Identification of Direct Socio-Geographical Price Discrimination

An Empirical Study on iPhones

Davidson Cheng
Department of Mathematics and Computer Science
Colorado College
Colorado Springs, CO, USA
<EMAIL_ADDRESS>

Abstract

Price discrimination is a practice where firms utilize varying sensitivities
to prices among consumers to increase profits. The welfare effects of price
discrimination is not agreed on among economists, but identification of such
actions may contribute to our standing of firms’ pricing behaviors. In this
letter, I use econometric tools to analyze whether Apple Inc, one of the
largest company in the globe, is practicing price discrimination on the basis
of socio-economical and geographical factors. My results indicates that
iPhones are significantly (p $<$ 0.01) more expensive in markets where
competitions are weak or where Apple has a strong market presence.
Furthermore, iPhone prices are likely to increase (p $<$ 0.01) in developing
countries/regions or markets with high income inequality.

##  1 Introduction

Naturally, markets contain consumers with different sensitivities towards
prices. Firms may choose to take advantage of such varying sensitivity to
maximize profit; this practice is called price discrimination or personalized
pricing. Apple Inc. is considered by many to have changed the personalized
computer and phone industry, it is also once the world’s largest company with
market capitalization in the trillions. The iPhone is a popular product from
Apple sold across the globe. In fact, the prices of iPhones vary in an
interesting fashion across different markets. For example, as of October 2021,
the iPhone 13 with 128gb of storage is sold at $799 in the U.S. and roughly
$1441 in Brazil, an economy with much less mean income. Selling iPhones in
Brazil will require additional costs that may otherwise be avoided in the U.S.
But when those additional costs are accounted for, are iPhones still priced
higher in countries such as Brazil than in the U.S?

In this letter, I examine Apple Inc’s pricing strategy across countries with
various economic status to identify whether apple Inc. is conducting price
discrimination in different geographical regions to increase its profit. I
first define price discrimination and survey both theoretical and empirical
work in the literature. Subsequently, the methodology is outlined and data is
introduced. Finally, I present and discuss my results with respect to theories
on price discrimination.

##  2 Definition and Background

In general, firms conduct price discrimination by offering different prices to
customers with different demands. Lower prices for price-sensitive customers
and higher prices for those relatively price-insensitive would increase the
firm’s overall profit. Pigou has classified price discrimination into three
degrees. In the first degree of price discrimination, or pure price
discrimination, the firm charges each customer the maximum price they are
willing to pay; the second degree is when prices are varied based on quantity
of goods purchased; the third degree refers to when different prices are
offered to different groups of customers [Pigou, 1920]. McAfee points out that
Pigou’s classificatons are flawed [McAFee, 2008], as the second degree do not
represent an intermediate step between the first and third degree. In
addition, the first and third degrees of price discrimination offer the
consumer a singular price while in the second degree of price discrimination
the consumer can choose the price by adjusting quantity purchased. A more
modern taxonomy of price discrimination includes direct and indirect price
discrimination, whereas direct price discrimination offers consumers different
prices based on observable features such as geographical location, age,
gender, and indirect price discrimination utilizes customers’ unobservable
features such as preferences and demands. Despite disagreements in
classifications, scholars have agreed that market power and arbitrage
difficulties are requisites to conducting price discrimination.

In the literature, criticisms to studies that claim to have identified price
discrimination speak to the failure to account for differentiated cost. Lott,
Russel, and Roberts have pointed out that differences in cost or quality can
explain price difference for alleged of price discrimination in gasoline ,
dinner, and airline prices [Lott, 1991]. Lott, Russel, and Roberts further
attempted to provide an explanation for this phenomenon: it is easier to
attribute price differences to a firm wielding its monopolistic power than
gathering empirical evidences that might account for the additional cost. Two
formal definitions of price discrimination that considers differentiated costs
have been popularly adopted. The first one, offered by Phlips in 1983,
proposes that differences in profits constitutes price discrimination, as in
price discrimination exists when the same commodity is sold at $price_{1}$ and
$price_{2}$, and

$price_{2}-cost_{2}\neq price_{1}-cost_{1}.$

The second definition follows Stigler’s concept which claims that price
discrimination is present when profit markups are unequal. Formally, price
discrimination is present whenever

$ln(price_{2})-ln(price_{2})\neq ln(cost_{2})-ln(cost_{1}).$

The two models are based on different assumptions of the firm’s profit
strategy. In the case of non discriminatory pricing, Philip’s measure assumes
constant profit while Stigler’s measure assumes constant markup. Clerides have
shown that rejection of price discrimination using one of the measure always
lead to acceptance in another. Therefore it is critical to pick and justify
the the measure before performing any empirical analysis.

##  3 Methodology

Based on the following assumptions, we choose Stigler’s measure over Phlips’
in this case study.

Assumption 1: If iPhone’s pricing is non-discriminatory, it would maintain the
same profit markup across variations of iPhones.

Assumption 2: Prices of iPhones do not dependent on quantity.

Assumption 3: Costs of iPhones can be linearly estimated using model and
market-specific parameters.

