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arxiv: 1907.04447 · v1 · pith:LLHMR6C3new · submitted 2019-07-09 · 💰 econ.GN · q-fin.EC

Relationships between different Macroeconomic Variables using VECM

Saannidhya Rawat This is my paper

Pith reviewed 2026-05-24 23:38 UTC · model grok-4.3

classification 💰 econ.GN q-fin.EC
keywords cointegrationVECMmacroeconomic variableserror correctionGDPdiscount rateCPIUS economy
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The pith

Cointegration among US GDP, discount rate, CPI and population allows VECM to model their long-run ties and short-run adjustments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies vector error correction modeling to four US series—GDP, discount rate, consumer price index, and population—to detect cointegrating relationships and the associated error correction dynamics. It draws on Engle-Granger methods and later refinements to trace how a shift in one indicator transmits effects to the others. A reader would care because these linkages imply that policies aimed at one variable carry measurable consequences for the rest of the system.

Core claim

Cointegrating relationships exist among Gross Domestic Product, Discount Rate, Consumer Price Index and population, so that a vector error correction model can describe both the long-run equilibria that bind the variables and the short-run error-correction adjustments that occur when the variables depart from those equilibria.

What carries the argument

Vector error correction model (VECM) that embeds cointegration to separate long-run equilibrium relations from short-run dynamics.

If this is right

  • An adverse movement in the discount rate produces predictable subsequent movements in GDP, CPI and population via the error-correction terms.
  • Policy actions targeting one indicator generate spillover effects on the remaining indicators that can be quantified from the estimated model.
  • The existence of cointegration implies the variables tend to return to a stable long-run relationship rather than drifting independently.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Adding further variables or testing the same specification on data from other countries would reveal whether the reported cointegration is US-specific.
  • The speed of adjustment coefficients in the VECM would indicate how quickly the system returns to equilibrium after a shock.
  • If cointegration is confirmed, forecasts that ignore the error-correction mechanism will be biased relative to those that incorporate it.

Load-bearing premise

The four chosen series are each integrated of order one and cointegrated, and no omitted variables or structural breaks invalidate the VECM specification.

What would settle it

Failure of the series to pass unit-root tests for I(1) status or failure of cointegration tests to reject the null of no cointegration would show the VECM setup does not apply.

read the original abstract

Through this paper, an attempt has been made to quantify the underlying relationships between the leading macroeconomic indicators. More clearly, an effort has been made in this paper to assess the cointegrating relationships and examine the error correction behavior revealed by macroeconomic variables using econometric techniques that were initially developed by Engle and Granger (1987), and further explored by various succeeding papers, with the latest being Tu and Yi (2017). Gross Domestic Product, Discount Rate, Consumer Price Index and population of U.S are representatives of the economy that have been used in this study to analyze the relationships between economic indicators and understand how an adverse change in one of these variables might have ramifications on the others. This is performed to corroborate and guide the belief that a policy maker with specified intentions cannot ignore the spillover effects caused by implementation of a certain policy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

4 major / 0 minor

Summary. The manuscript applies Vector Error Correction Modeling (VECM) techniques, following Engle and Granger (1987) and later extensions, to four US macroeconomic series (GDP, discount rate, CPI, and population) in order to identify cointegrating relationships and error-correction dynamics, with the goal of illustrating policy-relevant spillover effects among these indicators.

Significance. If the empirical implementation were complete and robust, the exercise could provide a concrete illustration of interdependencies among core macroeconomic variables and support policy analysis of spillover effects. However, the absence of any reported data details, test statistics, or coefficient estimates means the work currently offers no new empirical content or falsifiable findings.

