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Relationship, enables

Capital investment enables Economic output

The stored status is what a reviewer approved. The level below it is what the overlapping data support; the two are shown side by side and only a human moves the status.

Stored statusHypothesizedEvidence level (latest analysis)Level 1: Correlation only
The latest analysis supports only level 1 from the data alone, below the stored status. The stored status rests on the mechanism and evidence listed below, which statistics on two world series cannot confirm or remove.

Mechanism, evidence, reviewer judgements

The edge as stored

Capital investment enables Economic output2 evidenceHypothesized

Economic output depends on Capital investment.

Mechanism

Stated, not yet evidenced here: the share of output reinvested in buildings, machines and infrastructure raises the capital stock and, with a lag, output per person (the accumulation term in growth accounting). Investment also responds to expected growth, so the direction runs both ways.

Status
hypothesized
Reviewer confidence
0.60
Stated strength
not stated
Lag
not stated
Version
curated_seed_v1
Reviewed
2026-09-07

Confidence and strength are curated judgements recorded with the edge, not measured quantities.

Entity pages: Capital investment, Economic output.

Level 1 evidence, computed 2026-09-07 22:15 UTC

Correlation

DerivedLevel 1: Correlation only

Gross capital formation as share of GDP against GDP per person, constant 2015 US$, geography WLD, 55 overlapping years (1970 to 2024). Primary statistics on diff (first differences, because at least one series has a unit root; levels are shown for comparison).

Pearson r (diff)

0.626

p 0.0000

Spearman rho (diff)

0.716

p 0.0000

Pearson r (levels)