Apple have always offered iPhones of different graeds (“Pro”, “S”, “Mini”,
“SE”, etc.). If sales of premium iPhone models results in the same profit as
the other models, it must be true that more-premium models have a lower profit
margin. Regardless of societal and marketing benefits of premium models, this
would reduce Apple’s incentive to develop premium iPhone models. However,
Apple has always offered iPhones with different storage capacity options with
the high-storage models at higher prices. Since 2011, Apple has also been
offering iPhones with the affixes “S”, “Plus”, “Pro”, and is continuing to
develop premium models. We therefore can assume that the premium iPhone models
do not have lower profit markup than the rest, which justifies the first
assumption to a certain degree. The second assumption implies non-
discriminatorily priced iPhones will maintain equal profit markup when sold at
different quantities. This assumption is rather strong as it is well-known
that Apple offers one clear-cut price for customers regardless of their
demand: there is never “buy two get one 50% off” in the Apple Store. Companies
that offer lower prices to customers with high demand may be subject to
indirect or the second degree of price discrimination, as the customers with
higher demands are typically more price-sensitive. This practice is also
called nonlinear pricing. While Apple do not seem to price iPhones
nonlinearly, Apple does allow customers to trade-in their old iPhones to get
discounts. This can be considered a sign for indirect price discrimination, as
customers who are willing to trade-in their old phones are likely to be more
price-sensitive. The trade-in program is not considered in this study because
it is not available in every market.

Stigler’s definition of price discrimination takes in the products’ costs as a
variable. However, such information is not publicly available, so we make
Assumption 3 and apply a linear model to estimate the cost of iPhones:

$\hat{cost}=\beta_{0}+\beta_{mdl}\times X^{\prime}_{mdl}+\beta_{mkt}\times
X^{\prime}_{mkt}.$

The model-specific variables include variables that are independent across
markets (storage capacity, features, generation of the phone, etc.). The
market-specific variables account for differentiated cost for selling at a
different market (taxes, tariffs, operational cost, etc.); these variables are
independent of model-specific parameters. Substituting $\hat{cost}$ for $c$ in
equation (1), the first difference equation for $ln(proce)$ in Stigler’s
markup measure can be derived to

$\Delta ln(p)=\alpha+\Delta X^{\prime}\times ln(\beta)+\epsilon.$

The model, market variables and their corresponding coefficients have been
combined into $X^{\prime}$ in this equation. Rejecting the null hypothesis of
$\alpha=0$ indicates that change in price across products do not maintain
equal markup, thus constituting price discrimination by our definition.

##  4 Results

We collected data of 27 iPhone models in over fifty markets, and received 969
data points. The price of the iPhones are gathered from themacindex.com and
the market information are mostly from World Bank. An overview of the model
data is shown in Table 1. Summary and detailed data for market-specific
variables are shown in Table 5 and 6 in Appendix.

| Mean | Standard Deviation | Binary Variable | (Min, Max)
---|---|---|---|---
iPhoneXR | 0.115 | 0.319 | True | (0, 1)
iPhone11 | 0.125 | 0.331 | True | (0, 1)
iPhone12 | 0.556 | 0.497 | True | (0, 1)
iPhone13 | 0.204 | 0.403 | True | (0, 1)
se | 0.109 | 0.312 | True | (0, 1)
mini | 0.105 | 0.307 | True | (0, 1)
pro | 0.365 | 0.482 | True | (0, 1)
max | 0.248 | 0.432 | True | (0, 1)
storage | 273.24 | 204.60 | False | (64, 1024)
price | 1214.35 | 442.22 | False | (399, 2950)
Table 1: Summary Statistics of the dataset. Number of observations: 969.

If Assumption 1 holds, we expect the listed price to be in constant ratio to
the cost, which means we can examine the validity of Assumption 3 by testing
how well we can estimate price of iPhones. We first regress the proposed cost
function in equation (3), and the results are shown in Table 2.

| Adj R2 | Root MSE
---|---|---
With Model-specific Controls | 0.858 | 166.6
With Model and Market-specific Controls | 0.924 | 121.8
Table 2: OLS regression statistics of the estimated cost using model and
market-specific variables. Number of observations: 969.

