Market power and the Laffer curve

Main article

Arthur Laffer, who was recently awarded the Presidential Medal of Freedom, is famous for sketching an inverted U-shaped diagram of the supposed trade-off between tax rates and tax revenues. The Laffer curve helps to characterize how firms as well as consumers respond to tax changes, and this research uses it to evaluate whether commodity taxes are an effective tool for financing government expenditure. Applying the idea to taxation of distilled spirits in Pennsylvania, where retail sales only take place through a state-run monopoly, the study shows how firms with market power change their pricing when taxes are cut and what that implies for state tax revenues.

The Laffer curve refers to a trade-off between tax rates and tax revenues. It originates from a 1974 conversation between economist Arthur Laffer, Wall Street Journal reporter Jude Wanniski, and politicians Dick Cheney and Donald Rumsfeld. During the meeting, Laffer is said to have argued that then President Ford’s proposed tax rise would actually reduce tax revenue collected. He demonstrated the effect by sketching the first Laffer curve on a napkin, a replica of which is in the archives of the National Museum of American History.

In our research, we present a novel characterization of the Laffer curve resulting from market power by taxed firms to evaluate whether commodity taxes are an effective tool to finance government expenditure and to characterize the behavioral responses to tax changes not only of consumers but also of firms.

We focus on the use of ad-valorem taxes (such as sales taxes and value-added taxes) as such taxes are an important source of government revenue – accounting for 17.4% of all US tax revenue and 32.7% of all tax revenue in the average developed country in 2013. In addition, they are often levied on product categories where firms have market power.

We find that an increase in the tax rate depresses quantity demanded, leading firms with market power to reduce their prices in order to protect their profits. On net, this strategic response lowers and shifts the Laffer curve, reflecting not only less incremental tax revenue collected but also a higher optimal tax rate. We conclude that anticipating the strategic responses of firms is vital to enacting effective tax policy.

One unique aspect of our study is the flexibility with which we allow firms to respond to tax policy. Much of the existing research on optimal taxation abstracts from the strategic behavior of firms, assuming instead that they operate in perfectly competitive industries or set price as a constant percentage mark-up over marginal costs.

While such restrictions undoubtedly increase modeling tractability, industrial organization economists have documented the existence of market power across a wide range of industries. We therefore rely on a model that does not require any ex-ante restrictions on the pricing behavior of firms.

The resulting characterization of the Laffer curve stems from the existence of market power in the taxed industry rather than the diminished incentives to supply labor or capital commonly highlighted in macroeconomics and public finance.

Theoretical results

Our study first presents a simple theoretical derivation of equilibrium tax revenue as a function of the tax rate – the Laffer curve – that allows for the existence of market power by a single taxed firm. We show that the shape and location of the Laffer curve depend not only on the tax rate and consumer demand elasticity, but also on the firm’s response to taxation.

For a wide variety of demand functions, the firm chooses to reduce its price in response to a rise in the tax rate. This in turn dampens increases in the tax-inclusive price that consumers face and the tax per unit that the government collects. On net, despite quantity adjustments to the lower tax-inclusive price, the firm’s price response has the potential to reduce tax revenue significantly.

We show that the strategic price response of the firm results in a downward shift and flattening of the Laffer curve, unraveling, at least partially, the government’s ability to generate tax revenue. The implication is two-fold:

• First, a tax agency that fails to anticipate this pricing response will find that tax receipts under its chosen policy fall short, possibly significantly, of its tax revenue objective.
• Second, even anticipating the behavioral response of the firm, the ability of the tax agency to stimulate tax revenue through active tax policy is constrained.

 

Empirical results: spirits taxation in the state of Pennsylvania

We evaluate the theoretical predictions in the context of Pennsylvania’s taxation of distilled spirits. Motivated by this setting, we use a model that allows for consumer substitution across a wide variety of products and competition among multi-product firms.

In characterizing the empirical Laffer curve, we are particularly interested in comparing the tax revenue expected by a ‘näıve’ tax agency that mistakenly expects firm prices to remain fixed after a tax change to that realized by an agency that correctly anticipates firms’ responses to its actions.

We exploit several notable features of the data:

• First, all spirit sales in Pennsylvania originate in state-run stores operated by a government agency, the Pennsylvania Liquor Control Board (PLCB).
• Second, the PLCB determines retail prices using a publicly known, simple pricing rule that translates wholesale prices into retail prices via a single, uniform ad-valorem tax. Thus, upstream firms effectively choose retail prices taking account of this tax.
• Third, retail prices are the same in all stores so that heterogeneity of consumer preferences materializes in different market shares across stores. This allows us to control for consumer tastes across products and demographics, and to capture flexible substitution patterns across products.

Taken together, these data features enable us to estimate a flexible demand model without imposing constraints on either firm conduct or market power, as we observe both wholesale and tax-inclusive retail prices in the data.

Our data contain approximately monthly information for the period from 2002 to 2004 on wholesale and retail price, store-level quantity sold, and gross receipts at the UPC level for all spirits and wines across all Pennsylvania liquor stores.

As of January 2003, the PLCB operated a system of 593 state-run retail stores across the state. We drop wholesale and outlet stores, and combine sales of stores in the same zip code, resulting in 456 local markets, which we link with data on local population and demographic characteristics using the 2000 census.

We restrict our sample to 375ml, 750ml, and 1.75l bottles of spirits, representing 80.9% of total spirit category sales by volume and 91.6% by revenue. Many of these products, while available across stores, are rarely purchased. We therefore only include the highest selling products, which together account for 80% of sales in each bottle size and spirit type category.

