Demand Volatility, Adjustment Costs, Temporal
Aggregation, and Productivity∗
R. Andrew Butters†
Northwestern University
November 21, 2014
Abstract
Measures of productivity reveal large differences across producers even within narrowly defined industries. This paper proposes an explanation for the productivity differences. When adjusting production is costly, increases in demand volatility increase the
unit costs of otherwise identical producers. Furthermore, temporal aggregation conceals
mean preserving differences in demand volatility within the period of aggregation. Consequently, combining three factors, (i) differences in demand volatility (ii) adjustment
costs and (iii) temporal aggregation, leads to differences in measured productivity. I
document this effect empirically by comparing an industry with high adjustment costs
(hotels) to an industry with small adjustment costs (airlines). Differences in annual
demand volatility alone explain 35 percent of the measured productivity variation of
hotels at the metro area-segment-year level. In contrast, differences in annual demand
volatility have no effect on the measured productivity of airlines at the destinationairline-year level.
JEL Code: D24, L83, C43
Keywords: productivity, demand volatility, adjustment costs, temporal aggregation
∗
I would like to thank, without implicating, Meghan Busse, Thomas Hubbard, Michael Mazzeo, Daniel
Spulber, and seminar participants at Northwestern University, as well as, the generous funding of Kellogg
School of Management.
†
r-butters@kellogg.northwestern.edu
1
1
Introduction
Measures of productivity reveal large differences across producers even within narrowly defined industries (Bartelsman and Doms (2000), Syverson (2011)). Syverson (2004b) finds
within the average U.S. manufacturing industry a plant in the 90th percentile is nearly twice
as productive as a plant in the 10th percentile. These large productivity differences are
neither specific to the U.S nor short-lived. Hsieh and Klenow (2009) document productivity differences across producers in China and India that are even larger than those in the
U.S., while Foster et al. (2008) find the productivity levels of U.S. manufacturing plants are
persistent.
A considerable amount of work from academics and the popular press has tried to “put
a face on” the unexplained variation in productivity. Examples include both supply side
explanations such as the use of better management practices (Bloom and Van Reenen (2007),
Gibbons and Henderson (2012), The Economist (2014)) and the utilization of information
technology (Hubbard (2003), The Economist (2007), Bloom et al. (2012)), as well as demand
side explanations such as the level of differentiation in output markets (Syverson (2004a)).
Despite these efforts, a puzzling amount of variation in productivity is left unexplained.
This paper proposes an explanation for the productivity differences. When adjusting production is costly, increases in demand volatility increase the unit costs of otherwise identical
producers. Put simply, two producers with the same technical productivity but different
demand volatilities will have different unit costs, even if both use resources efficiently. Furthermore, temporal aggregation conceals mean preserving differences in demand volatility
within the period of aggregation. Consequently, variation in measured productivity might
not reflect variation in technical productivity if there are (i) differences in demand volatility,
(ii) adjustment costs, and (iii) temporal aggregation. In other words, differences in measured
productivity might not reflect differences in the competitive advantages nor capabilities of
producers, but instead differences in demand environments.
This straightforward economic intuition begs the questions: (i) Could the variation in
measured productivity that we observe across producers simply be due to differences in
demand volatility and the presence of adjustment costs and temporal aggregation? And if
so, (ii) how much of it? The answers to these questions are: (i) Yes and (ii) a lot.
To arrive at this assessment, I conduct a comparison of two industries: hotels and airlines.
While each industry’s characteristics provide the foundation for the empirical analysis, the
purpose of this paper is broader than understanding productivity differences in these two
2
industries. The main objective of this paper is to document how differences in demand
volatility, adjustment costs, and temporal aggregation affect productivity measures. This
effect has implications for several industries that have been the focus of productivity studies
including ready-mix concrete (Syverson (2004a), Collard-Wexler (2011)), electricity (Fabrizio
et al. (2007)), health care (Baker et al. (2004)), and the service industries (Morikawa (2012)).
I leverage several characteristics of the hotel and airline industries for the investigation. First, both industries produce a perishable good across many isolated markets because
of transportation costs. Additionally, each industry exhibits considerable variation in the
volatility of sales across locations that I observe at a monthly frequency. Despite the two industries being similar in many ways, they differ in one critical aspect: the size of adjustment
costs in capital. Hotels face high costs when adjusting the number of rooms, while airlines
face smaller costs when adjusting the number of available seats to any particular destination
in their network because of the mobility of aircraft.
Each characteristic mentioned above makes the comparison between hotels and airlines
ideal for my study. The large amount of variation in demand volatility (within the hotel and
airline industries) and in adjustment costs (across the hotel and airline industries) increases
the power of my hypothesis test. Additionally, with monthly observations I can characterize
the effect of annual levels of temporal aggregation, a common level of aggregation in productivity studies. Because of the isolated geographic markets, I am able to treat different metro
areas and destinations as independent observations and use the cross sectional variation in
demand volatility to identify its effect on measured productivity.
Figures (1) and (2) provide preliminary evidence of the main results. The figures display
measured productivity and annual demand volatility for both hotels (figure 1)) and airlines
(figure (2)). For hotels, I observe 2,063 separate metro area, segment (that is luxury, upscale,
economy), year combinations. For airlines, I observe 2,020 separate destination, airline, year
combinations (I go into more detail on the sources of the data and the construction of both
measured productivity and demand volatility below). Given the discussion above, demand
volatility should have a negative association with measured productivity in hotels and no
association with measured productivity in airlines. Figures (1) and (2) display exactly these
relationships.
In the analysis to follow, I find moving from no demand volatility to the maximum
observed in the sample is associated with a 20 percent decrease in measured productivity for
hotels. Differences in annual demand volatility explain 35 percent of the variation in measured
3
4
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0.1
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Demand Volatility (units)
0.8
0.9
1
I display the relationship between measured productivity and demand volatility among the 2,063 metro area-segment-years in my hotel
sample. Along the vertical axis is measured productivity as given by annual occupancy, while along the horizontal axis is the measure of
demand volatility. For an explicit summary of the construction of each variable see section (3) and for a discussion of the sources of the
data see section (4).
0.7
Figure 1: Measured Productivity and Demand Volatility for Hotels
Source: Smith Travel Research (STR) and author’s calculations
Annual Occupancy (%)
5
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0
0.4
0.5
0.6
0.7
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0.1
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Demand Volatility (units)
0.8
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1
I display the relationship between measured productivity and demand volatility among the 2,020 destination-airline-years in my airline
sample. Along the vertical axis is measured productivity as given by load factor, while along the horizontal axis is the measure of demand
volatility. For an explicit summary of the construction of each variable see section (3) and for a discussion of the sources of the data see
section (4).
0.7
Figure 2: Measured Productivity and Demand Volatility for Airlines
Source: Bureau of Transportation Statistics and author’s calculations
Load Factor (%)
productivity of hotels. The measured productivity ratio of the top to bottom decile is 1.45
for hotels. Differences in annual demand volatility alone generate a measured productivity
ratio of the top to bottom decile of 1.21. In contrast, differences in annual demand volatility
have no effect on the measured productivity of airlines. Similar levels of variation in demand
volatility and temporal aggregation have no effect on the measured productivity of airlines,
because airlines adjust their capacity at a destination to match fluctuations in demand.
This paper complements the literature that investigates the factors driving productivity
differences in two ways. First, it suggests that we should consider if the factors used to
explain productivity differences are robust to the effect of demand volatility. Second, the
effect outlined in this paper could serve as the explanation for how other factors influence
productivity. For example, utilization of IT or exposure to export markets might only affect
productivity in so much as they allow producers to accommodate demand volatility when
facing adjustment costs.
This paper relates to several other separate literatures as well. Here, I explore how
predictable demand volatility influences inferences of productivity. The influence of demand
volatility on industry dynamics including the return to capital and entry have been examined
(Bloom (2009), Collard-Wexler et al. (2011), Collard-Wexler (2013)), but in the context of the
volatility being linked to the level of uncertainty in the economic environment. Additionally,
the results presented here indicate that inferences of productivity are sensitive to the level
of temporal aggregation. Inferences in other settings are sensitive to temporal aggregation,
as well. The level of temporal aggregation contributes to the purchasing power parity (PPP)
puzzle (Taylor (2001)), as well as influences inferences of market integration (Butters and
Spulber (2014), Butters (2014)).