As expected, the Adj. $R^{2}$ and root MSE measures are both improved when
market-specific variables are included with the model-specific ones. With 969
samples, the cost estimation function explains 92.4$\%$ percent of price
variation in the original dataset, and the estimations are likely to be
$\$$121.8 away from the true price. Considering the average price of iPhones
in the dataset is $\$$1214.35, we consider this estimation accurate enough to
keep Assumption 3. The Breusch Pagan test indicates heteroskedasticiy in the
model; details of the regression along with robust standard errors are
reported in Table 7 (Appendix). To identify what variables within the cost
estimation model can be correlated with the error term, we regressed the
squared-residuals with respect to the model and market-specific variables, and
the coefficients on “iPhone11”, “iPhone12”, “iPhone13”, “storage”, “tariff”,
“gdppc”, and the constant appear to be significant at 5$\%$. The squared-
residual is smaller when “iPhone11”, “iPhone12”, or “iPhone13” equal to 1; it
increases as storage or tariff increases, and it decreases as gdppc increases.
We suspect that “iPhone XR”, the base model, might be priced differently than
the rest of the models, which can cause the error to increase when predicting
price for an “iPhone XR”. The storage, tariff, and gdppc variables may also
contain non-linear relationships to price; however, when we include storage2,
tariff2, and gdppc2 in the cost estimation function, the significance between
these variables and the squared-residuals in the subsequent Bruesch Pagan test
did not decrease. It is possible that these variables along with the presence
of heteroskedasticity imply non-linearity in Apple’s pricing, which may
indicate some sort of price discrimination. Next, we estimate the first
difference in $ln(price)$ model derived from Stigler’s definition of price
discrimination, the results are shown in Table 3.

| With Model-specific Controls |  | With Model-specific and
---
Market-specific Controls
$\alpha$ |  | 0.460***
---
(0.014, 0.021)
| 0.188***
---
(0.015, 0.022)
iPhone11 |  | 0.068***
---
(0.019, 0.024)
| 0.070***
---
(0.014, 0.021)
iPhone12 |  | 0.322***
---
(0.018, 0.023)
| 0.323***
---
(0.013, 0.020)
iPhone13 |  | 0.278***
---
(0.020, 0.024)
| 0.272***
---
(0.015, 0.021)
se |  | -0.607***
---
(0.018, 0.017)
| -0.607***
---
(0.014, 0.011)
mini |  | -0.120***
---
(0.018, 0.016)
| -0.121***
---
(0.014, 0.010)
pro |  | 0.185***
---
(0.018, 0.016)
| 0.185***
---
(0.014, 0.009)
max |  | 0.075***
---
(0.018, 0.016)
| 0.075***
---
(0.013, 0.009)
storage |  | 0.000623***
---
(2.73E-5, 2.91E-5)
| 0.000624)***
---
(2.03E-5, 2.34E-5)
| tariff
---
(simple mean of manufaced
products tariff applied)
_ |  | 0.018***
---
(0.002, 0.002)
| salestax
---
(VAT for OECD countries)
_ |  | 0.014***
---
(5E-4, 4.9E-4)
| gdppc
---
(GDP per Capita in 2019/2020)
_ |  | -5.29E-7*
---
(2.73E-7, 2.35E-7)
| consump
---
(household and NPISH final
Consumption expenditure per capita)
_ |  | 1.52E-6**
---
(7.22E-7, 6.7E-7)
Adj. R2 | 0.856 | 0.921
Breusch Pagan P-value | 0.005 | 0.0000
Table 3: Coefficients from regression price of iPhones. Coefficients are
displayed with standard errors in parentheses in format (Ordinary SE, Robust
SE); The asterisks *, **, and *** indicate significance levels at 10%, 5%, and
1%, respectively. The left column contains regression results using just
model-specific variables for estimation of price while the while column
utilizes both model and market-specific controls. The model-specific controls,
except for “storage”, are binary variables derived directly from the name of
the phone. For example, if a model’s listed name is “iPhone 12 Pro 128gb”, its
model-specific vector would contain (0,1,0,0,0,1,0,128). The data on tariff,
gdppc, and consump are gathered from World Bank, and data on salestax are
gathered from international Tax Competitiveness Index and Trading Economics.
The base case used to calculate the differences is the iPhone XR with 64gb of
storage.

All regressed variables in Table 3 are significant at 10 percent while most
are significant at 1 percent. The effect of the variables on $\Delta
ln(price)$ is as expected. The Pro and Max models are Apple’s premium models
while the SE and Mini are the more affordable ones. The iPhone XR, 11, 12, and
13 are released in chronological order with each being more expensive than the
previous one, except for the newly released iPhone 13, which is marginally
cheaper than the previous year’s model. Among the market-specific variables,
tariff and salestax are expected to increase listed price. The resultant
coefficients estimate that one percentage point of increment in tariff or
salestax will increase the listed price by $1.8\%$ and $1.4 %, respectively.
The null hypothesis that $\alpha=0$ implies that with differentiated cost
considered, the various prices of iPhone models sold in different markets
maintain constant profit markup. This null hypothesis is rejected at 0.1%
which implies that some sort of price discrimination may exist within iPhones’
pricing across different models and markets, we then attempt to determine
whether socio-economical factors are significant to Apple’s differentiated
prices.

