Figure 2: Used Prices across Generations of the Apple iPad

We begin our analysis in 2010, when the first Apple iPad model was introduced and spurred the surge in sales shown in figure 1.⁴ After dropping a few outliers, observations with incomplete data, and models from Motion Computing (which produces specialty tablets for industrial applications), our sample contains 4,049 used price observations for a set of 209 specific models at different points in time. The basic features of our sample are shown in table 1.⁵ As can be seen from the total number of observations, the variety of tablet PCs available for purchase (both new and used) grew substantially over the five-year period. Apple and Samsung dominated the market until the Microsoft Surface was introduced in 2013. The median price of used tablets sold was about $700 in 2010 and was roughly half that amount in 2014, for an average annual price decline of about 17 percent. Over the same period, the average age increased by about 8 months, reflecting the nascent nature of this new platform.

Table 2 shows the evolution of major characteristics for newly introduced models over the sample period. Processor clock speed for the median new model moved sideways through 2012, then increased sharply, a pattern due in large part to the entry of Microsoft tablets in the market. System memory climbed for the median new model fairly steadily at an average annual rate of 68 percent. Median hard disk storage, by contrast, was fairly stable over the five-year period.

Adjusting for Quality Improvements

As has been well documented, the fast pace of technological change in the high-tech sector presents challenges in the measurement of inflation, because the premium paid for successive product vintages reflects both price inflation and payment for improved performance relative to earlier models (Aizcorbe, 2014). One approach to apportioning this premium into quality and constant-quality price difference is to use hedonic regressions, an approach employed by many previous studies in the context of price measurement of high-tech products (e.g. Berndt and Rappaport, 2001). This methodology controls for characteristics that are associated with performance valued by consumers by removing the portion of price variation correlated with performance characteristics, which produces quality-adjusted estimates of price variation.

For several reasons, our analysis of prices in the market for used tablet computers is more complicated than conventional hedonic studies. First, advances in technology that reduce the cost of producing a computer with a given set of characteristics will naturally drive the performance-adjusted price of new computers down and consequently reduce the resale value of older tablets. In addition, even after controlling for quality change, the resale value of a used piece of equipment tends to decline with age. Older tablet computers decrease in value both because they have fewer remaining years of use before more demanding software pushes them into obsolescence, and because fewer years remain before the expected failure of their physical components. Both effects imply that a key variable that determines the price of a used computer is its 'model age', i.e., how much time has passed since that model was first introduced.⁶

Combining data on used tablet prices and observed performance characteristics with the vintage of the model at different points in time allows us to jointly estimate the effects of age (i.e. depreciation) and time (i.e. price inflation), after controlling for quality change. Specifically, following Doms et al. (2004), we assume a simple log-linear decomposition of the price of a tablet PC and adopt the following baseline regression specification:
$$$${\ln p_{i,t}\ }=\alpha+\phi a_{i,t}+\gamma t+\sum_j {\beta_jz_{j,i,t}}+\varepsilon_{i,t}$$$$
where $$p$$ is the retail price of a given used tablet computer, $$a$$ is the age of the model (i.e. how long since it was first sold), $$t$$ is a monthly time index, and $$z_j$$ is a set of performance characteristics, including the speed of the central processing unit, the amount of random access memory, and the storage capacity.⁷

In this setup, $$\gamma $$ is an estimate of the log-price change between successive periods, controlling for quality change and depreciation, while $$\phi$$ is an estimate of the (log-price) depreciation. Using an assumed retirement rate of 18 percent per year, we then adjust the estimated depreciation rate to account for non-functional tablets that have negligible value, since these observations do not appear in our dataset.⁸

The regression results are shown in table 3. With an adjusted R-squared of about 90 percent, the baseline specification (column 1) fits the data quite well. Each of the coefficients on the five included product characteristics are statistically significant with greater than 99 percent confidence and have magnitudes that suggest these features have appreciable effects on either consumer valuation or production costs. The coefficients on model age and time (both measured in months) also enter significantly and are negatively related to price. After accounting for the assumed retirement rate of 18 percent, the coefficient on model age implies an adjusted depreciation rate of about 27 percent per year, and the time coefficient implies a quality-adjusted price index that falls 24 percent per year (table 4).