Our final sample consists of 3,377,659 observations of market and time-period level purchases of 312 spirits made by 37 firms that span categories of brandy, cordials, gin, rum, vodka, and whiskey.

Demand estimates capture well-known consumption patterns. Demand for spirits is elastic: on average, a 1% increase in the price of a particular spirit results in a 3.86% decline in that spirit’s bottle sales. Demand increases during the summer and the holiday season, and consumers value brandies, cordials, and whiskeys more than gins, rums, and vodkas.

There is, however, substantial heterogeneity of tastes across demographic groups. High-income households are less price-responsive; educated consumers strongly favor vodkas, whiskeys, and larger bottle sizes; and minorities prefer brandies to gins and whiskeys sold in smaller bottles. The model also yields reasonable substitution patterns: for example, the best substitute for a 750ml bottle of Captain Morgan Spiced Rum is a 750ml bottle of Bacardi Light Rum.

With these estimates in hand, we make use of the available wholesale pricing information to recover product-specific marginal costs. We assume that wholesale prices represent the non-cooperative equilibrium in an oligopoly model with horizontally differentiated products. We can then recover marginal costs using the firms’ profit maximization conditions.

Counterfactual analysis confirms that, as in the motivating monopoly model, the tax rate and upstream firm prices are strategic substitutes: a 1% tax rate increase above the observed level of 53.4% (30% mark-up × 18% sales tax) is on average met by a 0.20% reduction in the upstream prices charged by firms, thus limiting the ultimate effect on the retail price facing consumers. We also find substantial heterogeneity in this ‘undoing’ effect as it is typically greatest among inexpensive and 375ml products.

Characterizing the Laffer curve in the Pennsylvania liquor market

We use our demand and upstream marginal cost estimates to measure the effect of firms’ pricing responses on state tax revenue.

Figure 1 summarizes our findings by depicting the Laffer curve for the Pennsylvania liquor market under two different market equilibria. The red ‘näıve’ Laffer curve corresponds to the tax rate-revenue trade-off of a tax agency that – mistakenly – believes that upstream firms lack the interest or ability to react to changes in tax policy. For this ‘mechanical effect’ of taxation, firms do not revise their pricing, but consumers adjust their purchases in response to changes in retail prices.

We find that for small values of the tax rate, the Laffer curve is steep, reflecting lower demand elasticities for spirits. As we move past the peak, the downward sloping region of the Laffer curve becomes flatter as demand elasticity stabilizes.

We identify the degree to which upstream firms can unravel the PLCB’s taxation policy by comparing the näıve Laffer curve to the dashed ‘firm response’ Laffer curve where firms exploit their market power and revise their pricing in response to the PLCB’s näıve policy.

This is the ‘behavioral response’ of taxation, which accounts for the pricing decisions of upstream firms. We observe that the ‘firm response’ Laffer curve is flatter and lies below the näıve Laffer curve for tax rates below the PLCB’s current choice. The change in location and shape reflects firms maximizing profits by moving their wholesale prices in the opposite direction of any change in the PLCB tax rate.

We conclude that current tax policy overprices spirits, restricts demand, and depresses tax revenue regardless of the ability of firms to respond to commodity taxation. The two equilibria produce substantially different revenue-maximizing tax rates, however: 30.7% with unchanged wholesale prices relative to 39.3% under optimal firm pricing.

The fact that the agency chooses a higher optimal tax rate in anticipation of wholesale price adjustments reflects the induced lower pass-through of the tax rate increase, thereby limiting possible declines in quantity demanded under the new tax regime.

Policy implications

Our simple theoretical model generates two implications for policy-makers related to the value of anticipating firms’ strategic responses. We now evaluate the quantitative magnitude of each prediction using the estimated equilibrium model.

First, we evaluate the cost of näıve policy-making in our context. From Figure 1, we observe that a näıve agency would conclude that the state could increase tax revenues by 7.75% (or $28.74 million) by reducing the tax rate from 53.4% to 30.68%.

At this tax rate, firms choose wholesale prices that are on average 3.79%, or 34 cents, higher than those observed in the data. While this change in firm prices may appear small, the fact that firms price on the elastic region of demand leads to a significant change in quantity demanded by consumers.

Ultimately, the offsetting price adjustment allows firms to convert 87% of the incremental tax revenue into profit. Equivalently, firms’ response limits tax revenue gains to only 12.97% of the näıvely forecasted incremental revenues ($3.73 vs. $28.74 million) – a sizable budget shortfall.

In contrast, an agency that correctly predicts the firm response would choose to lower the tax rate to only 39.31% when attempting to maximize tax revenue. While this tax rate level raises tax receipts by 2.23% over baseline, the incremental revenue is far less than the 7.75% increase we predict absent a firm response.

Thus, the empirical results confirm that the behavioral firm response materially disciplines the ability of government to generate revenue to fund its expenditures. Moreover, we find that profits among upstream firms increase 30.80%, as does their share of integrated industry profits – from 29.5% to 34.9%.

Conclusion

Put together, our results highlight that the strategic response of firms has a quantitatively important impact on tax policy design and the government’s ability to finance expenditure via commodity taxation. Our study therefore underscores the importance of recent efforts by the Congressional Budget Office to incorporate the behavior not only of workers and consumers but also of firms when it evaluates proposed legislation – a practice known as ‘dynamic scoring’.

This article summarizes ‘Market Power and the Laffer Curve’ by Eugenio J Miravete , Katja Seim and Jeff Thurk, published in Econometrica in September 2018.

Eugenio J. Miravete is at the University of Texas at Austin. Katja Seim is at the Wharton School at the University of Pennsylvania. Jeff Thurk is at the University of Notre Dame.