This paper proceeds as follows. Section (2) develops a theoretical model of production
with demand volatility and adjustment costs. Section (3) outlines my empirical strategy
through a comparison of the hotel and airline industries. Section (4) briefly summarizes the
data, and section (5) presents the empirical results. Section (6) provides a series of robustness
checks, and section (7) offers an alternative estimator of productivity.
2
Simple Model of Production
In this section, I present a simple two period model of production with demand volatility
and adjustment costs. The goal of this section is threefold. First, the model formalizes the
6
intuition for how increases in demand volatility together with adjustment costs and temporal
aggregation lead to decreases in measured productivity. Second, the model illustrates that
as the elasticity of substitution between inputs decreases, the effect of demand volatility on
productivity measures is concentrated to the input with adjustment costs. Third, the model
provides a testable prediction for the level of the elasticity of substitution between inputs.
There are two firms (A and B) both with identical constant elasticity of substitution
1/σ
production functions defined by Y = Ω αk K σ + αl Lσ
, where Y is the output resulting
from using K units of capital and L units of labor, Ω is the Hicksian neutral total factor
productivity of each firm and σ is a parameter governing the elasticity of substitution between
the two inputs of production. For ease of exposition, I use the term technical productivity
to denote the Hicksian neutral total factor productivity, Ω, for the rest of the paper.1
Firms A and B face the same set of prices for both capital, r, and labor, w, with each
input supplied by a competitive market. Each firm produces for two periods and storage is
impossible. Even though the setting is dynamic, the firms do not discount the costs in period
2. Because of adjustment costs in capital, each firm’s level of capital remains fixed over the
two periods. In contrast, labor is perfectly flexible.
Up to this point, firms A and B are identical by construction. The two firms differ,
however, in the volatility of their demand. Specifically, firm A faces constant demand each
period, and produces the same, profit maximizing output of Q units in both periods 1 and
A
2, QA
1 = Q2 = Q. Firm B, on the other hand, faces lower demand in period 1 than in period
2, and its profit maximizing response is to produce Q − units in period 1 and Q + units
B
in period 2; QB
1 = Q − , Q2 = Q + .
Figure (3) displays the cost minimizing production plans for firms A and B. The left
panels display firm A’s cost minimizing production plan, while the right panels display firm
B’s cost minimizing production plan. The top panels display the production plans for firms
A and B when the elasticity of substitution between inputs is one, while the bottom panels
display the production plans when the elasticity of substitution is zero. I keep all the other
parameters of the model constant, including the technical productivity of both firms.2 In
each panel, the production isoquants of each firm are displayed for both periods. Each panel
1
The constant elasticity of substitution production function implies constant returns to scale.
The parameter values include the parameter governing the elasticity of substitution in the production
function, σ. In the top two panels, σ → 0, while in the bottom two panels σ → −∞. The other parameter
values are the same across all the panels in the figure and include the share parameter of capital, the share
parameter of labor (αl = αk ), the price of capital r = 1, the price of labor w = 1, and the technical
productivity of each firm Ω = 1, as well as the demand parameters Q = 20 and = 5.
2
7
labels the optimal production points on each isoquant and displays the price vector of capital
and labor at the production points. In the case with some technical substitution, I also
display the average of the two isoquants to better illustrate the cost minimization behavior
of firm B (top right panel). The average of firm B’s two isoquants is different than the Q
isoquant, because of Jensen’s inequality and the convexity of the isoquants.
Firm A, with constant demand, faces a straightforward cost minimization problem. The
most cost effective level of capital and labor is the same in both periods. Using the same
amount of capital in both periods is cost effective even with no adjustment costs.
The cost minimization problem for firm B is quite different, because the constraint on
adjusting capital is binding. Because of the demand volatility, firm B weighs the benefits
of more capital in period 2 with the costs of excess capital in period 1. Firm B chooses a
level of capital that balances this tradeoff. Ultimately, firm B uses more capital than firm A,
as well as uses more total labor than firm A over the two periods. Thus, firm B uses more
inputs than firm A over the two periods, to produce the same amount of output; 2Q.
Any measure of productivity equates using more inputs over a period of time to produce
the same level of output as being less productive. The two period model of production
provides the intuition for how demand volatility, adjustment costs, and temporal aggregation
together affect measured productivity. Over the two periods, the measured productivity of
firms A and B are different. The difference in measured productivity comes despite both
firms having identical technical productivity. More specifically, the firm experiencing more
demand volatility is inferred to be less productive.
Temporal aggregation conceals the differences in the volatility of quantity demanded
across firms. If adjustment costs are important, this concealing of the demand environment
is problematic for inferences of productivity. Alternatively, if adjustment costs are small the
impact of demand volatility and temporal aggregation on measured productivity are minimal.
When the elasticity of substitution is zero, firm B’s use of more inputs is concentrated to
the input with adjustment costs (capital); see bottom right panel. Firm B’s total use of the
flexible input (labor) is the same as firm A’s. As the elasticity of substitution decreases, the
influence of demand volatility and temporal aggregation on measured productivity becomes
more concentrated to the input facing adjustment costs.
Furthermore, with no technical substitution, relative input prices do not effect the cost
minimizing mix of inputs. The bottom panels of figure (3) illustrate this insight by noting
that the optimal production plan for both firms is invariant to rotations of the price vector.
8
9
Units of Capital
KA
KA
LA
1,2
LA
1,2
Units of Labor
Q Isoquant
Price Vector
Units of Labor
Q Isoquant
Price Vector
KB
K
B
KA
KA
LB
1
LB
1
Q − 0 Isoquant
LA
B
Q + 0 Isoquant
L
L
B
Q − 0 Isoquant
LA
LB
2
Q + 0 Isoquant
Units of Labor
Price Vector
Units of Labor
LB
2
Price Vector
Average Isoquant
This figure displays the optimal production plans of firm A in the left panels and firm B in the right panels. In the
top panels the elasticity of substitution between capital and labor is one, while in the bottom panels the elasticity
of substitution between capital and labor is zero. On the horizontal axis of all panels are units of labor, and on the
vertical axis of all panels are units of capital. In each figure the isoquants of each firm for both periods are displayed
in black, while the price vector for capital and labor at a point of production are displayed in gray. For each firm the
optimal production plan is denoted by the black dashed lines.
Units of Capital
Figure 3: Firm A’s and B’s Optimal Production Plans
Units of Capital
Units of Capital
Essentially, how input ratios vary with variation in relative input prices identifies the elasticity
of substitution.
For the rest of the paper, I use the insights of this section to investigate empirically the
effect of demand volatility with adjustment costs and temporal aggregation on measured
productivity.
3
Empirical Strategy
Two characteristics of the hotel and airline industries provide the basis for my empirical strategy. The first key is the availability of monthly observations of output. Observing monthly
observations of output, allows me to measure the volatility of demand within a year; the key
independent variable of interest. Second, the similarity of the hotel and airline industries,
with the exception of the size of adjustment costs in capital at any one location, serves as the
point of comparison. Finding that increases in demand volatility lead to decreases in measured productivity for hotels and not for airlines supports the predictions of the theoretical
model.
The foundation of the empirical analysis involves four distinct components. First, I require
a measure of productivity. Second, I need a measure of demand volatility. Third, I need
an estimating equation that identifies the effect of interest. Fourth, I require a source of
exogenous variation in demand volatility.
3.1
Productivity: Concept and Measure
The keys to my measure of productivity are two assumptions involving the production technology of hotels and airlines. I assume there is no technical substitution between capital
(rooms in hotels and available seats in airplanes) and other inputs, as well as constant returns to scale. While labor, materials, and energy are all necessary to produce output in
both the hotel and airline industry, there is no technical substitution between capital and
these other inputs.3 Furthermore, for both hotels and airlines assuming constant returns to
3
As a robustness check, in section (6.1) I estimate the elasticity of substitution between capital and
labor in hotels using regional variation in relative input prices. I find no evidence of technical substitution
between capital and labor. Recent evidence suggests that even for manufacturing industries the elasticity of
substitution between capital and labor is less than one (Oberfield and Raval (2012), Raval (2014)).
