Do Wages Lead Inflation, or Lag Land-Driven Cost Pressures?

The Question

The usual public debate often collapses into a wage-price spiral story: wages rise, firms raise prices, inflation follows. This analysis tests a different timing story.

The empirical chain is credit and mortgage conditions first, housing and land prices second, shelter/rent/CPI pressure third, and wage growth last.

Main read The results are more consistent with a land/housing-cost transmission channel than with a wage-led inflation channel. Wages appear downstream of prior shelter and CPI pressure in forecasting tests.

Stage 1Mortgage rates and credit conditions validate the marginal housing bid.

Stage 2Housing and land prices show predictive content for shelter-linked CPI pressure.

Stage 3Shelter, rent, and CPI pressure show predictive content for later wage growth.

Stage 4Paired direction tests compare cost pressure -> wages against wages -> cost pressure.

How To Read The Charts

All lines are either year-over-year growth rates or percentage-point changes. The zero line is not a target; it is the boundary between acceleration and decline. The key visual question is not whether two lines overlap perfectly, but whether pressure tends to appear upstream before wages adjust.

Chart tip Look for sequence: housing or shelter pressure rises first, then wage growth catches up later. A lead-lag chart is evidence about timing and predictive content, not proof of structural causality.

1. The Full Chain In One View

This overview puts mortgage-rate changes, NHPI inflation, CPI shelter inflation, and wage growth on the same timeline. It is intentionally broad: the goal is to see whether the system behaves like a sequence rather than a single simultaneous event.

Credit, housing, shelter CPI, and wage growth overview chart — Credit, housing, shelter CPI, and wage growth. Mortgage-rate changes are a credit-condition indicator; NHPI is the housing-price state variable; CPI shelter and wage growth are downstream measures.

How to read it Do not over-focus on month-to-month wiggles. The important pattern is that housing and shelter pressures can move sharply before wage growth shows its strongest response.

2. Housing Prices Before Shelter CPI Before Wages

The NHPI, shelter CPI, and wage chart is the clearest version of the proposed chain. Housing prices are treated as a state variable for the shelter-cost environment; wages are tested as a delayed adjustment to the cost of living.

NHPI, CPI shelter, and wages chart — NHPI inflation, CPI shelter inflation, and wage growth. The lead-lag scan identifies NHPI inflation as strongest against mortgage-interest CPI at a 22-month lead, and CPI shelter inflation as strongest against LFS hourly wage growth at a 12-month lead.

Link	Best predictor	Best target	Best lag	Correlation	N
Credit/rates -> housing	mortgage_credit_growth	nhpi_canada_inflation	0 months	0.559	423
Housing -> shelter/rent CPI	nhpi_canada_inflation	cpi_mortgage_interest_inflation	22 months	0.628	510
CPI shelter/rent -> wages	cpi_shelter_inflation	lfs_hourly_wage_growth	12 months	0.577	341

3. Shelter And Rent Pressure Against Wage Growth

This chart narrows the view to CPI shelter, CPI rent, and wage measures. The wage lines are noisier than price indexes, but the direction test asks a specific question: do shelter costs forecast wages better than wages forecast shelter costs?

CPI shelter and wage growth chart — CPI shelter and rent inflation compared with LFS hourly wage growth and SEPH hourly earnings growth.

+18.3Direction score: CPI shelter -> LFS hourly wage growth

+18.7Direction score: mortgage-interest CPI -> SEPH hourly earnings

+4.9Average direction score across tested pairs

How to read it A positive direction score means the cost-pressure-to-wages tests were stronger than the reverse wage-to-cost-pressure tests. It is a forecasting comparison, not a causal estimate.

4. Direction Test: Wage-Led Or Wage-Lagged?

The central test compares two directions for each wage and cost measure: cost pressure leading wages, and wages leading cost pressure. Most combinations favor the delayed wage catch-up interpretation, though weekly earnings have two counterexamples.

Direction test summary chart — Positive bars favor cost pressure leading wages. Negative bars favor a wage-led channel in the paired Granger direction test.

Wage measure	Cost pressure	Direction score	Read
SEPH hourly earnings	Mortgage-interest CPI	+18.7	Strongly wage-lagged
LFS hourly wage	CPI shelter	+18.3	Strongly wage-lagged
LFS hourly wage	All-items CPI	+9.5	Wage-lagged
SEPH weekly earnings	Mortgage-interest CPI	-16.2	Counterexample

5. Regression Checks

The reduced-form regressions use lag choices suggested by the lead-lag scans and HAC/Newey-West standard errors. They are meant to check whether the sequence survives a more formal reduced-form setup.

Model	Key term	Coefficient	p-value	Interpretation
NHPI inflation	mortgage_rate_change_lag0	3.569	0.00065	Rate changes have predictive content for housing-price inflation in this specification.
NHPI inflation	credit_impulse_lag8	5.264	0.00042	Credit impulse enters as an upstream housing variable.
CPI shelter inflation	nhpi_canada_inflation_lag19	0.180	0.00266	Housing-price inflation predicts later shelter inflation.
LFS hourly wage growth	cpi_shelter_inflation_lag12	0.412	0.00004	Shelter inflation predicts later wage growth.

6. Dynamic Chain Model

The pipeline estimated a VAR for the preferred monthly variables. These impulse-response-style plots are not structural shocks, but they help visualize whether the dynamic ordering is consistent with the chain.

Dynamic chain impulse response chart — Mortgage or credit shock response across NHPI, CPI shelter, and wage growth.

Shelter to wages impulse response chart — Shelter CPI shock response in wage growth.

Wages to shelter impulse response chart — Wage-growth shock response in CPI shelter.

7. What This Does And Does Not Prove

The evidence supports a timing interpretation: wages look downstream of shelter and CPI pressure in forecasting tests. That is not the same as proving a structural causal model.

Supported read Wages appear more like delayed catch-up to land and housing-driven cost pressure than like the initiating source of inflation.

Boundary Lead-lag scans, Granger tests, and reduced-form regressions identify predictive content. They do not prove policy-invariant causality.

Suggested Twitter/X Thread Breakdown

Use the boxed sections above as screenshot panels. A practical thread would be 8 to 10 posts; each post should make one claim and attach one screenshot.

Post 1: HookCanadian inflation is often framed as a wage-price spiral. I tested a different sequence: credit -> housing/land -> shelter CPI/rent -> delayed wages.

Post 2: MethodThis is a lead-lag and forecasting exercise using local StatCan and Bank of Canada data. It is not a structural causality claim.

Post 3: Full chain chartShow the overview chart and explain that the goal is sequence, not perfect overlap.

Post 4: Housing to shelterShow NHPI vs CPI shelter/wages. Note the best housing-to-CPI link: NHPI leading mortgage-interest CPI by 22 months.

Post 5: Shelter to wagesShow CPI shelter vs wages. Note CPI shelter leading LFS hourly wage growth by 12 months in the lead-lag scan.

Post 6: Direction testExplain direction scores: positive favors cost pressure -> wages; negative favors wages -> cost pressure.

Post 7: Regression checkUse the regression table. Highlight CPI shelter inflation lag 12 predicting wage growth with p-value near 0.00004.

Post 8: CaveatLead-lag structure is not structural causality. The honest claim is predictive timing: wages look downstream, not upstream.

Post 9: ConclusionThe evidence is more consistent with a land/housing-cost transmission channel than a wage-price spiral.

Post 10: Data noteState that the analysis uses local StatCan ZIP exports and Bank of Canada CSVs, with outputs reproducible from the Python pipeline.