Theoretical Inflation During Stay-in-Place Behaviorby Rachel Soloveichik

Virtual FCSM Conference, November 2021

Disclaimer: The views in this presentation reflect those of the author and not necessarily those of the Department of Commerce or the Bureau of Economic Analysis.

Outline of Talk

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Preview of empirical results

Discussion of price measurement literature

Imputing prices for unavailable products:

Official price index method

Theoretical method for products which are only available remotely

Theoretical method for products which are completely unavailable

Measuring theoretical inflation by state:

Hypothetical impact of a full stay-in-place policy

Observed impact of actual stay-in-place policies

Preview of Results: Cumulative Inflation in U.S.

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This paper doesn’t study any health effect, so it doesn’t address the benefits from stay-in-place policies.  Instead, it focuses on quantifying one cost using price measurement theory.

Preview of Results: Inequality Across States

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Previous Price Index Research

Theoretical papers studying imputed prices:

“New Goods”: (Hausman 1999), (Hausman 1997), (Petrin 2002), (Goolsbee and Petrin 2004), (Berndt et al. 1996), (Nordhaus 1996), (Diewert and Feenstra 2019), and (Diewert et al. 2019)

“Outlet Substitution Bias”: (Reinsdorf 1993), (Hausman and Liebtag 2009), and (Greenlees and Mclelland 2008)

“Variety Bias”: (Feenstra 1994), (Broda and Weinstein 2010), (Handbury and Weinstein 2014), and (Dolfen et al. 2021)

Measurement papers studying practical issues:

Price aggregation formulas: (Diewert 2003), (Diewert 2001), (Passero, Garner, and McCully 2015), and (Barret, Levell, and Milligan 2015) 

Price weights in pandemics: (Cavallo 2020) and (Diewert and Fox 2020)

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Theoretical Price Measurement Problem

Standard price indexes summarize prices for products 1 to n into a single value

Laspeyres Price Indext = w10(p1t/p10)+ w20(p2t/p20)+...+ wn0(pnt/pn0)

Standard price index formulas require prices for every product in the market basket

Economists generally can’t observe unavailable product prices

Some businesses might list a price for unavailable products – but that list price isn’t economically meaningful

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Some businesses might list a price on their website – but that listed price is not economically meaningful

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Official Price Index Imputation Method

Bureau of Labor Statistics (BLS) assumption:

Imputed prices for unavailable products track observed prices for similar available products

This assumption works well in normal economic times (Bradley 2003)

BEA’s price indexes are based on BLS price indexes

Products which are only available remotely:

Assumption: BLS links remote prices at a retail outlet to the previous in-person prices at that retail outlet without adjustment

Products which are completely unavailable:

Assumption: BLS links each unavailable product with a similar available product and uses that product’s observed prices as an extrapolator

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I’m fairly sure that’s how BLS handled products which are only available remotely.  In fact, BLS did the same for essential products early in the pandemic because they didn’t want to send surveyers to stores unnecessarily.

I’m less sure that’s how BLS handled completely unavailable products.  It’s also possible that they just took reported list prices for those products from store websites and other sources.  The two different methods might matter during an era of very rapid inflation – but that wasn’t the case early in the coronavirus pandemic.

In practice, this paper isn’t really concerned with measuring official inflation precisely.  So, it’s not going to analyze BLS’s method in much detail.

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Products Only Available Remotely

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Assumption: remote shopping is only a partial substitute for in-person shopping

All nonessential goods and some nonessential services are unavailable in-person but available remotely during a full stay-in-place policy.

The welfare loss from unavailable in-person shopping tracks the welfare gain from the introduction of remote shopping

Restaurant Meal: In-Person vs. Remote

In theory, one could have a bad equilibrium where everybody prefers remote but they’re stuck in-person because of coordination issues, government rules, etc.  That story might make sense for something like office work or medical care.  But it clearly doesn’t apply to products like electronics, books, restaurant meals where there was a larger and easy to use remote market in 2019.

Completely Unavailable Products

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Assumption: remote services aren’t even partial substitutes for some in-person services

Most nonessential in-person services are completely unavailable during a full stay-in-place policy

Assumption: the welfare loss from completely unavailable products tracks the welfare gain for tourists from specialized leisure amenities

Gambling: In-person vs. Remote

In general, services that can be delivered remotely remained available throughout the coronavirus pandemic.  But sports cable was canceled because live events were considered too dangerous.

It may be true that the remote service is produced by the same industry as the in-person service and has the same product code.  But that doesn’t mean that they’re even partial substitutes.

Appendix A has much more details on the model set-up and the data used to solve it.

If anything, the price premium that tourists pay for leisure amenities is probably a lower bound.  After all, most people think that Broadway plays, skiing, and other tourist amenities are less important than non-emergency medical care, childcare, etc.

