Sims (1980) Macroeconomics and Reality

Summary

Sims (1980) argues that the exclusion restrictions used to identify large simultaneous-equation macroeconometric models are "incredible" — not grounded in genuine economic theory but imposed as arbitrary normalizations. As an alternative he proposes treating all variables as jointly endogenous in an unrestricted Vector Autoregression (VAR), identified for structural interpretation only via the minimal assumption of a recursive (Cholesky) ordering. He demonstrates the approach on a six-variable quarterly system for the U.S. and West Germany, recovering impulse responses, variance decompositions, and block exogeneity tests that reveal the dominant role of money in U.S. nominal dynamics and prices in German dynamics.

Key Claims

Critique of Incredible Identification (Section 1)

• The exclusion restrictions of large structural models (Klein-Goldberger, MPS, FMP) are not derived from genuine economic theory; they are normalizations that make the model identifiable but have no credible theoretical basis.
• Three sources of the identification problem:
  • (A) A priori restrictions as normalizations. Researchers impose zero restrictions on equations to achieve identification, but these zeros cannot be derived from optimizing theory — they are assumed for convenience. Liu (1960) earlier made this point.
  • (B) Dynamics. Hatanaka (1975) showed that unknown lag lengths require an exogenous instrument for every right-hand-side (RHS) endogenous variable at every lag — a condition essentially never met. Under rational expectations, identifying the forward-looking component $b^+$ of dynamic response is orders of magnitude harder than identifying the backward-looking component $b^-$: even if information about future exogenous variables were available, cross-equation restrictions from the model's full solution would be needed.
  • (C) Forecasting vs. structure. False restrictions may still allow useful forecasting because restricted estimators beat unrestricted ones in high-dimensional problems even under misspecification; but this is a statistical argument, not a structural one.
• Conclusion: imposing false restrictions yields biased impulse responses and invalid policy experiments; the appropriate response is to minimize restrictions to those that are genuinely credible.

VAR as a Minimally-Restricted Alternative (Section 2)

• Treat all variables as jointly endogenous in a reduced-form VAR; estimate each equation by Ordinary Least Squares (OLS).
• Structural interpretation requires only one restriction beyond the reduced form: an ordering of variables for the Cholesky factorization of the residual covariance matrix. This recursive assumption is far less restrictive than the hundreds of exclusion restrictions in a structural model.
• The orthogonalized innovations — variances set to unity — are the "structural shocks" for purposes of impulse response analysis and variance decomposition.

Empirical Application — U.S. and West Germany (Sections 3–5)

System: Six quarterly variables — money $M$, real output $Y/P$, unemployment $U$, nominal wages $W$, price level $P$, import prices $PM$ — plus a constant and time trend.

Data periods: U.S.: 1949Q1–1975Q4 ($T = 108$); West Germany: 1958Q1–1976Q2 ($T = 74$).

Lag length. Sims (1980) tests $p = 4$ against $p = 8$ using a likelihood ratio (LR) statistic corrected by $(T - k)$ rather than $T$ (to reduce finite-sample over-rejection): $$\chi^2(144) = (T - k)(\log|\hat\Sigma_4| - \log|\hat\Sigma_8|)$$ Results: U.S. $\chi^2 = 166.09$ (barely exceeds 5% critical value $\approx 172$); Germany $\chi^2 = 142.53$ (below critical value). Both countries: $p = 4$ accepted; 144 unrestricted parameters.

Identification. Cholesky triangularization in the ordering $(M, Y, U, W, P, PM)$: money ordered first (does not respond contemporaneously to any other variable in the same quarter); import prices ordered last.

Impulse responses (Section 4 / Figures 1–4):

• U.S.: innovations to $M$ are very persistent in their effects on nominal variables $W$, $P$; real effects on $Y$ are modest.
• Germany: price innovations are the dominant disturbance, while U.S. money innovations have little effect.
• Import price ($PM$) innovations drive significant price and wage responses in both countries.

Variance decompositions (Tables III–IV):

Horizon $k$	U.S.: share of $W$ forecast error due to $M$	U.S.: share of $P$ forecast error due to $M$
1	0%	3%
9	37%	30%
33	64%	60%

Horizon $k$	Germany: share of $P$ forecast error due to $P$ itself	Germany: share of $Y$ forecast error due to $Y$ itself
1	86%	93%
33	~50%	~55%

U.S.: money dominates W and P at long horizons; Germany: prices and real Gross National Product (GNP) are dominated by their own innovations.

Block exogeneity tests (Table V). If rational expectations market-clearing held, the real sector $(Y, U, W, P)$ should not be Granger-caused by money $M$ or import prices $PM$. Sims tests this as a zero-restriction Wald test on cross-variable lag blocks:

Hypothesis	U.S. statistic	Germany statistic	Conclusion
Real sector exogenous to money	$\chi^2(24) = 64.63$, $p < 0.001$	$\chi^2(32) = 52.10$, $p \approx 0.01$	Rejected both countries
Real + money sector jointly exogenous	$\chi^2(36) = 42.54$, $p = 0.21$	—	Not rejected (U.S.)

The rejection of real-sector exogeneity to money is the key empirical finding: money matters for real variables in both countries, contradicting the strong-form rational expectations–market-clearing view.

Concepts Introduced or Extended

• Structural Identification — "incredible identification" argument: normalizations vs. genuine theory; Hatanaka dynamics; rational expectations forward-identification difficulty
• Vector Autoregression — empirical 6-variable application; $(T-k)$-corrected lag-length LR test; recursive Cholesky Impulse Response Functions (IRFs); variance decompositions; block exogeneity tests
• Granger Causality — block exogeneity tests as Granger non-causality tests across variable groups; empirical results for U.S. and Germany
• Impulse Response Function — recursive IRF methodology from orthogonalized Cholesky innovations
• Variance Decomposition — forecast error variance decompositions from the orthogonalized VAR

Entities Mentioned

• Christopher Sims — author; University of Minnesota (1980)
• Clive Granger — Granger causality concept underlying block exogeneity tests

Quotes

"It will be argued here that the restrictions used to achieve identification are often incredible, and that the construction of models that do not use such restrictions deserves consideration." (p. 1)

"By an 'incredible' identifying restriction, I mean one which, if used to determine the list of included and excluded variables in equations, could not survive careful examination of its justification." (p. 1)

"The main difficulty with using false restrictions for forecasting... is that the model cannot be used for policy analysis." (p. 3)

"In effect, what I am proposing is that the econometrician treat all the variables as jointly endogenous, and trace out the dynamic response of the system to various disturbances." (p. 17)

My Take

Sims (1980) is one of the most influential methodology papers in macroeconometrics. The critique of identification is devastating and correct: large structural models rested on hundreds of implausible exclusion restrictions, and the pretense of identifying structural shocks from such models was hard to defend. The VAR alternative is genuinely more honest about what the data can and cannot tell us. The empirical application is modest by modern standards (6 variables, 4 lags, recursive identification) but the conceptual contribution — block exogeneity tests as a way of testing structural hypotheses without committing to a full structural model — has been enormously productive. The one limitation acknowledged in the paper is that reducing restrictions to a minimum still leaves the Cholesky ordering as an assumption, and results can be sensitive to it.