10
scale is warranted.4 Given these assumptions and the insights of the theoretical section, I
construct measured productivity given observations of Yimt and Kimt , where Yimt is the level
output, Kimt is the level of capital for metro area (destination) i, segment (airline) m, in year
t.5 Specifically, I define the measured productivity for hotels and airlines to be:
Measured Productivityimt =
Yimt
Kimt
=
Room Nights Soldimt
≡ Occupancy Rateimt
Room Nights Availableimt
=
Passenger Milesimt
≡ Load Factorimt .
Available Seat Milesimt
Measured productivity is at the level of a metro area-segment-year or destination-airlineyear.6 For the rest of the paper, I interchange occupancy rate and load factor with measured
4
The assumption of constant returns to scale can be empirically tested. In section (6.4), I provide estimates
of the returns to scale for hotels across several different estimation specifications. For all specifications, the
estimate of the returns to scale is within 0.05 of one, and the results presented here are not sensitive to using
any of the values suggested by this exercise.
5
For a more thorough description of the methods to estimate productivity see Ackerberg et al. (2007) and
Van Biesebroeck (2007, 2008). Bernanke and Parkinson (1991) utilized the technical substitution assumption
to estimate a value added production function when they observed gross output without observing material
use. Gandhi et al. (2011) discuss the collinearity issues of estimating the production function and how this
relates to the distinction between the gross output production function and the value added production
function. Empirically the capacity of airlines at the destination level is not fixed, at least at the monthly
frequency that I observe. The purpose of including airlines in the study is for exactly this fact. Despite
the capacity of airlines not being fixed, I still assume that concentrating on this input is acceptable when
measuring productivity because it is likely to be more fixed at the destination level than labor, fuel and
other energy inputs and does not have any technical substitution between these other inputs. Busse (2002)
suggests that airport slot restrictions, and the need to coordinate with other airlines using the same airport
make an airline’s flight schedule fixed to some extent.
6
At this level of observation, some amount of aggregation is taking place across hotel establishments and
individual aircrafts serving different origins. Given the assumption of constant returns to scale, the measured
productivity given above constitutes the output weighted average productivity of the individual hotels and
aircrafts serving different origins. For a discussion on the role cross sectional aggregation might have on
the results see section (6.5). Additionally, this measure of productivity abstracts from the use of labor,
materials and energy. To the extent that firms minimize costs and these inputs are flexible, achieve constant
returns to scale and have no technical substitution with capital, the difference between the productivity
measure given above and a more traditional measure including all inputs would only be a constant. Given
that the goal of this paper is to explain productivity differences, this constant shift would have no impact
on the results presented here. Alternatively, one could interpret the measure of productivity above as the
“traditional measure of productivity” accounting for all the other inputs plus a measurement error. Under
this interpretation, the results presented here serve as a lower bound estimate of the role of demand volatility
11
productivity.7
3.2
Demand Volatility: Concept and Measure
The basis for my measure of demand volatility is that the supply conditions in both of these
industries remain relatively constant over the year. In principle, if supply side conditions
remain constant, volatility in quantity demanded (and prices) reflect volatility in demand.
Conceptually, I assume demand for any metro area (destination) i, segment (airline) m, year
t and month s takes the constant elasticity form given by the following equation:
log(Qimts ) = log(Dimts ) − ηimt log(Pimts )
(1)
where Qimts is quantity demanded, Pimts is the price, Dimts is a demand shifter and ηimt
is the price elasticity of demand. Under this formulation, annual demand volatility is how
much Dimts moves within the year.
With constant marginal costs and stable input prices and market structure over the year,
volatility in quantity demanded (Qimts ) corresponds to the volatility in demand (Dimts ).
Assuming constant marginal costs is linked to the assumption of constant returns to scale
and is discussed above. The primary input prices for both these industries are likely to
be stable within the year, and any variation is unlikely to be correlated with the demand.
Consequently, for the main empirical results I use the volatility of quantity demanded as my
measure of demand volatility.8
and temporal aggregation provided that the covariance between demand volatility and the idiosyncratic use
of other inputs conditional on total output produced is positive. For a formal derivation of this argument
see section (A.3) in the appendix. If neither of these arguments are persuasive, the measure above is the
conventional measure of the productivity of capital.
7
Mazzeo (2002a) and Conlin and Kadiyali (2006) use the number of rooms as a measure of capacity in
their study of the lodging industry. Baltagi et al. (1998) investigate several different measures of capacity
for the airline industry one of which is available seat miles. Unlike, some productivity studies I observe
the quantities of inputs as opposed to expenditures on inputs. Because I observe input quantities directly,
I avoid having to deflate expenditures potentially with an industry deflator and confounding differences in
input prices with differences in productivity.
8
A potential problem with using this measure arises when capacity constraints exist. In section (6.2),
I provide a robustness check for hotels by incorporating the volatility of prices in my measure of demand
volatility as well. If shifts in demand when capacity is constrained results in movements in price this alternative measure should appropriately capture the amount of demand volatility. Another potential problem
involves the assumption that the price elasticity of demand is constant over time. This is done primarily for
convenience. As soon as the price elasticity of demand varies within the year, annual “demand volatility”
12
I utilize the coefficient of variation as my measure of volatility, and the log-normal transformation to accommodate the skewness in my sample for quantity demanded. The coefficient
of variation, a normalized measure (with the mean serving as the scale), measures the dispersion of a distribution by taking the ratio of the standard deviation and the mean; σ/µ.
Using a normalized measure allows demand volatilities across demands with varying mean
levels to be comparable. Formally, for a given metro area (destination) i, segment (airline)
m, year t, I use the monthly observations (denoted by s) of quantity demanded and calculate
the coefficient of variation given by the following equation:
q
Demand Volatilityimt =
2
estd(ln(Qimts )) − 1
(2)
where std(ln(Qimts )) is the standard deviation of the logarithm of monthly room nights sold
(passengers flown) within the year.9
This measure of demand volatility captures the volatility within a year. Differences in
volatility occurring at this frequency are concealed when data is observed at the annual level.
I focus on the annual frequency because it is the most common in the productivity literature.
Another key feature of demand volatility at the annual frequency is that it is predictable.
The reasons why many more tourists come to some locations in one month relative to another month are understood by hotel and airline industry participants, and are persistent.10
cannot be distilled into one summary measure but instead involves the volatility of two separate components:
(i) volatility in demand shifts (Dimts ) and (ii) volatility in demand tilts (ηimts ). On the one hand, volatility
in the price elasticity of demand that results in volatility of quantity demanded through changes in the equilibrium price will still be captured by my measure of demand volatility. On the other hand, these movements
will be attributed to shifts in the demand curve as opposed to tilts in it. Because this distinction is not
important for understanding the effect under study, the benefits of the simplification outweigh the costs.
9
Four alternative specifications of demand volatility include (i) using the measure above but applying
1
a small sample correction (1 + 4n
) ≈ 1.021, (ii) using sales as opposed to quantities, (iii) using the nonparametric quartile coefficient of dispersion, i.e. the interquartile range divided by the median, (iv) and
using the sum of quantity sold and some scale of the average price. Using the sum of quantity sold and a
scale of price has the interpretation of being the residual of a constant elasticity of demand function, with the
scale used representing the price elasticity of demand. Both the measure involving a scale of price and the
volatility of sales do not suffer from the censoring problem generated by the capacity constraint. It turns out
the results presented are robust to each of these alternative measures of demand volatility. Results involving
either (i) the small sample correction, (ii) sales or (iii) the quartile coefficient of dispersion are available from
the author upon request. Results using the quantity and a scale of price are presented in the robustness
checks section (6.2).
10
The correlation of the contemporaneous demand volatility and the one year lag of demand volatility for
hotels is 0.86.
13
Consequently, the volatility of demand from month to month within a year is much easier
to predict than movements from week to week or year to year.11 The volatility of demand
from week to week is driven by unforseen factors, while the movements of the factors that
drive year to year fluctuations in demand such as personal income and the business cycle are
difficult to predict.
3.3
Main Estimating Equation
The main objective of the empirical section is to identify how variation in annual demand
volatility affects measured productivity. The regression equation I use in the main results to
estimate that effect takes the following form:
log(Measured Productivity)imt = ρ Demand Volatilityimt + Xit β + λt + ψm + εimt (3)
where λt is a year fixed effect, ψm is a segment (airline) fixed effect, and εimt is an error
term. Additionally, Xit includes a set of variables summarizing input prices, the overall level
of demand, and the price elasticity of demand as well as other demographic or metro area
(destination)-year controls.12 The theoretical section predicts that ρ will be negative for
industries with large adjustment costs, and zero for industries with small adjustment costs.