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Calculating Theoretical Inflation

Products which are only available remotely:

Elasticity of online shopping is estimated at 4.3 (Dolfen et al. 2021)

Theoretical price for product = (official price for product)*(1+1/4.3) 

Products which are completely unavailable:

Elasticity for unavailable products is estimated at 1.7 based on a model of tourist behavior and BEA’s regional price parities

Theoretical price for product = (official price for product)*(1+1/1.7)

Aggregate inflation formula:

Theoretical inflation = Official inflation +

 (normal budget share for products that are only available remotely)*0.23+

(normal budget share for completely unavailable products)*0.59

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The 4.3 number is based on pre-pandemic data.  So, it measures elasticity relative to offline shopping rather than elasticity when non-essential stores are closed.

Given those two parameters, one can easily calculate aggregate inflation by simply multiplying the budget share for products which are only available remotely by 0.23 and the budget share for products that are completely unavailable by 0.59

Measuring Theoretical Inflation By State:Hypothetical Impact of a Full Stay-in-Place Policy

Assumptions:

Goods and services purchased remotely in 2019 are available

Essential in-person services are available, but non-essential in-person services are either only available remotely or completely unavailable

Goods purchased in-person at essential retailers are available, but other goods are only available remotely

Datasets used:

Product detail by state and industry from the 2017 Economic Census

BEA’s statistics report 15 categories of consumer spending by state

Earnest Research reports remote shopping by purchaser residence 

Section 2 of the paper estimates spending and availability for 52 subcategories of consumer spending by state

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In theory, the line between remote services and essential services is a little fuzzy.  For example, which category does housing fall into?  In practice, this distinction doesn’t really matter for product unavailability – so I won’t discuss it further.

Essential Products in 2019

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Nonessential Goods Sold in Essential Stores

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Theoretical Inflation in a Full Stay-In-Place Policy

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Measuring Theoretical Inflation By State:Observed Impact of Actual Stay-in-Place Behavior

Data tracking actual stay-in-place behavior by state and month was not located

Some sources track official government rules – but the actual stay-in-place behavior depend on voluntary choices as well as laws

Google’s COVID-19 community mobility reports are used to proxy for theoretical inflation:

Assumption: time spent at retail and recreational locations proxies for availability of nonessential products sold both there and elsewhere

Assumption: Google’s sample of smartphones is representative of overall consumer spending

Assumption: theoretical inflation is linearly with product unavailability

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The paper does not distinguish between consumers who could not purchase a product because it was banned by the government, and businesses which stopped producing a product to avoid coronavirus transmission, consumers who stopped buying a product because of coronavirus transmission, or other complex reasons for product unavailability.  

Google tracks time spent at grocery stores and pharmacies in a separate category – so those essential retailers don’t really influence this paper’s analysis.  Similarly, health care facilities aren’t included in the retail and recreation category.  The essential businesses studied here include general merchandise stores, auto supply stores, laundromats, etc. stayed open.  

Raw Monthly Retail Time, Selected States

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The ATUS regional data doesn’t match BEA’s geofips data precisely.  The paper uses its best judgment to match the regions which are close, and then drops regions which can’t be matched.

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Adjustments to Google’s Raw Retail Time

Daily retail time is higher during moderate weather, so the paper controls for daily weather

Weather matters more when sunset is later because people have more time to enjoy the pleasant weather after work

The impact of weather is similar before and during coronavirus

Daily retail time is adjusted for holidays using data from the American Time Use Survey (ATUS)

Google’s category ‘retail and recreation’ includes essential stores – so retail time can’t fall to zero

Adjusted mobility formula: (observed mobility)/(potential mobility)

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Adjusted vs. Unadjusted Mobility, Smoothed

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The unadjusted mobility data show much more recovery than the adjusted data.  This is due to the fact that mobility is seasonal and normally increases when weather gets good.  

Unadjusted Minus Adjusted Mobility, Average 3/20-6/21

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Average Theoretical Inflation by State

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This graph shows that high income states have both higher theoretical inflation in a full stay-in-place policy, and also higher theoretical inflation in actual stay-in-place behavior.  The two lines have the same slope because high income states typically imposed much stricter stay-in-place policies than poorer states.  In other words, all state exempted the same absolute spending share.

Cumulative Inflation, U.S. Average

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Inequality Across States by Quarter

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20 percent for available housing; 27 percent for available goods; 5 percent for unavailable goods; 31 percent for available services; 17 percent for unavailable services; and 2 percent for unavailable amenities

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Conclusion

This paper developed a simple formula to calculate theoretical inflation during stay-in-place behavior

The theoretical model in this paper does not imply any data problems or computational mistakes with published government price indexes

Revisions to monthly inflation:

0.11 (official) vs. 0.47 (theoretical) percentage point for 2020

0.22 (official) vs. -0.11 (theoretical) for first half 2021

Higher income states have higher theoretical inflation

Based on official statistics, the paper calculates that real regional inequality in 2020 grew 3 percent

This reverses to a 4 percent decline in theoretical regional inequality

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Partial reopenings are generally much more complicated than full stay-in-place orders.  In addition, compliance with official government orders has fallen dramatically.  As a result, it may be much harder to analyze prices in the Q2 than Q1.

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