In an effort to gauge the importance of Apple in the price dynamics for this new platform, we also tested a regression specification that allowed the coefficients on both model age and time to vary between Apple and Samsung (table 3, column 2).⁹ The depreciation rates for Apple and Samsung tablet computers are similar; notably, however, the average annual rates of quality-adjusted price declines that prevailed over this period are noticeably different among brands. In particular, prices for Apple tablets fell 8 percentage points more slowly than Samsung (table 4), a pattern that is consistent with the declining market share for Apple (figure 1).

In a third regression, we restrict the sample to observations with the highest price for each individual model in its year of introduction--essentially, prices for those instances when a model is sold as new in the secondary market, such as items marketed as "new in box" on eBay. By excluding observations for older used tablets, we avoid any bias that could potentially be introduced by jointly estimating the effects of time and age. As can be seen in table 4, however, this regression indicates that quality-adjusted prices of 'new' tablet PCs declined at an annual rate of 22 percent over the sample period, a similar rate of decline to the baseline results.¹⁰

Finally, we tested a specification that included the full sample and assumed a constant (geometric) depreciation rate but replaced the single time index with indicator variables for each time period in the sample, thus allowing the magnitude of price changes to vary over time.¹¹ As shown in the bottom rows of table 4, the results for this regression show that prices declined especially sharply in 2011 (43 percent per year), when tablets were rapidly penetrating the market. From 2012 to 2014, price declines ranged from 20 to 25 percent per year.

Implications for Productivity

Our estimates for the rates of constant-quality depreciation and price change of tablet PCs are different from those currently used to estimate real investment and capital stocks of PCs in the national economic accounts. In particular, between 2010 and 2014, the average annual rates of depreciation and price decline in the national accounts are about 36 percent and 4 percent per year, compared with our baseline estimates of 27 percent and 24 percent, respectively.¹² As tablets have become an increasing share of the PC equipment stock, these differences may have meaningful implications for the dynamics of business investment and productivity.

Since capital services are measured as the product of the accumulated productive capital with its income share, the contribution of PC equipment to productivity growth depends fundamentally on the interaction of the rates of constant-quality depreciation and price change. More precisely, if rates of depreciation and inflation are constant, then the real capital stock,$$K_t$$, can be written as
$$$$K_t=\frac{1}{P_0}\sum^{t-1}_{i=0}{\frac{{\left(1-\delta\right)}^i}{{\left(1+\pi\right)}^{t-i}}I^N_{t-i}}+{(1-\delta)}^tK_0$$$$
where $$K_0$$ and $$P_0$$ are the initial price and stock of capital, $$I^N_{t-i}$$ is the series of nominal investment flows, $$\delta$$ is the depreciation rate, and $$\pi$$ is the rate of inflation.

If we assume that both the nominal investment flows and the initial capital stock and price are not affected by any measurement issues, we can draw the following conclusions. First, both lower depreciation and faster price declines (more negative $$\pi$$) boost the pace of capital accumulation.¹³ Second, the accumulated capital will depend on how the overall variation in constant-quality prices of used tablet PCs (i.e., $$\delta-\pi$$) is apportioned between depreciation and price change, with faster price declines implying higher contributions to capital deepening.¹⁴

Our estimates of depreciation and price changes for tablet PCs suggest there is a downward bias to the measured contribution of computer equipment to productivity growth in recent years. If our estimates for tablet PCs alone were folded into the national accounts, we would expect a faster pace of price declines for computers and peripheral equipment (CPE) by about 5 percentage points per year, and a lower depreciation rate by up to 2 percentage points per year.¹⁵ Moreover, as suggested in Byrne, Dunn, and Pinto (2016), it seems that the measurement issues raised here apply to all PC platforms (which are treated equally in the national accounts). If so, we estimate that the much slower price declines and still-high depreciation rate in the national accounts are biasing down the contribution of CPE to labor productivity growth by about 0.1 percentage point per year.¹⁶