In this specification, I control for any systematic differences across hotel segments or airlines through the segment/airline fixed effect. The variation used to identify the demand
volatility coefficient will be within segments/airlines not across them. Variation of demand
volatility across metro areas (destinations) within segments (airlines) is less likely to confound
how aspects of pricing, vertical differentiation, and switching costs impact the distribution of
demand volatility across segments (airlines) within a metro area (destination).13 A notewor11
Demand for hotel rooms and airplane seats have significant periodic fluctuations over days of the week.
Industry trade papers suggest that demand for hotel rooms peaks on Tuesdays and Wednesdays mostly from
business travelers. Because I only observe quantities and prices at a monthly frequency, I abstract from any
variation markets or destinations have in demand volatility at the daily frequency.
12
None of the metro area (destination)-year controls included in Xit vary across the segments (airlines)
within a metro area (destination)-year. Accordingly, the estimates of the coefficients on Xit are primarily
identified off of differences in these variables across metro areas (destinations). In principle, the coefficient
on Xit could vary by segment (airline), that is, I could estimate Xit βm . I choose this more limited set-up for
the main empirical specification with the intention of not suffering from overfitting the model. The resulting
coefficient estimates of ρ for the more flexible specification, with βm , are qualitatively similar to the ones
presented here.
13
I looked into estimating the model with segment-year fixed effects, φmt , as well. These did not change
14
thy omission from the regression equation is any measure of market structure. Consequently,
the results are sensitive to misspecification due to the strategic interaction between firms.14
3.4
Source of Exogenous Variation in Demand Volatility
The goal of my identification strategy is to isolate the component of demand volatility that is
exogenous to technical productivity. To achieve this goal, I argue that the demand volatility of
an aggregate metro area or destination is exogenous to the technical productivity of the hotels
in the metro area or airlines serving that destination. Furthermore, I argue the exposure of
an individual hotel segment or airline to that aggregate demand volatility will be related to
its market share.
To operationalize this identification strategy, I construct an instrument similar to Bartik
(1991) and other studies of the effect of local market conditions on labor market outcomes
(Charles et al. (2013)). To create this instrument for any metro area (destination) i, segment (airline) m, at year t, I interact the demand volatility at the aggregate metro area
(destination) level i in that year t with the average share of that segment (airline) m over
all other metro areas (destinations) that year. Formally, the Bartik-style instrument for my
application is given by:
the estimated coefficient of ρ significantly.
14
Mazzeo (2002b) documents the presence of such strategic interaction in a study of endogenous product
quality and entry in the lodging industry. Conlin and Kadiyali (2006) find evidence of excess capacity in more
concentrated markets in a sample of Texas hotels. Campbell (2011) provides a non-parametric hypothesis
test in which the null hypothesis is atomistic competition. Campbell (2011) derives the test by building a
general model of competition that generates the testable prediction that if firms’ choices are related to market
size then strategic considerations exist between firms. This test is not appropriate, however, in a setting of
fluctuating demand, a characteristic of both hotel and airline demand. I explore if market structure could
affect my results in two ways. First, I run the same main empirical specification in equation (3), but I include
two measures of market structure (i) the concentration of capacity in the particular metro area-segment-year
as measured by the Herfindahl index and (ii) the number of hotels in the metro area-segment-year. Including
these two measures of market structure do not affect the coefficient estimates on demand volatility. Next, I
run the empirical specification in equation (3), but instead of using the logarithm of the occupancy rate as
the dependent variable, I use the logarithm of the revenue per available room (REVPAR) in the metro areasegment-year. In this specification, I find after controlling for segment level fixed effects demand volatility has
no effect on the revenue per available room, an implication that would result from a model of monopolistic
competition. The regression results including the two measures of market structure are available from the
author upon request. The regression results with revenue per available room are reported in table (21) in
the appendix.
15
i
Bartikimt = Smt
× Demand Volatilityit
i
=
Smt
X Yjmt
1
P
.
#M arkets − 1 j6=i l Yjlt
(4)
(5)
Two conditions support the credibility of this instrument. First, this instrument must
relate to the demand volatility faced by any individual segment (airline) in a metro area
(destination). This condition is empirically testable, and is likely to hold given that an
individual segment (airline) in a metro area (destination) inherits the demand conditions of
the metro area (destination) as a whole, and that market shares of segments (airlines) should
be similar across metro areas (destinations).15 Second, this instrument must not be affected
by the technical productivity of that segment (airline) in the metro area (destination). I
argue the second condition is reasonable given the size of the metro areas (destinations)
in my sample. The technical productivity of a particular metro area-segment (destinationairline) is unlikely to affect the aggregate demand volatility of the metro area (destination)
nor the market share of that segment (airline) nationally. With this empirical strategy in
mind, I now summarize the key variables that I use to implement this empirical strategy and
their sources.
4
Summary of the Data
The primary source of information for the hotel application comes from the consulting firm
Smith Travel Research (STR).16 The STR report includes monthly hotel performance data
for 92 large metro areas from 2006–2009. In general, these metro areas resemble the Census
Bureau’s Metropolitan Statistical Areas (MSA), but in some cases align more closely to
Metropolitan Statistical Divisions.17 STR gathers individual hotel occupancy, room count,
and daily rate information from participating hotels in each metro area and summarizes the
15
For the scatter plot of the measure of demand volatility and the Bartik instrument for the hotel and
airline samples see figures (7) and (8) in the appendix.
16
More information on STR’s research initiative can be found at: www.str.com/products/share-center.
17
For an exhaustive list of the matches between STRs definition of a geographic market and the MSA or
Metro Statistical Division I use, see tables (13)-(14) in the appendix. For the geographic definitions of the
Census Bureau’s MSA and Metro Statistical Divisions see www.census.gov/population/metro/data/def.html.
16
observations for industry participants.18 The overall coverage of the hotels in the STR sample
represents close to 40 percent of the total number of hotels in the country and 60 percent
of national sales. To prevent revealing performance information of any individual hotel,
STR provides summary measures at the geographic level. In addition to the geographic
location, STR separates hotels in each metro area into seven different scales or segments.
These scales range from economy to a luxury segment, and include an independent segment
as well.19 With at most seven different segments across 92 metro areas, I have close to 620
units of observation in the cross section each year. For any given metro area-segment-year, I
have monthly observations of occupancy rates, room nights sold, number of rooms available,
revenue, and average daily rates.
The primary source of information for the airline application comes from the United
States Department of Transportation (DOT) Bureau of Transportation Statistics (BTS).20
Sample construction for the airline application was done to best parallel the geographic make
up of the hotel sample. To accomplish this goal, I focus only on airports in the 92 metro
areas in the STR sample. All the available information including passenger counts, and load
factors was gathered for any of the five major airlines (American Airlines, Delta, Southwest,
US Airways, and United) that maintained operations at an airport in any of the 92 metro
areas over the entire duration of the sample 2003-2013.
For each airline-destination-year, I gather monthly passenger counts, passenger-miles,
available seat-miles, load factors, and number of flights.21 With five different airlines each
serving an average of 45 destinations in the sample, I have 225 units of observation in the
cross section.
To control for other factors that might influence measured productivity, I gather information on input prices, the level of demand, and the price elasticity of demand and other
key demographic characteristics. For an exhaustive list of these variables and their sources
18
STR does impute values for hotels in their census of hotels that do not participate in the individual
surveys. STR imputes these values using hotels of similar scale and type that do report, to impute the
missing values. This source of measurement error is unlikely to drive any of the main results. Of the 2,063
individual metro area-segment-years, over 80 percent of the markets have 80 percent coverage as measured
by number of rooms. Furthermore, the results are qualitatively similar if I drop the observations from metro
area-segment-years where less than 80 percent of rooms in the market are covered by the STR respondent
sample.
19
A full list of the hotel chains that constitute each segment is available from the author upon request.
20
For more information on the information gathered by the Bureau of Transportation Statistics see:
www.rita.dot.gov/bts/sites/rita.dot.gov.bts/files/subject areas/airline information/index.html.