| Model I. | Model II. | Model III. | Model IV.
---|---|---|---|---
| gini
---
(Gini Index)
| 12.863 ***
---
(2.897, 3.319)
- |  | 9.128 ***
---
(3.056, 3.06)
| 9.568 ***
---
(3.1, 3.146)
| high10
---
(Percentage of income held
by the highest 10%)
| -7.07 *
---
(4.11, 4.21)
- |  | -7.943 *
---
(4.409, 4.271)
| -9.401 **
---
(4.62, 4.625)
| ishighinc
---
(High Income Economy)
- |  | -43.657 **
---
(18.01, 19.444)
| -35.737 *
---
(20.149, 22.854)
| -29.878
---
(20.192, 22.236)
| isuppermiddleinc
---
(Upper Middle Income
Economy)
- |  | 82.554 ***
---
(14.639, 19.475)
| 72.352 ***
---
(15.363, 18.068)
| 71.262 ***
---
(15.328, 17.578)
| hhi
---
(Herfindahl-Hirschman
Index)
- | - |  | 0.188 ***
---
(0.0517, 0.048)
| 0.165 **
---
(0.0667, 0.065)
hhi2 | - | - |  | 1.03E-5 ***
---
(3.56E-6, 3.4E-6)
| -4.73E-6
---
(4.3E-6, 4.13E-6)
| iosshare
---
(Share of IOS)
- | - | - |  | 11.835 ***
---
(4.456, 4.471)
iosshare2 | - | - | - |  | -0.133 ***
---
(0.045, 0.044)
Breusch Pagan P-value | 0.0000 | 0.0000 | 0.0000 | 0.0000
RESET P-value | 0.0000 | 0.0000 | 0.0000 | 0.0000
Table 4: Coefficients from four Regression Models. Coefficients are displayed
with standard errors in parentheses in format (Ordinary SE, Robust SE); The
asterisks *, **, and *** indicate significance levels determined with robust
SE at 10%, 5%, and 1%, respectively.

We include socio-economical factors of the market into the price prediction
function, the model and market-specific variables are kept as controls. Table
4 displays the regression results. The significance of gini and high10 are
significant across models I, III, and IV. The Gini Index here is on a scale of
0-100. The coefficients on gini indicate that for every 1% point increase in
gini, the price of an iPhone is likely to increase by around $9. The variable
high10 is not very significant across most models, but it indicates that
iPhones are cheaper in countries where the top 10% income group have more
wealth. The markets are divided into high income economies, upper middle
income economies, and middle income economies with the middle income markets
being the base. The coefficients indicate that being an upper middle income
economy likely increases iPhone prices by over $70 dollars, which is
consistently significant throughout the models. This relation is reversed for
high income economies, but loses significance as more variables are added.

The Herfindahl-Hirschman Index (HHI) measures the competitiveness of a market;
a lower HHI would indicate high market competitiveness while a high HHI
indicates saturation. The hhi and hhi2 are both significant in Model III, but
their significance drop significantly when IOS market share variables are
included. There is likely to be correlations between hhi and iosshare which
means Model III. suffer from omitted variable bias. When both hhi and iosshare
are present in Model IV, we see that as competition weakens, the price of
iPhones increase. Keep in mind that the HHIs are in the magnitude of
thousands, so the coefficient of 0.165 on hhi in Model IV. can potentially
account for price difference of hundreds of dollars between competitive and
saturated markets. We observe an significance second degree polynomial
relationship between iosshare and price of iPhones in Model IV. It is
estimated that for every percentage point of increase in share of IOS in a
market, the price increases but at a diminishing rate. The parabola has been
graphed in Figure 1. The domain of iosshare in this dataset is between 2.91
(India) and 67.25 (Japan), which is within the domain where iosshare
positively affects price.

Figure 1: The modeled relationship between IOS market share and price of
iPhones across various markets.

##  5 Discussion & Conclusion

In this paper, price discrimination in iPhones has been identified with
Stigler’s definition on the basis of socio-economical factors. We find many
variables to be both statistically and economically significant. For example,
the market share of IOS can incur an increment of $263.28 to an iPhone’s price
when it is at 44.49%. One unit of increment in Gini Index can increase price
by over $9. Our results also show that iPhones are cheaper in high income than
middle income than upper middle income economies. This may imply that iPhones
are generally more expensive in countries where wealth is less balanced. This
is consistent with our hypothesis that the prices of iPhones are higher in
markets where iPhones are deemed as premium or luxury goods. The classical
theories on price discrimination agree that market power and lack of
incentives for arbitrage lead to price discrimination. We are able to consider
market power and competitiveness which will be discussed later in this
section. By not including controls for arbitrage in our models, we do not deny
the significance of arbitrage in identifying price discrimination. The cost of
arbitrage is simply too difficult to define and quantify in this context.