0.005

two trending series correlate in levels by construction

Rolling r

0.853

min 0.394, max 0.966, 0 sign changes

Gross capital formation as share of GDP and GDP per person, constant 2015 US$, each scaled to its own range over 1970 to 2024Aligned series, scaled 0 to 1 over the overlap00.51Gross capital formation as share of GDP, 1970: 26.584Gross capital formation as share of GDP, 1971: 26.350Gross capital formation as share of GDP, 1972: 26.555Gross capital formation as share of GDP, 1973: 27.715Gross capital formation as share of GDP, 1974: 27.863Gross capital formation as share of GDP, 1975: 25.492Gross capital formation as share of GDP, 1976: 26.293Gross capital formation as share of GDP, 1977: 26.567Gross capital formation as share of GDP, 1978: 26.910Gross capital formation as share of GDP, 1979: 27.175Gross capital formation as share of GDP, 1980: 26.599Gross capital formation as share of GDP, 1981: 25.935Gross capital formation as share of GDP, 1982: 24.559Gross capital formation as share of GDP, 1983: 24.111Gross capital formation as share of GDP, 1984: 25.242Gross capital formation as share of GDP, 1985: 25.002Gross capital formation as share of GDP, 1986: 25.055Gross capital formation as share of GDP, 1987: 25.269Gross capital formation as share of GDP, 1988: 26.386Gross capital formation as share of GDP, 1989: 26.941Gross capital formation as share of GDP, 1990: 26.569Gross capital formation as share of GDP, 1991: 25.876Gross capital formation as share of GDP, 1992: 25.259Gross capital formation as share of GDP, 1993: 24.705Gross capital formation as share of GDP, 1994: 25.024Gross capital formation as share of GDP, 1995: 25.047Gross capital formation as share of GDP, 1996: 24.846Gross capital formation as share of GDP, 1997: 24.631Gross capital formation as share of GDP, 1998: 24.209Gross capital formation as share of GDP, 1999: 24.339Gross capital formation as share of GDP, 2000: 24.698Gross capital formation as share of GDP, 2001: 23.891Gross capital formation as share of GDP, 2002: 23.254Gross capital formation as share of GDP, 2003: 23.427Gross capital formation as share of GDP, 2004: 24.095Gross capital formation as share of GDP, 2005: 24.459Gross capital formation as share of GDP, 2006: 25.007Gross capital formation as share of GDP, 2007: 25.466Gross capital formation as share of GDP, 2008: 25.460Gross capital formation as share of GDP, 2009: 23.423Gross capital formation as share of GDP, 2010: 24.627Gross capital formation as share of GDP, 2011: 25.350Gross capital formation as share of GDP, 2012: 25.487Gross capital formation as share of GDP, 2013: 25.597Gross capital formation as share of GDP, 2014: 25.879Gross capital formation as share of GDP, 2015: 25.925Gross capital formation as share of GDP, 2016: 25.666Gross capital formation as share of GDP, 2017: 26.122Gross capital formation as share of GDP, 2018: 26.662Gross capital formation as share of GDP, 2019: 26.564Gross capital formation as share of GDP, 2020: 26.457Gross capital formation as share of GDP, 2021: 27.237Gross capital formation as share of GDP, 2022: 27.474Gross capital formation as share of GDP, 2023: 26.658Gross capital formation as share of GDP, 2024: 26.288GDP per person, constant 2015 US$, 1970: 4964.267GDP per person, constant 2015 US$, 1971: 5060.962GDP per person, constant 2015 US$, 1972: 5235.595GDP per person, constant 2015 US$, 1973: 5464.502GDP per person, constant 2015 US$, 1974: 5466.805GDP per person, constant 2015 US$, 1975: 5409.878GDP per person, constant 2015 US$, 1976: 5590.919GDP per person, constant 2015 US$, 1977: 5710.217GDP per person, constant 2015 US$, 1978: 5843.072GDP per person, constant 2015 US$, 1979: 5978.088GDP per person, constant 2015 US$, 1980: 5980.250GDP per person, constant 2015 US$, 1981: 5986.165GDP per person, constant 2015 US$, 1982: 5902.836GDP per person, constant 2015 US$, 1983: 5947.172GDP per person, constant 2015 US$, 1984: 6119.787GDP per person, constant 2015 US$, 1985: 6233.016GDP per person, constant 2015 US$, 1986: 6325.607GDP per person, constant 2015 US$, 1987: 6446.303GDP per person, constant 2015 US$, 1988: 6619.581GDP per person, constant 2015 US$, 1989: 6741.216GDP per person, constant 2015 US$, 1990: 6804.126GDP per person, constant 2015 US$, 1991: 6773.416GDP per person, constant 2015 US$, 1992: 6801.305GDP per person, constant 2015 US$, 1993: 6818.570GDP per person, constant 2015 US$, 1994: 6944.091GDP per person, constant 2015 US$, 1995: 7057.773GDP per person, constant 2015 US$, 1996: 7202.740GDP per person, constant 2015 US$, 1997: 7381.771GDP per person, constant 2015 US$, 1998: 7478.784GDP per person, constant 2015 US$, 1999: 7638.929GDP per person, constant 2015 US$, 2000: 7879.618GDP per person, constant 2015 US$, 2001: 7932.442GDP per person, constant 2015 US$, 2002: 8010.647GDP per person, constant 2015 US$, 2003: 8151.037GDP per person, constant 2015 US$, 2004: 8408.565GDP per person, constant 2015 US$, 2005: 8639.359GDP per person, constant 2015 US$, 2006: 8913.157GDP per person, constant 2015 US$, 2007: 9191.474GDP per person, constant 2015 US$, 2008: 9265.527GDP per person, constant 2015 US$, 2009: 9028.221GDP per person, constant 2015 US$, 2010: 9322.218GDP per person, constant 2015 US$, 2011: 9514.520GDP per person, constant 2015 US$, 2012: 9653.627GDP per person, constant 2015 US$, 2013: 9811.026GDP per person, constant 2015 US$, 2014: 10000.583GDP per person, constant 2015 US$, 2015: 10191.975GDP per person, constant 2015 US$, 2016: 10355.045GDP per person, constant 2015 US$, 2017: 10591.555GDP per person, constant 2015 US$, 2018: 10822.575GDP per person, constant 2015 US$, 2019: 10996.910GDP per person, constant 2015 US$, 2020: 10575.219GDP per person, constant 2015 US$, 2021: 11167.604GDP per person, constant 2015 US$, 2022: 11452.020GDP per person, constant 2015 US$, 2023: 11670.822GDP per person, constant 2015 US$, 2024: 11894.252Gross capital formation as share oGDP per person, constant 2015 US$Rolling correlation, window 10 (on the primary transform)-101rolling r ending 1980: 0.85rolling r ending 1981: 0.86rolling r ending 1982: 0.89rolling r ending 1983: 0.86rolling r ending 1984: 0.94rolling r ending 1985: 0.96rolling r ending 1986: 0.95rolling r ending 1987: 0.95rolling r ending 1988: 0.95rolling r ending 1989: 0.95rolling r ending 1990: 0.95rolling r ending 1991: 0.94rolling r ending 1992: 0.91rolling r ending 1993: 0.92rolling r ending 1994: 0.90rolling r ending 1995: 0.93rolling r ending 1996: 0.85rolling r ending 1997: 0.72rolling r ending 1998: 0.67rolling r ending 1999: 0.77rolling r ending 2000: 0.83rolling r ending 2001: 0.80rolling r ending 2002: 0.77rolling r ending 2003: 0.75rolling r ending 2004: 0.89rolling r ending 2005: 0.93rolling r ending 2006: 0.94rolling r ending 2007: 0.95rolling r ending 2008: 0.89rolling r ending 2009: 0.97rolling r ending 2010: 0.96rolling r ending 2011: 0.95rolling r ending 2012: 0.96rolling r ending 2013: 0.96rolling r ending 2014: 0.96rolling r ending 2015: 0.95rolling r ending 2016: 0.94rolling r ending 2017: 0.95rolling r ending 2018: 0.96rolling r ending 2019: 0.83rolling r ending 2020: 0.41rolling r ending 2021: 0.65rolling r ending 2022: 0.65rolling r ending 2023: 0.43rolling r ending 2024: 0.3919701983199720112024
  • significant association on diff (n 55)
  • no one-way predictive lead/lag