21
For a list of the destinations and the associated airport I use for each airline in that destination see table
(15) in the appendix.
17
Table 1: Descriptive Statistics of Productivity, Demand Volatility and Capacity Counts for
Hotels and Airlines
Hotel Sample N = 2063
log(Occupancy) (log(%))
Demand Volatility (units)
Number of Hotels
Number of Rooms
Number of Rooms Volatility (units)
Market Share (Room-nights Sold)
Airline Sample N = 2020
log(Load Factor) (log(%))
Demand Volatility (units)
Number of Flights
Available Seat Miles (thous.)
Number of Flights Volatility (units)
Available Seat Miles Volatility (units)
Market Share (Passengers)
Mean
Std
Min
Max
-0.50
0.16
43
5292
0.04
16.55
0.14
0.06
48
7346
0.02
8.21
-1.03
0.04
4
521
0.02
1.17
-0.12
0.46
577
141036
0.21
85.19
-0.25
0.15
12196
1338061
0.11
0.12
15.54
0.10
0.11
21849
2526128
0.11
0.13
16.75
-0.76
-0.05
0.03
2.39
295
210750
28080 27858478
0.02
1.81
0.02
2.34
0.12
97.25
Source: STR and author’s calculations for the occupancy, demand volatility, number of hotels, number of
rooms and market share for each of the 2,063 metro area-segment-years observed in the hotel sample. BTS
and author’s calculations for the load factor, demand volatility, number of flights, number of available seat
miles, and market share for each of the 2,020 destination-airline-years observed in the airline sample.
see the appendix section (A.1).
Table (1) provides summary statistics of the key variables used in the empirical analysis
for both hotels and airlines.22 Several facts pertinent to the empirical strategy are evident
immediately from the summary statistics. First, there is significant variation in occupancy
rates and load factors. Next, the metro areas and destinations in both samples are large.
On average, there are 43 hotels in a metro area-segment and over 5,000 rooms. The average
number of annual flights by an airline to a destination is over 12,000. Furthermore, the
segment shares suggest that the average individual hotel sells less than 1 percent of the
annual total of room-nights sold in its metro area (across all segments). Similarly, even
though airlines are large in terms of their scope nationally, the average airline’s share of
22
For a full summary of the data used in the hotel application see table (17) in the appendix. For a full
summary of the data used in the airline application see table (18) in the appendix.
18
passengers at any one destination is less than one fifth of the total. There is also evidence
of the difference in adjustment costs between the industries. Despite the average demand
volatility in hotels (0.16) and airlines (0.15) being similar, the volatility (measured by the
coefficient of variation) of capacity of hotels (0.04) is a third of the volatility in capacity of
airlines (0.12).
5
Results
Table (2) provides the regression results for several alternative specifications of the regression
specified by equation (3) for the hotel industry. Specifications (a) and (b) summarize the
explanatory power of demand volatility and temporal aggregation on measures of productivity in the hotel industry. The results from specifications (a) and (b) indicate that demand
volatility has a strong negative and statistically significant effect on measured productivity,
explaining a significant share of the variation in measured productivity for hotels. Specification (a) suggests that the correlation between demand volatility and measured productivity
explains close to 15 percent of the variation of measured productivity. The interpretation
of the coefficient is a semi-elasticity. Based on the coefficient from specification (a), moving
from no demand volatility to the maximum amount observed in the sample (0.47) leads to a
44 percent decrease in measured productivity.
In specification (c), the full array of controls including those designed to control for longer
run movements in demand are used as well as segment and year fixed effects. Controlling for
these additional factors, results in an estimated coefficient on demand volatility of -0.53. In
specification (d), I use the Bartik instrument described in the empirical strategy section.23 In
this specification the coefficient decreases slightly in absolute magnitude to -0.48.24 Using this
estimate of the direct effect of demand volatility suggests a one standard deviation increase in
demand volatility leads to a 4 percent, or a seventh standard deviation, decrease in measured
productivity.
Specifications (e) and (f) provide estimates for alternative sub-samples. Specification (e)
reports the regression results dropping all metro area-segment-year observations involving
23
Because the F -statistics from the first stage regressions for each regression using the Bartik instrument
((d)-(g)) are all greater than 10, I can reject the hypothesis that the Bartik instrument is a weak instrument
(Staiger and Stock (1997)).
24
Using the Hausman test for endogeneity, however, I am unable to reject the hypothesis that the demand
volatility at the segment level is exogenous.
19
Table 2: Main Regression
(a)
(b)
ρ
-0.97 -0.72
(0.05) (0.05)
Dep. Variable: log(Yimt /Kimt )
Mean:
-0.50 -0.51
Year/Segment FEs
Indirect Controls
yes
Full Controls
Drop Independents
Drop 2008
Bartik Instrument
Use Employment
Hausman Endogeneity Test
F -stat (1st stage)
R2
0.14
0.48
N
2063
1837
Results for Hotels
(c)
(d)
(e)
-0.53
-0.48
-0.52
(0.04) (0.05) (0.05)
(f)
-0.40
(0.05)
(g)
-0.58
(0.07)
-0.51
yes
yes
yes
-0.51
yes
yes
yes
-0.51
yes
yes
yes
-0.51
yes
yes
yes
yes
0.73
1837
no
239.43
0.73
1837
-0.50
yes
yes
yes
yes
yes
no
191.13
0.72
1597
yes
yes
no
176.13
0.74
1327
yes
no
86.05
0.73
1837
Regression results for several alternative versions of the regression specified in equation (3) for hotels. The
estimated coefficient of demand volatility is reported for all specifications in the first row, with the heteroskedasticity robust standard errors reported in the second row within parenthesis. Additional statistics
for each specification are given including if the Hausman endogeneity test was significant at the 1 percent
level (if applicable), the F -statistic of the first stage regression (if applicable), the r-squared (R2 ) and the
number of observations (N ) in the last rows. Specification (a) reports the coefficient, absent any fixed effects
or metro area-year controls. Specification (b) reports the coefficient from a regression including controls for
input prices, level of demand, and price elasticity of demand including: hotel occupancy tax rate, logarithm
of the average wage in the hotel industry, logarithm of the U.S. Department of Housing and Urban Development’s fair market rent for a 3 bedroom, logarithm of personal income per capita, logarithm of employment in
the leisure and hospitality industry, and the unemployment rate. Specification (c) adds a set of demographic
controls at the metro area-year level including: logarithm of employees in leisure and hospitality sector per
square mile, the logarithm of the share of total non-farm employment in the leisure and hospitality sector,
logarithm of personal income, five year log change in personal income, five year log change in personal income
per capita, and five year log change in employment in the leisure and hospitality as well as year and segment
fixed effects. In specification (d), a Bartik type instrument is used for demand volatility. Specification (e)
reports the coefficient when one drops the segment-year observations that involve independently affiliated
hotels. Specification (f) reports the coefficient when one drops the segment-year observations that were in
2008. Specification (g) reports the coefficient when one uses the annual coefficient of variation in employment
in leisure and hospitality at the metro area-year level as the instrument for demand volatility.
20
independents. In the STR report, hotels included in the independent segment could be an
economy or a luxury hotel, but are not affiliated with a national chain. Because of this reporting practice, the ability for the segment fixed effects in the main specification to control
for the role of vertical differentiation could be limited. Additionally, I provide regression results dropping all metro area-segment-year observations that occurred in 2008, the lone year
in the STR sample experiencing a recession as defined by the National Bureau of Economic
Research (NBER) over the entire twelve months of the year.25 In both specifications (e) and
(f) the estimate of the demand volatility coefficient remains close to the previous specifications. These results suggest that the underlying variation in the sample that generated the
results in specifications (a)-(d) are not confined to either the independent hotels or the height
of the Great Recession.
Lastly, I provide the regression results substituting the coefficient of variation of employment in the leisure and hospitality sector at the metro area-year level for the Bartik
instrument of demand volatility (specification (g)). Employment in the leisure and hospitality sector should track with movements in demand for hotels. Employment in the leisure
and hospitality sector does not suffer from any censoring that measuring demand with roomnights might suffer from.26 With the employment series substitution, the estimate of the
demand volatility coefficient suggests a strong negative effect that falls within the ranges of
all the previous specifications in magnitude.