One persistent issue that occurs across this study is rejection of the null
hypothesis when running the Breusch-Pagan test, which can indicate
heteroskedasticity in the model. We believe heteroskedasticity can arise from
both model-specific and market-specific variables. Our assumption that the
cost of iPhones can be predicted linearly lead to the cost estimation model,
which assumes that tags such “pro” has the same effect on an iPhone XR on an
“iPhone 13”, but this may not be the case. This will cause heteroskedasticity;
but keep in mind that this will not be correlated with any geographical
variables, therefore will not affect conclusions of this study. Price
discriminations can arise from price variation across products of different
quality or across products sold at different geographical locations, and we
are interested in the latter. Thus, heteroskedasticity that arise from market-
specific variables are more important in this study. To discuss the presence
of heteroskedasticity, we first propose that when more than two prices are
being compared, identification of price discrimination using equation (4) will
likely lead to heteroskedasticity. In equation (4), $\alpha$ symbolizes the
difference in markups. When we are only comparing two prices, there is only
one difference and $\alpha$ may be a constant. When we compare more than two
prices, the value of $\alpha$ turns into a sample from a distribution and a
constant can no longer represent such difference in markups any more. This
means a portion of differences in markups, which is correlated with
explanatory variables, is integrated with the error term, and we get
heteroskedasticity. Table 9 (Appendix) indicates the error term is correlated
with tariff and GDP per capita, these variables may very well serve as basis
for price discrimination. Heteroskedasticity caused by model-specific
variables are not necessarily relevant to this study, and heteroskedasticity
caused by market-specific variables may be a result of price discrimination;
So our solutions to heteroskedasticity is to maintain the original model and
report the robust standard errors.

One may also argue that most of our prices are gathered from developed
economies: 61% of markets included in this study belong to high income
economies. This is certainly a limitation to our study, but is also one that
we could not avoid. In general, more iPhone models are available in high-
income markets. The HHI and IOS market share are both found to be positively
correlated with price of iPhones. This confirms the classical theory that
market power is a requirement to price discrimination, and that lack of
competition encourages price discrimination. It is worth noting that reverse
causality may be present between price of iPhones and IOS market share. The
price of iPhones directly influence sales and thus affects IOS market share.
To address this issue requires additional instrumental variables, which may be
done as an extension of this study. Including instrument variables for
arbitrage may also be future work that stems from this study.

The purpose of this study is to identify and quantify socio-economical and
geographical influences to iPhone prices. Our results confirms traditional
theories on price discrimination and found economically significant factors.
It is certainly unethical if a company provides higher prices to poorer
markets to maximize profit, especially when the company’s mission statement is
“To make a contribution to the world by making tools for the mind that advance
humankind”, according to the Economist. But price discrimination is not
unlawful. After all, Apple is a public company pressured by the board of
trustees to show revenue growth in its annual reports.

## References

  * [1] Mark Armstrong and John Vickers.  Competitive non-linear pricing and bundling.  The Review of Economic Studies, 77(1):30–60, 2010.
  * [2] Sofronis Clerides.  Price discrimination with differentiated products: Definition and identification.  Economic Inquiry, 42:402–412, 2004.
  * [3] John R Lott and Russell D Roberts.  A guide to the pitfalls of identifying price discrimination.  Economic Inquiry, 29(1):14, 1991.
  * [4] R. Preston McAfee.  Price discrimination.  In Issues in Competition Law and Policy, pages 465–484. ABA Book Publishing, 2008.
  * [5] Louis Phlips.  The economics of price discrimination.  Cambridge University Press, 1983.
  * [6] Arthur Cecil Pigou and Nahid Aslanbeigui.  The economics of welfare.  Routledge, 2017.
  * [7] Stephen A. Rhoades.  The herfindahl-hirschman index.  Fed. Res. Bull., 79:188, 1993.

##  6 Appendix

Variable | # of Observations | Mean | Std. Dev. | Min | Max
---|---|---|---|---|---
gdppc | 54 | 27785.75 | 25209.94 | 1155.1 | 115873.6
gini | 54 | 34.1 | 7.01 | 25 | 63
tariff | 54 | 3.15 | 2.87 | 0 | 14
consump | 54 | 14370.94 | 10852.34 | 606 | 40706
high10 | 54 | 26.91 | 5.36 | 19.5 | 50.5
povhead | 54 | 1.7 | 4.36 | 0 | 22.5
salestax | 54 | 17.21 | 6.05 | 0 | 27
highinc | 54 | 0.61 | 0.49 | 0 | 1
uppermiddleinc | 54 | 0.22 | 0.42 | 0 | 1
middleinc | 54 | 0.17 | 0.38 | 0 | 1
iosshare | 54 | 26.06 | 15.89 | 2.91 | 67.245
ioshhi | 54 | 6532.74 | 1139.57 | 4961.22 | 9080.31
Table 5: Summary statistics of the market-specific variables.

gdppc: GDP per capita. Source: World Bank
gini: Gini Index. Source: World Bank
tariff: Simple mean of manufaced products tariff applied. Source: World Bank
consump: household and NPISH final Consumption expenditure per capita. Source:
World Bank
high10: Income share held by highest 10%. Source: World Bank
povhead: Poverty headcount ratio at $1.9 a day. Source: World Bank
salestax: Sales Tax. Source: international tax competitiveness index & trading
economics.
highinc: Identified by World Bank as high income economy.
uppermiddleinc: Identified by World Bank as upper middle income economy.
middleinc: Identified by World Bank as middle income economy.
Iosshare: Share of IOS users in the market. Source: StatCounter.
ioshhi: Herfindahl-Hirschman Index. Calculated using data from StatCounter.

