Penn World Table and the framework (cyan, upper left), growth accounting (lavender, upper right), development accounting (green, bottom). Then the thesis on the next slide.

Measured inputs explain much of growth but little of income gaps; productivity, the residual, carries most of the difference

Open the Appendix D notebook in Colab, choose your own countries, and redo every chart

The thesis of the appendix and of the mind map. Accounting splits output into what measured inputs explain and a residual, TFP. Since 1990, TFP explains more than half of China’s growth, close to half of U.S. growth and none of Mexico’s. Across 143 economies in 2023, the capital–output term is close to the U.S. level almost everywhere and schooling explains part of the gap, but TFP carries most of it. Accounting says where the differences are, not why.

Sources: data, methods and figures

• Data. Penn World Table 11.0 (Feenstra, Inklaar and Timmer 2015), rug.nl/ggdc/productivity/pwt, doi:10.34894/FABVLR; World Bank, World Development Indicators, total natural resources rents (% of GDP). Prepared files data/appD/pwt_accounting.csv and nat_res_rents.csv.
• Growth accounting method. The Growth Atlas, PWT growth accounting 1990–2023; our numbers reproduce it.
• Development accounting method. Caunedo, J. (2021), STEG Lecture 2: income accounting, Stata code, translated to Python.
• Live charts (eight). Built for this deck with the notebook’s own functions (growth_accounting, dev_accounting, relative_to_us, success); each menu offers every economy with data.
• Book appendix. Data Science and Macroeconomic Models, Appendix D: Growth and Development Accounting.

Sources: research cited

• Abramovitz, M. (1956). Resource and output trends in the United States since 1870. American Economic Review 46(2), 5–23.
• Caselli, F. (2005). Accounting for cross-country income differences. In P. Aghion and S. Durlauf (eds.), Handbook of Economic Growth, vol. 1A, 679–741. Elsevier.
• Feenstra, R. C., Inklaar, R., and Timmer, M. P. (2015). The next generation of the Penn World Table. American Economic Review 105(10), 3150–3182.
• Gollin, D. (2002). Getting income shares right. Journal of Political Economy 110(2), 458–474.
• Hall, R. E., and Jones, C. I. (1999). Why do some countries produce so much more output per worker than others? Quarterly Journal of Economics 114(1), 83–116.
• Hendricks, L., and Schoellman, T. (2023). Skilled labor productivity and cross-country income differences. American Economic Journal: Macroeconomics 15(1), 240–268.
• Hsieh, C.-T., and Klenow, P. J. (2009). Misallocation and manufacturing TFP in China and India. Quarterly Journal of Economics 124(4), 1403–1448.
• Levy, S. (2018). Under-Rewarded Efforts: The Elusive Quest for Prosperity in Mexico. Inter-American Development Bank.
• Solow, R. M. (1957). Technical change and the aggregate production function. Review of Economics and Statistics 39(3), 312–320.
• Textbook. Jones, C. I. (2024). Macroeconomics, 6th ed. W. W. Norton (Chapters 3–6).