To provide further context for the results, I present a summary of the coefficient estimates
for the controls included in the main regression results. Table (3) reports these coefficient
estimates across the specifications (b)-(g).27
Very few of the other indicators have as strong of an effect on measured productivity as
demand volatility.28 For example, the size of the effect of demand volatility on measured
25
The Great Recession began in December of 2007 and lasted until June of 2009. For business cycle dates
from the NBER of past recessions see: www.nber.org/cycles.html.
26
For an additional robustness check regarding the censoring (from above) that might exist in the demand
volatility measure, see section (6.2).
27
Table (22) in the appendix provides a summary of the the expected sign, the sign of the estimated
coefficient (if it is the same for all specifications (b)-(g)), as well as if the coefficient estimate is statistically
significant from zero for all of the specifications (b)-(g) at a 5 percent significance level for a subset of the
control variables included in the main hotel regressions.
28
The overall size of the effect of demand volatility with adjustment costs and temporal aggregation on
measured productivity of hotels is not the only reason why the effect is important. Omitting the role of
demand volatility and temporal aggregation on measured productivity lead to misleading inferences of other
contributing factors to hotel productivity. For example, using the same sample of hotel data, I find that
omitting demand volatility controls would alter the inference of the role of right to work state legislation on
hotel productivity as well as the share of chain affiliated hotels versus independents (see table (11) in the
21
Table 3: Estimated Coefficients for Control Variables in Hotel Regressions
(b)
0.04
(0.02)
0.05
(0.01)
0.09
(0.02)
-0.04
(0.02)
-0.02
(0.02)
0.03
(0.00)
-0.03
(0.00)
log(Avg. Hotel Salary)
log(Avg. Electricity Price)
log(Avg. 3-bedroom Rental Price)
log(Personal Income/capita)
log(Occupancy Tax Rate)
log(Emp in Leisure & Hospitality)
Unemployment Rate
log(Emp in Leisure & Hospitality)/sq. mile
log(Share of Total Emp in Leisure & Hospitality)
log(Personal Income)
5 year log diff in Personal Income
5 year log diff in Personal Income/capita
5 year log diff in Emp in Leisure & Hospitality
Year/Segment FEs
Indirect Controls
Full Controls
Drop Independents
Drop 2008
Bartik Instrument
Use Employment
N
yes
1837
22
(c)
0.02
(0.02)
0.01
(0.01)
0.10
(0.01)
0.02
(0.02)
-0.01
(0.02)
0.07
(0.01)
-0.01
(0.00)
0.00
(0.00)
-0.01
(0.02)
-0.04
(0.01)
0.03
(0.06)
0.56
(0.08)
0.31
(0.05)
yes
yes
yes
1837
(d)
0.02
(0.02)
0.01
(0.01)
0.11
(0.01)
0.01
(0.02)
-0.00
(0.02)
0.07
(0.01)
-0.01
(0.00)
0.00
(0.00)
-0.01
(0.02)
-0.04
(0.01)
0.03
(0.06)
0.56
(0.07)
0.32
(0.05)
yes
yes
yes
(e)
0.02
(0.02)
0.01
(0.01)
0.09
(0.01)
0.01
(0.02)
-0.01
(0.02)
0.07
(0.01)
-0.01
(0.00)
0.00
(0.00)
-0.02
(0.02)
-0.04
(0.01)
0.04
(0.07)
0.55
(0.08)
0.32
(0.06)
yes
yes
yes
yes
(f)
0.04
(0.02)
0.02
(0.01)
0.11
(0.02)
-0.01
(0.02)
0.01
(0.02)
0.06
(0.01)
-0.01
(0.00)
0.00
(0.00)
-0.01
(0.02)
-0.03
(0.01)
0.04
(0.07)
0.51
(0.09)
0.33
(0.06)
yes
yes
yes
yes
yes
yes
yes
1837
1597
1327
(g)
0.01
(0.02)
0.01
(0.01)
0.10
(0.01)
0.02
(0.02)
-0.01
(0.02)
0.07
(0.01)
-0.01
(0.00)
0.00
(0.00)
-0.01
(0.02)
-0.04
(0.01)
0.03
(0.06)
0.56
(0.07)
0.31
(0.05)
yes
yes
yes
yes
1837
productivity is three times as large as the effect of demand density (as measured by the logarithm of employees in the leisure and hospitality sector per square mile) in hotels. Syverson
(2004a) found increases in demand density raised the average productivity levels and reduced
the spread of productivity in ready-mix concrete. Here, I find that increasing demand density
does lead to an increase in the measured productivity of hotels, but this effect is small in
comparison to the effect of annual demand volatility on measured productivity.
A couple of patterns across the alternative specifications are worth highlighting. First,
the role of the price of capacity, as measured by HUD’s fair market rent for a 3 bedroom unit
has a positive, and statistically significant, effect on the measured productivity of hotels. As
one would expect, as the cost of a room (occupied or otherwise) increases the incentive to
expand capacity decreases. The consequence of this incentive along with demand volatility
is higher measured productivity.
Second, the price of labor as measured by the average hotel employee’s salary in the metro
area and the price of energy as measured by the average state wide price of electricity for
commercial customers also both have positive associations with measured productivity, although these are not statistically significant across all specifications. Again, this is consistent
with the incentive to decrease capacity as the marginal cost of a rented room increases.
Lastly, the overall level of demand is positively associated with measured productivity.
Here, I use the employment in the leisure and hospitality sector in the metro area and the
metro area’s unemployment rate to measure both the activity of the leisure and tourism sector as well as the overall state of business activity. These two measures provide a summary
measure of both the level of demand from the transient (tourism) segment of travelers as
well as the business segment. In both cases, increases in demand are positively associated,
and statistically significant across all specifications, with measured productivity. This positive association is consistent with the effect level shifts in demand will have on measured
productivity when demand fluctuates.
Other broad trends that can be found from the additional controls include the role of
longer run movements in the personal income and tourism activity of a metro area. Both the
five year log change in personal income per capita and the five year log change in employment
appendix for the regression results as well as a brief discussion of the estimating regression). In separate
regressions, omitting controls for demand volatility lead to negative and statistically significant coefficients on
both a “right-to-work dummy” variable as well as a share of chain affiliated units variable. These results are
not robust to the role of demand volatility and temporal aggregation. As soon as, demand volatility controls
are included in each regression, the coefficients on the “right-to-work” and the share of chain affiliation
variables are not statistically distinguishable from zero.
23
in the leisure and hospitality sector are positively associated with measured productivity.
These results provide further support for the large adjustment costs in capacity for hotels.
Even five year movements in demand have significant impacts on measured productivity.
The important role of demand volatility and temporal aggregation on measured productivity, however, does not translate to the airport industry. Table (4) provides the regression
results for several alternative specifications of the regression specified by equation (3) for
the airline industry. In specification (a) the regression is run absent any demographic or
destination-year controls, while in specification (b) controls for input prices, the level of demand and the price elasticity of demand are included. In both specifications (a) and (b) the
estimate of the demand volatility coefficient is negative but very small. The direct effect of
demand volatility on measured productivity has no explanatory power.
In specification (c), factors summarizing long run trends in the level of demand and price
elasticity of demand are included as well as airline and year fixed effects. Controlling for these
additional factors, has a limited effect on the estimate of the demand volatility coefficient,
which remains close to zero. In specification (d), I report the coefficient on demand volatility
using the Bartik instrument described in section (3). In this specification the coefficient
increases slightly to 0.08.29 The coefficient is a semi-elasticity, that is a unit increase in the
coefficient of variation of demand increases measured productivity by 8 percent. This effect
is barely statistically distinguishable from zero.
Based on the results thus far, demand volatility has little effect on temporally aggregated
measures of productivity for airlines at the destination level. Specification (e) provides a
robustness check. US Airways experienced a significant merger with America West during
the sample. In specification (e), the estimate of the demand volatility coefficient remains
close to zero. This result suggests that the underlying variation in the sample that generated
the results in the previous specifications is not confined to US Airways. All of the alternative specifications provide a similar pattern; demand volatility has no effect on measured
productivity at the destination level for the airline industry.