country | gdppc | gini | tariff | consump | high10 | povhead |  | sales
---
tax
| high-
---
inc
| upper-
---
middle-
inc
| midd-
---
leinc
iosshare | ioshhi
Australia | 51812.2 | 34.4 | 2.1 | 30552 | 27 | 0.5 | 10 | 1 | 0 | 0 | 55.49 | 4990.6927
Austria | 48105.4 | 30.8 | 1.8 | 23019 | 23.9 | 0.6 | 20 | 1 | 0 | 0 | 30.625 | 5575.7416
Belarus | 6411.2 | 25.3 | 5.3 | 4888 | 21.3 | 0 | 20 | 0 | 1 | 0 | 13.81 | 7437.5679
Belgium | 44594.4 | 27.2 | 1.8 | 22209 | 22.2 | 0.1 | 21 | 1 | 0 | 0 | 36.2975 | 5361.9009
Brazil | 6796.8 | 53.3 | 14 | 6743 | 40.2 | 4.6 | 17 | 0 | 1 | 0 | 12.22 | 7638.5577
Canada | 43241.6 | 33.3 | 1.5 | 28220 | 25.3 | 0.2 | 5 | 1 | 0 | 0 | 52.2375 | 4965.988
Chile | 13231.7 | 44.4 | 1 | 8644 | 36.3 | 0.3 | 19 | 1 | 0 | 0 | 15.785 | 7498.8816
China | 10500.4 | 38.5 | 5.2 | 3339 | 29.4 | 0.5 | 13 | 0 | 1 | 0 | 21.7025 | 6835.0196
Croatia | 13828.5 | 29.7 | 1.8 | 9011 | 22.7 | 0.4 | 25 | 1 | 0 | 0 | 13.745 | 7953.7572
Cyprus | 26623.8 | 32.7 | 1.8 | 19755 | 27.2 | 0 | 19 | 1 | 0 | 0 | 22.3125 | 6493.4033
| Czech
---
Republic
22762.2 | 25 | 1.8 | 11051 | 21.5 | 0 | 21 | 1 | 0 | 0 | 19.925 | 6666.6377
Denmark | 60908.8 | 28.2 | 1.8 | 29349 | 23.5 | 0.2 | 25 | 1 | 0 | 0 | 52.3575 | 5038.8947
Egypt | 3547.9 | 31.5 | 4.8 | 2379 | 26.9 | 3.8 | 14 | 0 | 0 | 1 | 11.475 | 7847.1135
Estonia | 23312.3 | 30.3 | 1.8 | 10623 | 22.4 | 0.2 | 20 | 1 | 0 | 0 | 31.04 | 5576.1933
Finland | 49041.3 | 27.3 | 1.8 | 25058 | 22.6 | 0.1 | 24 | 1 | 0 | 0 | 27.91 | 5908.748
France | 38615.1 | 32.4 | 1.8 | 21950 | 26.7 | 0 | 20 | 1 | 0 | 0 | 31.7175 | 5824.9742
Georgia | 4278.9 | 35.9 | 0.8 | 4140 | 27.6 | 3.8 | 18 | 0 | 1 | 0 | 21.0425 | 6549.3361
Germany | 45723.6 | 31.9 | 1.8 | 24206 | 24.6 | 0 | 19 | 1 | 0 | 0 | 29.86 | 5679.252
Greece | 17676.2 | 32.9 | 1.8 | 15170 | 24.9 | 0.1 | 24 | 1 | 0 | 0 | 13.1575 | 7386.4622
Hungary | 15899.1 | 29.6 | 1.8 | 8869 | 23.2 | 0.2 | 27 | 1 | 0 | 0 | 16.66 | 6727.6703
India | 1900.7 | 35.7 | 8.9 | 1101 | 30.1 | 22.5 | 18 | 0 | 0 | 1 | 2.9075 | 9080.3126
Indonesia | 3869.6 | 38.2 | 6.2 | 2377 | 29.9 | 2.7 | 10 | 0 | 0 | 1 | 5.2 | 8547.8537
Ireland | 83812.8 | 31.4 | 1.8 | 22560 | 25.4 | 0.2 | 23 | 1 | 0 | 0 | 43.8875 | 5091.4367
Israel | 43610.5 | 39 | 1.4 | 18472 | 27.8 | 0.2 | 17 | 1 | 0 | 0 | 22.6125 | 6468.5106
Italy | 31676.2 | 35.9 | 1.8 | 19385 | 26.7 | 1.4 | 22 | 1 | 0 | 0 | 24.895 | 6185.3164
Japan | 40113.1 | 32.9 | 1.3 | 27024 | 26.4 | 0.7 | 10 | 1 | 0 | 0 | 67.245 | 5352.4879
| Kazak-
---
hstan
9055.7 | 27.8 | 4.6 | 5887 | 23.5 | 0 | 12 | 0 | 0 | 1 | 21.1725 | 6676.858
Latvia | 17620 | 35.1 | 1.8 | 9296 | 26.9 | 0.3 | 21 | 1 | 0 | 0 | 25.5825 | 6179.8669
| Luxem-
---
bourg
115873.6 | 35.4 | 1.8 | 31970 | 26.6 | 0.3 | 17 | 1 | 0 | 0 | 45.895 | 5093.8953
Malaysia | 10401.8 | 41.1 | 5.8 | 6717 | 31.3 | 0 | 10 | 0 | 0 | 1 | 17.39 | 6582.9937
Mexico | 8346.7 | 45.4 | 3.1 | 5985 | 36.4 | 1.7 | 16 | 0 | 1 | 0 | 15.6525 | 7355.4853