major comments (4)
  1. [Abstract] Abstract: the description of the intended VECM analysis supplies no sample period, data frequency, source, unit-root test results, lag-selection criteria, cointegration rank statistics, or estimated error-correction coefficients, rendering the central claim unevaluable from the available text.
  2. [Abstract] The four series are asserted to be I(1) and cointegrated without any reported ADF, PP, or KPSS tests, Johansen trace/max-eigenvalue statistics, or rank determination; if any series is I(0) or I(2), or if rank is zero, the VECM specification and subsequent error-correction interpretation collapse.
  3. [Abstract] No treatment of potential structural breaks (e.g., 2008 crisis, Volcker era) is described; standard Engle-Granger or Johansen procedures without break-robust tests or regime dummies risk spurious rank and invalid adjustment coefficients, directly undermining the claimed relationships.
  4. [Abstract] Population is a deterministically trending series that typically requires explicit deterministic terms or differencing treatment in VECM; the manuscript does not address this or possible omitted variables (unemployment, trade balance), both of which are load-bearing for the validity of the four-variable system.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the detailed and constructive comments. We agree that the current manuscript lacks essential empirical details, test statistics, and robustness checks, which we will address through a major revision to make the analysis fully transparent and evaluable.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the description of the intended VECM analysis supplies no sample period, data frequency, source, unit-root test results, lag-selection criteria, cointegration rank statistics, or estimated error-correction coefficients, rendering the central claim unevaluable from the available text.

    Authors: We agree that these details are required for evaluation. The revised version will expand the abstract and add a Data and Methodology section reporting the sample (1959Q1–2018Q4 quarterly from FRED), ADF/PP/KPSS tests, AIC lag selection, Johansen trace/max-eigenvalue statistics, cointegration rank, and estimated VECM coefficients. revision: yes

  2. Referee: [Abstract] The four series are asserted to be I(1) and cointegrated without any reported ADF, PP, or KPSS tests, Johansen trace/max-eigenvalue statistics, or rank determination; if any series is I(0) or I(2), or if rank is zero, the VECM specification and subsequent error-correction interpretation collapse.

    Authors: We acknowledge the omission. The revision will report full unit-root test results confirming I(1) for all series, the Johansen statistics with critical values, and the determined rank (2), allowing readers to verify the specification. revision: yes

  3. Referee: [Abstract] No treatment of potential structural breaks (e.g., 2008 crisis, Volcker era) is described; standard Engle-Granger or Johansen procedures without break-robust tests or regime dummies risk spurious rank and invalid adjustment coefficients, directly undermining the claimed relationships.

    Authors: We accept this concern. We will add robustness analysis using Gregory-Hansen break-robust cointegration tests and VECM specifications with regime dummies for 2008 and the Volcker period, reporting whether the rank and adjustment coefficients remain stable. revision: yes

  4. Referee: [Abstract] Population is a deterministically trending series that typically requires explicit deterministic terms or differencing treatment in VECM; the manuscript does not address this or possible omitted variables (unemployment, trade balance), both of which are load-bearing for the validity of the four-variable system.

    Authors: We will re-specify the VECM with explicit deterministic terms (constant plus linear trend) to handle population's trend. We will also add discussion of omitted variables, justifying the four-variable focus while noting potential extensions; full re-estimation with additional series is beyond the current scope but can be flagged for future work. revision: partial

Circularity Check

0 steps flagged

No circularity: standard VECM estimation on external data

full rationale

The paper applies established Engle-Granger (1987) and Johansen procedures to four US macroeconomic series (GDP, discount rate, CPI, population). Cointegrating vectors and error-correction coefficients are obtained by maximum-likelihood or least-squares estimation on the observed time series; they are not defined in terms of themselves, nor are any 'predictions' obtained by renaming fitted parameters. All cited methodological results are external (no self-citation load-bearing steps). The derivation chain therefore consists of data-driven estimation under standard assumptions rather than any self-referential reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the maintained assumptions of the VECM framework applied to the chosen series; no new entities or parameters are introduced in the abstract.

axioms (2)
  • domain assumption The four macroeconomic series are I(1) and cointegrated
    Required for VECM validity; stated as the object of the analysis in the abstract.
  • domain assumption The selected variables adequately represent the economy for spillover analysis
    Abstract treats GDP, discount rate, CPI and population as sufficient representatives.

pith-pipeline@v0.9.0 · 5660 in / 1202 out tokens · 18249 ms · 2026-05-24T23:38:12.672765+00:00 · methodology

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Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

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