The strong differences in results between the hotel and airline applications are consistent
with the flexibility of capital for both industries. Hotels face large adjustment costs in available rooms, while airlines are more flexible in adjusting the available seats to any destination
in their network. As mentioned before, this intuition appears in the summary statistics of
29
Because the F -statistics from the first stage regressions for each regression using the Bartik instrument
((d)-(e)) are all greater than 10, I can reject the hypothesis that the Bartik instrument is a weak instrument
(Staiger and Stock (1997)).
24
Table 4: Main Regression
(a)
ρ
-0.02
(0.02)
Dep. Variable: log(Yimt /Kimt )
Mean:
-0.25
Airline/Year FEs
Indirect Controls
Full Controls
Bartik Instrument
Drop US Airways
Hausman Endogeneity Test
F -stat (1st stage)
R2
0.00
N
2420
Results for Airlines
(b)
(c)
(d)
-0.00 -0.02
0.08
(0.02) (0.02) (0.03)
-0.25
yes
0.34
2420
-0.26
yes
yes
yes
0.44
2200
-0.25
yes
yes
yes
yes
yes
41.34
0.43
2200
(e)
0.05
(0.03)
-0.25
yes
yes
yes
yes
yes
yes
48.33
0.45
1890
Regression results for several alternative versions of the regression specified in equation (3) for airlines.
The estimated coefficient of demand volatility is reported for all specifications in the first row, with the
heteroskedasticity robust standard errors reported in the second row within parenthesis. Additional statistics
for each specification are given including if the Hausman endogeneity test was significant at the 1 percent
level (if applicable), the F -statistic of the first stage regression (if applicable), the r-squared (R2 ) and the
number of observations (N ) in the last rows. Specification (a) reports the coefficient, absent any fixed
effects. Specification (b) reports the coefficient simply controlling for input prices, level of demand, and
price elasticity of demand including: passenger facility charge tax rate, logarithm of the U.S. Department of
Housing and Urban Development’s fair market rent for a 3 bedroom, logarithm of personal income, logarithm
of personal income per capita, logarithm of employment in non-farm employment, and the unemployment
rate. Specification (c) adds a set of demographic controls at the destination-year level including: five year log
change in personal income, five year log change in personal income per capita, and five year log change in total
non-farm employment as well as airline and year fixed effects. In specification (d), a Bartik type instrument is
used for demand volatility. Specification (e) reports the coefficient when one drops the observations involving
US Airways.
25
both these industries. The average volatility of the number of available rooms within the
year for hotels in the sample is 0.04 with a maximum of 0.21. Alternatively, the average
volatility of the number of available seat miles within a year for all five airlines used in the
airline sample was 0.12, with a maximum of 2.33.
Figures (4) and (5) provide further empirical evidence of the role of adjustment costs.
In each figure, I display the peak to trough levels of capacity and quantity demanded for
hotels (figure (4)) and airlines (figure (5)). Along the vertical axis the percentage of the
peak value is displayed, while along the horizontal axis the month’s rank of that year for
quantity demanded (descending) is reported. For both the hotels and airlines, the 90th and
10th percentiles are provided for capacity with light gray shading, and quantity demanded
with dark gray shading. For airlines, I also provide the average across all five airlines in my
sample of the peak to trough fall of the total number of flights across all U.S. destinations
over the year.
The strong difference in the movement of capacity relative to demand across the two
industries is clear from figures (4) and (5). Hotels while exhibiting similar median peak to
trough falls in quantity demanded, have as little as a third of the movement in capacity along
the peak to trough. Furthermore, the large spread in the troughs of quantity demanded for
hotels between the 90th and 10th percentiles illustrates the key variation used in this section.
Airlines ability to fluctuate capacity to be meet demand, seems to only be partially explained
by movements on the number of flights. This fact suggests that a large amount of substitution
of capacity occurs across destinations within a year.
To summarize the effect of demand volatility with adjustment costs and temporal aggregation on measured productivity in hotels, I construct a variance decomposition of measured
productivity. The empirical analysis up to this point has shown that differences in demand
volatility and temporal aggregation affect measured productivity in hotels because adjustment costs make capital effectively fixed over the year. The limited technical substitution
between capital and other inputs suggests the effect of demand volatility on measured productivity is concentrated to the input facing adjustment costs, capital.
To motivate the variance decomposition I revisit the measured productivity of firm B, the
firm with demand volatility in the theoretical model. Figure (6) illustrates the component
of measured productivity that is driven by demand volatility. In the setting where capital is
fixed over the year and there is no technical substitution between capital and other inputs,
the effect of demand volatility on measured productivity can be summarized by the difference
26
27
0.5
1
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
2
3
4
5
6
7
8
9
Rank of Month (Descending from peak)
Quantity Demanded
Capacity
11
12
I display the the 90th and 10th percentiles of annual peak to trough patterns for both quantity demanded (dark gray) and capacity (light
gray) among hotels. Along the vertical axis for both panels is the percentage of the peak value, while along the horizontal axis is the
month’s rank of quantity demanded for the year. For an explicit discussion of the sources of the data see section (4).
10
Figure 4: Annual Peak to Trough Demand and Capacity for Hotels
Source: Smith Travel Research (STR) and author’s calculations
Percentage of Peak Value (%)
28
0.5
1
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
2
3
4
5
6
7
8
9
Rank of Month (descending from peak)
Number of National Flights
Quantity Demanded
Capacity
11
12
I display the the 90th and 10th percentiles of annual peak to trough patterns for both quantity demanded (dark gray) and capacity (light
gray) among airlines. I also display the average annual peak to trough pattern of the total number of flights (crosses) across all U.S.
destinations for each of the 5 airlines in my sample. Along the vertical axis for both panels is the percentage of the peak value, while along
the horizontal axis is the month’s rank of quantity demanded for the year. For an explicit discussion of the sources of the data see section
(4).
10
Figure 5: Annual Peak to Trough Demand and Capacity for Airlines
Source: Bureau of Transportation Statistics and author’s calculations
Percentage of Peak Value (%)
Figure 6: Variance Decomposition: Demand Volatility with No Technical Substitution
Q + 0 Isoquant
Units of Capital
KB = Q + 0
Q
Q − 0 Isoquant
}
Demand Volatility Effect
LB
1
L
B
LB
2
Units of Labor
The figure displays the optimal production plan of firm B when the elasticity of substitution
is zero. On the horizontal axis are units of labor, and on the vertical axis are units of capital.
The isoquants of firm B are displayed in solid lines, and the optimal production plan is
denoted by the dashed lines.
between the maximum and the average quantity demanded within the period of aggregation.
Following the discussion above, I construct a variance decomposition of measured productivity that is defined by the following equation:
Measured Productivityimt = Demand Volatility Effectimt + Technical Productivityimt
= λMeasured Productivityimt
+ (1 − λ) Measured Productivityimt
where λ is equal to the reciprocal of the maximum monthly occupancy rate achieved by the
hotel segment over the year. This decomposition assigns the component of measured produc-
29
tivity that can be attributed solely to variations in monthly quantity demanded over the year
to the Demand Volatility Effect, while the rest is attributed to Technical Productivity. Not
surprisingly, the variance in the measured productivity coming from the demand volatility
effect alone in this decomposition is significant. The ratio of the top to bottom decile of measured productivity differences attributed to demand volatility is 1.21. This ratio compares to
a ratio of the top to bottom decile of measured productivity of 1.45.30 The demand volatility
effect explains up to 35 percent of the variance in measured productivity for hotels.
6
Robustness of Results
To document the role of demand volatility, adjustment costs and temporal aggregation on
measurements of productivity, I use several assumptions and make several modeling choices.
In this section, I provide justifications or alternative specifications for several of the key assumptions and modeling choices to provide evidence of the robustness of the results. Because
the primary results of the paper pertain to the effect of demand volatility with adjustment
costs and temporal aggregation on the measured productivity of hotels, I limit the discussion
in this section to the hotel application.
6.1
Technical Substitution of Capital & Labor
In the hotel industry capital in the form of available rooms serves a fundamental role in
producing output (room nights sold). While other inputs are necessary to generate a roomnight sold, there is almost no technical substitution between available rooms and these other
inputs. In the previous section, I use the lack of technical substitution between capital and
other inputs to justify my choice of focusing on output and capital alone when measuring
productivity.
I justify this choice in two different ways. First, I use the insight from the theoretical
section and estimate the elasticity of substitution using variation in regional relative input
prices.31 Next, I construct an alternative of measured productivity where I assume that the
elasticity of substitution between capital and labor is one. In both cases, I find the main
results are robust to alternative assumptions regarding the elasticity of substitution.