Moldova | 4551.1 | 25.7 | 4.9 | 3141 | 22 | 0 | 20 | 0 | 1 | 0 | 13.315 | 7484.3698
Nepal | 1155.1 | 32.8 | 12.6 | 606 | 26.4 | 15 | 15 | 0 | 0 | 1 | 6.7425 | 8624.8983
| Nether-
---
lands
52304.1 | 28.1 | 1.8 | 22163 | 23 | 0.1 | 21 | 1 | 0 | 0 | 39.225 | 5183.256
Norway | 67294.5 | 27.6 | 0.3 | 37546 | 22.2 | 0.3 | 25 | 1 | 0 | 0 | 52.6025 | 5054.6859
Peru | 6126.9 | 32.8 | 1.3 | 3797 | 31.1 | 2.2 | 18 | 0 | 1 | 0 | 8.1275 | 8325.3837
Philippines | 3298.8 | 42.3 | 3.4 | 2098 | 33.5 | 2.7 | 12 | 0 | 0 | 1 | 17.3975 | 7277.6911
Poland | 15656.2 | 30.2 | 1.8 | 9806 | 24 | 0.2 | 23 | 1 | 0 | 0 | 3.2025 | 8891.6067
Portugal | 22439.9 | 33.5 | 1.8 | 14893 | 26.6 | 0.3 | 23 | 1 | 0 | 0 | 23.33 | 6464.4478
Romania | 12896.1 | 35.8 | 1.8 | 8010 | 24.9 | 2.4 | 19 | 0 | 1 | 0 | 17.645 | 6949.1804
Russia | 10126.7 | 37.5 | 5.3 | 5936 | 29.9 | 0 | 20 | 0 | 1 | 0 | 25.625 | 6254.728
Slovakia | 19156.9 | 25 | 1.8 | 11069 | 19.5 | 0.2 | 20 | 1 | 0 | 0 | 18.7975 | 6704.4614
| South
---
Africa
5090.7 | 63 | 7.5 | 4264 | 50.5 | 18.7 | 15 | 0 | 1 | 0 | 12.815 | 7336.7496
| South
---
Korea
31489.1 | 31.4 | 2.4 | 13006 | 24 | 0.2 | 10 | 1 | 0 | 0 | 25.33 | 6332.7454
Spain | 27057.2 | 34.7 | 1.8 | 15952 | 25.3 | 0.9 | 21 | 1 | 0 | 0 | 20.28 | 6741.028
Sri Lanka | 3682 | 39.3 | 8.1 | 2763 | 32.6 | 0.9 | 8 | 0 | 0 | 1 | 8.4825 | 8062.1371
Sweden | 51925.7 | 30 | 1.8 | 25893 | 22.9 | 0.7 | 25 | 1 | 0 | 0 | 53.5425 | 4977.8659
| Switzer-
---
land
86601.6 | 33.1 | 0.7 | 40706 | 25.8 | 0 | 7.7 | 1 | 0 | 0 | 54.475 | 4961.2151
Thailand | 7189 | 34.9 | 7.3 | 3314 | 27.2 | 0.1 | 7 | 0 | 1 | 0 | 21.15 | 6126.7236
Turkey | 8538.2 | 41.9 | 1.3 | 9038 | 31.6 | 0.4 | 18 | 0 | 1 | 0 | 16.905 | 7322.2835
UAE | 43103.3 | 26 | 4.1 | 15847 | 20 | 0 | 5 | 1 | 0 | 0 | 21.1475 | 6068.3613
Ukraine | 3726.9 | 26.6 | 1.9 | 2821 | 22.3 | 0 | 20 | 0 | 0 | 1 | 19.4125 | 6910.2928
| United
---
Kingdom
40284.6 | 35.1 | 1.8 | 24819 | 26.7 | 0.3 | 20 | 1 | 0 | 0 | 49.745 | 4975.0528
| United
---
States
63543.6 | 41.4 | 0 | 38594 | 30.8 | 1 | 0 | 1 | 0 | 0 | 55.87 | 5166.6969
Table 6: Detailed market-specific parameters employed. Model Fit
---
# of Observations | 969
F(8,960) | 732.5
Prob >F | 0.000
R-squared | 0.859
Adj. R-squared | 0.858
Root MSE | 166.3
ANOVA
Source | SS | DoF | MS
Model | 162655620 | 8 | 20331952.4
Residual | 26644484.8 | 960 | 27754.68
Total | 189300104 | 968 | 195557.959
Coefficients
price | Coefficient | Std. Err. | T-statistic | P $>$ $|$t$|$ | 95% Conf. Interval
siphone11 | 40.49823 | 21.89588 | 1.85 | 0.065 | -2.471073 | 83.4675
isiphone12 | 293.5196 | 21.16419 | 13.87 | 0.000 | 251.9862 | 335.05
siphone13 | 241.5425 | 23.41358 | 10.32 | 0.000 | 195.5948 | 287.490
isse | -519.6685 | 21.44105 | -24.24 | 0.000 | -561.7452 | -477.591
ismini | -124.4113 | 21.67966 | -5.74 | 0.000 | -166.9563 | -81.8663
ispro | 251.2743 | 21.52617 | 11.67 | 0.000 | 209.0305 | 293.518
ismax | 127.0259 | 21.04017 | 6.04 | 0.000 | 85.73583 | 168.315