Faster price declines and a lower depreciation rate would increase the CPE productive stock, raising its contribution to productivity growth to about its value in the second half of the 2000s, but still well short of its contribution in the late 1990s. This reflects, in part, a CPE income share that would be little affected by the changes we consider, remaining well below its value in the second half of the 1990s.¹⁷ However, to the extent that a large fraction of information technology capital has price and depreciation trends that mirror those for CPE, the downward bias to productivity growth implied by these measurement issues could be broader in scope and thus more economically significant.¹⁸

Conclusions

Although official U.S. price statistics do not publish consumption or investment price indexes specifically for tablet computers, we observe that our quality-adjusted price indexes for tablets fall noticeably faster than the broader price indexes for PCs and overall computer and peripheral equipment, and the differences are large enough to have implications for measures of business investment and productivity. In addition, our analysis highlights the importance of estimation of depreciation rates concurrently with price indexes: if computer investment prices have slowed dramatically since 2010, as the price index employed in the national economic accounts indicates, the appropriate rate of depreciation to use in the estimation of capital stocks and service flows may have slowed as well. Our results show empirically, and theory indicates, that prices and depreciation rates move sympathetically with one another.

References

Aizcorbe, Ana M. A Practical Guide to Price Index and Hedonic Techniques. New York, NY: Oxford University Press, 2014.

Berndt and Rappaport, 2001. "Price and Quality of Desktop and Mobile Personal Computers: A Quarter-Century Historical Overview." American Economic Review, Papers and Proceedings of the Hundred Thirteenth Annual Meeting of the American Economic Association, vol. 91, no. 2, pp. 268-273. National Bureau of Economic Research, Inc.

Byrne, David, Wendy Dunn, and Eugenio Pinto, 2016. "Time Variation in Rates of Depreciation and Price Change for Personal Computers." Available at http://conference.nber.org/confer/2016/SI2016/PRCR/Byrne_Dunn_Pinto.pdf.

Byrne, David, Stephen D. Oliner, and Daniel E. Sichel, 2016. "A New Look at Prices of Personal Computers, Tablets, and Cell Phones." Available at http://conference.nber.org/confer/2016/SI2016/PRCR/Byrne_Oliner_Sichel.pdf.

Byrne, David, and Eugenio Pinto, 2015. "The Recent Slowdown in High-Tech Equipment Price Declines and Some Implications for Business Investment and Labor Productivity." FEDS Notes, March 26 2015.

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Krebs, David. 2013. "Mobile Device TCO Models for Line of Business Solutions." VDC Research, Inc. Available at https://www.xploretech.com/downloads/Proven_Results_Construction/WP_VDC_Mobile_Device_TCO.pdf.

Nightingale, Edmund B., John R. Douceur, and Vince Orgovan. "Cycles, Cells and Platters: An Empirical Analysis of Hardware Failures on a Million Consumer PCs." In Proceedings of the Sixth Conference on Computer Systems, 343–356. ACM, 2011.

Pakes, Ariel. 2003. "A Reconsideration of Hedonic Indexes with an Application To PC's (PDF) ." American Economic Review, 93, pp. 1578-1614. National Bureau of Economic Research, Inc.

Triplett, Jack. Handbook on Hedonic Indexes and Quality Adjustments in Price Indexes: Special Application to Information Technology Products. Paris and Washington, D.C.: Organisation for Economic Co-operation and Development, 2006.

Please cite as:
Byrne, David, Wendy Dunn, and Eugenio Pinto (2016). "Prices and Depreciation in the Market for Tablet Computers," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, December 5, https://doi.org/10.17016/2380-7172.1885.