Overview
This project examined the relationship between cigarette prices and per-capita cigarette consumption using U.S. state data.
The analysis began with a simple cross-sectional regression and then compared progressively different specifications, including pooled OLS, state and year fixed effects, first differences and instrumental-variable estimation. The objective was to examine how estimated cigarette-price elasticity changes when the model accounts for observed controls, persistent differences across states and potential price endogeneity.
Analytical Question
How responsive is per-capita cigarette consumption to changes in real cigarette prices, and how sensitive is the estimated relationship to econometric specification?
A central issue is that cigarette prices may be correlated with other determinants of cigarette consumption. States can differ in smoking norms, regulation, economic conditions and other factors that may affect both prices and consumption, making a simple price-consumption regression difficult to interpret causally.
Data
The core analysis uses a state-level cigarette dataset covering 48 continental U.S. states in 1985 and 1995, providing 96 state-year observations.
The primary outcome is the logarithm of cigarette packs consumed per capita. Real cigarette price is constructed by adjusting average price by the CPI and then taking its logarithm.
The panel specifications also include real per-capita income and state unemployment. Supplemental state economic controls were assembled using FRED data, including unemployment, House Price Index and minimum-wage series.
Methodology
The analysis compares several approaches.
A 1995 cross-sectional OLS regression provides the initial estimate of price elasticity. Panel specifications then use pooled OLS, state fixed effects, year effects and two-way state-and-year fixed effects.
A 1985–1995 first-difference specification examines changes within states over the decade.
Finally, instrumental-variable models use changes in state tax measures as instruments for changes in real cigarette prices. Robust or state-clustered standard errors are used depending on the specification.
Price Endogeneity
Price is potentially endogenous because factors that affect cigarette consumption may also be related to cigarette prices.
State fixed effects remove persistent, time-invariant differences across states, while year effects account for factors common across states at a point in time. First differencing provides another way of eliminating time-invariant state characteristics.
The IV analysis takes a different approach by using changes in state tax variables to generate variation in cigarette prices. The first-stage diagnostics show strong instrument relevance, although interpreting the IV estimates causally still depends on the instruments satisfying the required exclusion assumptions.
Results & Interpretation
The simple 1995 OLS model estimated a cigarette-price elasticity of approximately −1.21, indicating a strong negative association between real cigarette prices and per-capita consumption.
Across the panel specifications, the estimated elasticity changes materially. Pooled OLS produces an estimate of approximately −1.33, while the two-way fixed-effects and first-difference specifications produce estimates near −0.94.
The instrumental-variable specifications produce larger-magnitude estimates. Using both submitted tax instruments gives an estimated elasticity of approximately −1.25. The IV first stage is strong according to the reported weak-identification diagnostics, while the overidentification test does not reject at the 5% level.
Rather than pointing to one specification as mechanically “correct,” the exercise illustrates how assumptions about unobserved heterogeneity and identification affect both the estimated coefficient and the strength of the interpretation that can be attached to it.
Regression comparison
Estimated elasticity of cigarette demand across four specifications.
| Specification | Pooled OLS | Two-way fixed effects | First difference | IV · both tax instruments |
|---|---|---|---|---|
| Price elasticity | −1.332*** | −0.935*** | −0.935*** | −1.253*** |
| Standard error | (0.154) | (0.146) | (0.148) | (0.205) |
| Real per-capita income | 0.331* | 0.454* | 0.454 | 0.450 |
| Unemployment | 0.016 | −0.136*** | −0.136*** | — |
| Observations | 96 | 96 | 48 | 48 |
| R² | 0.552 | 0.919 | 0.623 | 0.539 |
* p < .10, ** p < .05, *** p < .01. Standard errors are robust for OLS, first differences and IV; clustered by state for two-way fixed effects.
This is a method comparison, with different controls across specifications. The IV model uses changes in real per-capita income but excludes the unemployment change included in the first-difference model. Its instruments are changes in the submitted sales-tax and excise-tax variables.
IV diagnostics
- Kleibergen–Paap F
- 60.169
- Hansen J
- 2.893
- Hansen p-value
- 0.0889
The first-stage diagnostics support instrument relevance. The overidentification test does not reject at the 5% level; it does not prove the exclusion restriction or establish instrument validity.
What I Learned
The project reinforced that econometric analysis is not simply a matter of running a regression and reporting a coefficient.
Comparing pooled OLS, fixed effects, first differences and instrumental variables showed how the same economic question can produce materially different estimates depending on the variation being used and the assumptions imposed by the model.
It also strengthened my practical experience with Stata, panel-data methods, robust and clustered inference, data integration and instrumental-variable diagnostics. Most importantly, the project developed my understanding of the distinction between a statistically significant relationship and a defensible causal interpretation.