storage | .8928689 | .032018 | 27.89 | 0.000 | .8300355 | .955702
_cons | 731.5272 | 16.49331 | 44.35 | 0.000 | 699.1601 | 763.894
Table 7: Regression Results of the estimated cos function. Model Fit
---
# of Observations | 969
F(8,960) | 983.63
Prob >F | 0.000
R-squared | 0.9251
Adj. R-squared | 0.9241
Root MSE | 121.8
ANOVA
Source | SS | DoF | MS
Model | 175116970 | 12 | 14593080.9
Residual | 14183134 | 956 | 14835.9142
Total | 189300104 | 968 | 195557.959
Coefficients
price | Coefficient | Std. Err. | T-statistic | P $>$ $|$t$|$ | 95% Conf. Interval
isiphone11 | 43.47096 | 16.01576 | 2.71 | 0.007 | 12.04085 | 74.90107
isiphone12 | 293.7764 | 15.47377 | 18.99 | 0.000 | 263.4099 | 324.1429
isiphone13 | 234.4498 | 17.12221 | 13.69 | 0.000 | 200.8483 | 268.0512
isse | -519.4791 | 15.68073 | -33.13 | 0.000 | -550.2517 | -488.7065
ismini | -125.0481 | 15.85741 | -7.89 | 0.000 | -156.1674 | -93.92873
ispro | 251.9801 | 15.74284 | 16.01 | 0.000 | 221.0856 | 282.8746
ismax | 126.9829 | 15.38546 | 8.25 | 0.000 | 96.78975 | 157.1761
storage | .893907 | .0234136 | 38.18 | 0.000 | .847959 | .9398549
tariff | 26.55665 | 1.88023 | 14.12 | 0.000 | 22.86679 | 30.2465
salestax | 16.18443 | .6136097 | 26.38 | 0.000 | 14.98025 | 17.3886
gdppc | -.0010508 | .0003155 | -3.33 | 0.001 | -.00167 | -.0004315
consump | .0032476 | .000833 | 3.90 | 0.000 | .001613 | .0048823
_cons | 357.1204 | 21.66925 | 16.48 | 0.000 | 314.5956 | 399,6451
Table 8: Regression results with both model and market-specific variables.
Model Fit
---
# of Observations | 969
F(8,960) | 10.06
Prob >F | 0.000
R-squared | 0.1121
Adj. R-squared | 0.1010
Root MSE | 39076
ANOVA
Source | SS | DoF | MS
Model | 1.8439e+11 | 12 | 1.5366e+10
Residual | 1.4597e+12 | 956 | 1.5269e+09
Total | 1.6441e+12 | 968 | 1.6985e+09
Coefficients
ressq | Coefficient | Std. Err. | T-statistic | P $>$ $|$t$|$ | 95% Conf. Interval
isiphone11 | -20416.57 | 5138.075 | -3.97 | 0.000 | -30499.78 | -10333.36
isiphone12 | -22059.83 | 4964.197 | -4.44 | 0.000 | -31801.81 | -12317.85
isiphone13 | -22070.66 | 5493.038 | -4.02 | 0.000 | -32850.46 | -11290.85
isse | -702.5599 | 5030.593 | -0.14 | 0.889 | -10574.84 | 9169.72
ismini | 891.6443 | 5087.273 | 0.18 | 0.861 | -9091.867 | 10875.16
ispro | 6213.118 | 5050.518 | 1.23 | 0.219 | -3698.263 | 16124.5
ismax | 7077.545 | 4935.865 | 1.43 | 0.152 | -2608.835 | 16763.93
storage | 23.78953 | 7.511397 | 3.17 | 0.002 | 9.048803 | 38.53026
tariff | 2181.633 | 603.2036 | 3.62 | 0.000 | 997.8773 | 3365.389
salestax | -76.94466 | 196.8544 | -0.39 | 0.696 | -463.2612 | 309.3719
gdppc | -.3347586 | .1012255 | -3.31 | 0.001 | -.5334084 | -.1361087
consump | .3678688 | .2672236 | 1.38 | 0.169 | -.1565439 | .8922814
_cons | 24594.87 | 6951.791 | 3.54 | 0.000 | 10952.34 | 38237.4
Table 9: Regression results of the squared-residuals in the cost estimation
function with respect to model and market-specific variables