Cross-correlation scan and Granger-style tests

Lead and lag

Cross-correlation by lag between Gross capital formation as share of GDP and GDP per person, constant 2015 US$; positive lag means Gross capital formation as share of GDP leadsCross-correlation by lag (positive lag: Gross capital formation as s leads)-1-0.500.51lag -5: r -0.04 (n 49)-5lag -4: r 0.07 (n 50)-4lag -3: r 0.01 (n 51)-3lag -2: r -0.29 (n 52)-2lag -1: r 0.02 (n 53)-1lag 0: r 0.63 (n 54), strongest0lag 1: r 0.04 (n 53)+1lag 2: r -0.15 (n 52)+2lag 3: r -0.06 (n 51)+3lag 4: r 0.01 (n 50)+4lag 5: r -0.07 (n 49)+5lag in periods; strongest at 0 (r 0.63), same period r 0.63
DirectionTestedlag 1 plag 2 plag 3 plag 4 plag 5 pmin pReading
Gross capital formation as share of GDP helps predict GDP per person, constant 2015 US$yes0.4940.5960.7580.8340.8020.4943no predictive information beyond own past
GDP per person, constant 2015 US$ helps predict Gross capital formation as share of GDPyes0.9960.6900.7390.7220.5930.5934no predictive information beyond own past

Granger-style F-tests on the primary transform: whether lagged values of one series improve a regression of the other on its own lags. Predictive information is not causation; a common driver that moves one series earlier produces the same pattern.

Reading: neither series adds predictive information about the other beyond its own past.

Cointegration
no (p 0.233)
Changepoints
Gross capital form: 2, GDP per person, co: 1
ADF p (levels)
0.096, 0.997
Service
causal-service/0.1.0

Not computed

Causal estimate

A causal estimate is attempted only for edges at mechanism supported or above: without a documented mechanism there is no graph to adjust on, and a regression coefficient alone would be pattern discovery dressed as a cause.

Alternative explanations for the association

What else could explain it

  • Both series trend with world development; the primary statistics use first differences to limit that, not remove it.
  • A common driver (income, urbanisation, technology) can move both series with different lags and produce a lead/lag pattern without any direct effect.
  • World aggregates hide country composition: a change in which countries report can move a world series.
  • Reverse direction: Economic output may act on Capital investment.
  • Both series are revised by their source; the analysis uses the current vintage, not the vintage available at the time.

What each rung means

Levels

  1. Level 0: No association found

    the overlapping data show no significant association.

  2. Level 1: Correlation only

    statistically associated in the overlapping periods; no direction, no mechanism.

  3. Level 2: Predictive lead/lag

    one series historically contains predictive information about the other.

  4. Level 3: Mechanism supported

    a documented physical, economic or institutional mechanism with cited evidence.

  5. Level 4: Causally supported

    a backdoor-adjusted estimate that survived refutation, on stated assumptions.

  6. Level 5: Established relation

    follows from engineering, accounting or scientific structure.

Every stored run, newest first

Analysis history

  • 2026-09-07 22:15 correlate level 1 n 55 causal-service/0.1.0