30
Figure (11) in the appendix displays the kernel density estimates of the distribution of measured productivity for this decomposition.
31
A similar strategy is used by Raval (2014) to estimate the elasticity of substitution between capital and
labor.
30
To estimate the elasticity of substitution I assume a constant elasticity of substitution
production function for capital and labor in metro area i in year t.32 Formally, the production
function is given by the following equation:
Yit = Ωit (αKitσ + (1 − α)Lσit )1/σ
(6)
1
is the elasticity of substitution between capital and labor. Assuming cost minwhere 1−σ
imization, I solve for the conditional factor demand functions of both capital and labor.
Using the factor demand functions, I characterize the capital-labor ratio given by the following equation:
Kit
=
Lit
Rit
Wit
1 σ−1
1−α
α
1
σ−1
(7)
where Rit is the price of capital and Wit is the wage.
Equation (7) formalizes the intuition of the theoretical section. Variation in the capitallabor ratio resulting from exogenous variation in relative input prices (Rit /Wit ) identifies the
elasticity of substitution. To operationalize this strategy, I use both measures of capital from
the STR reports as well as labor use from the County Business Patterns at the metro areayear level together with the measures of price of capital and labor to estimate the following
regression:
log (Kit /Lit ) = Constant +
1
[rit − wit ] + it .
σ−1
(8)
The estimated coefficient on relative input prices corresponds to the negative of the elasticity of substitution. For hotels, I find the point estimate of the elasticity of substitution to
be a small positive number barely statistically significant from zero.33 This result supports
the assumption of the elasticity of substitution between capital and labor to be zero.
Assuming technical substitution between labor and capital does not change the results of
32
The use of labor that I observe comes from the County Business Patterns data which is aggregated to
the metro area level. Consequently, I am unable to conduct this empirical analysis at the segment level.
33
Regression results are available from the author upon request. Figure (13) in the appendix displays the
correlation between the capital-labor ratio and the relative input prices.
31
the previous section, either. To demonstrate robustness to the substitution pattern between
capital and labor, I provide an alternative form of the production technology given by:
Yimt = min{Vimt , g(Mimt , Eimt )}
?
k
l
α
Vimt = eωimt +imt Kimt
Lαimt
(9)
(10)
where Mimt is material use and Eimt is energy use, while g(·) is some function that aggregates
the two inputs and Vimt constitutes the value added portion of the production function.
Furthermore, the value added elasticity of capital is αk and labor is αl . I assume constant
returns to scale in value added, that is, αk ≡ α and αl ≡ 1 − α. The alternative measure
?
of log productivity is given by ωimt
. In the formulation given by equations (9) and (10), the
production function of gross output Yimt is Leontief in value added Vimt and some aggregate
of materials and energy, while the production function of value added is Cobb-Douglas in
labor and capital.34 In other words, I assume the elasticity of substitution between capital
and labor is one.
To derive an alternative of measured productivity, I solve for the cost minimizing labor
demand as a function of quantity, the price of capital, and the wage where both inputs
are supplied by competitive markets. Substituting the conditional labor demand into the
production function allows me to define the alternative of measured productivity as follows:
log (Measured Productivity)?imt = yimt − kimt − (1 − α) [rit − wit ]
(11)
where rit is the log price of capital and wit is the log wage. With auxiliary information on α,
I construct an alternative for measured productivity.35
Table (5) provides the regression estimates of the main estimating equation (equation
(3)) using the alternative of measured productivity given by equation (11) and a value of
34
The formulation used here is similar to the formulation of the production function of Burnside et al.
(1995) and Basu and Kimball (1997).
35
I also looked into constructing an alternative of measured productivity, using the labor measure used in
estimating the elasticity of substitution. Using labor at the metro area-year level and the same assumptions
regarding the output elasticities used here, does not change the qualitative results. Demand volatility still
has a strong negative association with measured productivity.
32
α = 0.4.36 The results in table (5) are almost the same as the results presented earlier.
If anything, the absolute magnitude of the effect of demand volatility on this alternative
of measured productivity is larger across similar specifications. Overall, the pattern along
alternative specifications compared to the baseline results is also very similar, suggesting
that allowing for technical substitution between labor and capital does not effect the results
significantly.37
6.2
Measure of Demand Volatility
In the main results the measure of demand volatility is a dispersion measure of the quantity of
room nights sold within the year. While this measure was easy to compute from the available
data, it suffers from two potential problems. First, the number of room-nights demanded is
censored (from above) by the aggregate capacity of the hotels in any metro area-segment.38
It should be noted that at the aggregate metro area level at a monthly frequency I do not
observe any such censoring. Second, using quantity demanded as a measure of demand,
might confound movements along the demand curve with shifts in the demand curve.
I test whether the main empirical results are sensitive to either of these potential problems
by putting more structure on the demand side of the hotel market. I assume that the
aggregate demand for hotels of any particular metro area-segment, im, in year t and month
−η
s is given by the constant elasticity functional form Qimts = Dimts Pimts
, where Pimts is the
average daily price, and η is the (constant) price elasticity of demand with η > 1. Taking logs
and rearranging this function allows me to construct an alternative measure of the demand
for any particular metro area-segment-year-month:
log(Dimts ) = log(Qimts ) + η log(Pimts ).
36
(12)
According to the Economic Census, labor’s cost share of revenue for all hotels (NAICS: 721110) in 2007
was 0.26. According to the Bureau of Labor Statistics, the average cost share of labor among expenditures
on labor and capital alone was 0.62 for the entire Accommodation sector (NAICS: 721) for the four years
in the STR sample (2006–09). The results presented are not sensitive to the choice of α. Regression results
with alternative choices of α are available from the author upon request.
37
The results here are likely to generalize to any other inputs including materials and energy. For a formal
derivation of this argument see section (A.3) in the appendix.
38
Censored dependent variables are common place in the standard econometric toolbox. Handling independent variables that are censored is somewhat less common. For interval censored regressors see Manski
and Tamer (2002). For endogenous censored regressors see Rigobon and Stoker (2009).
33
Table 5: Regression Results for Cobb-Douglas Technical Substitution
(a)
(b)
(c)
(d)
(e)
(f)
(g)
ρ
-1.06 -0.70 -0.51
-0.46
-0.50
-0.38
-0.56
(0.07) (0.05) (0.04) (0.05) (0.05) (0.05) (0.07)
Dep. Variable: log(Yimt /Kimt ) − 0.6[rit − wit ]
Mean:
-3.73 -3.73 -3.73
-3.73
-3.73
-3.73
-3.73
Year/Segment FEs
yes
yes
yes
yes
yes
Indirect Controls
yes
yes
yes
yes
yes
yes
Full Controls
yes
yes
yes
yes
yes
Drop Independents
yes
Drop 2008
yes
Bartik Instrument
yes
yes
yes
Use Employment
yes
Hausman Endogeneity Test
no
no
no
no
F -stat (1st stage)
239.43 191.13 176.13 86.05
2
R
0.11
0.67
0.82
0.82
0.82
0.83
0.82
N
2063
1837
1837
1837
1597
1327
1837
Regression results for several alternative versions of the regression specified in equation (3) with alternative
of measured productivity given by equation (11) and α = 0.4. The estimated coefficient of demand volatility
is reported for all specifications in the first row, with the heteroskedasticity robust standard errors reported
in the second row within parenthesis. Additional statistics for each specification are given including if the
Hausman endogeneity test was significant at the 1 percent level (if applicable), the F -statistic of the first
stage regression (if applicable), the r-squared (R2 ) and the number of observations (N ) in the last rows.
Specification (a) reports the coefficient, absent any fixed effects or metro area-year controls. Specification
(b) reports the coefficient from a regression including controls for input prices, level of demand, and price
elasticity of demand including: hotel occupancy tax rate, logarithm of the average wage in the hotel industry,
logarithm of the U.S. Department of Housing and Urban Development’s fair market rent for a 3 bedroom,
logarithm of personal income per capita, logarithm of employment in the leisure and hospitality industry,
and the unemployment rate. Specification (c) adds a set of demographic controls at the metro area-year level
including: logarithm of employees in leisure and hospitality sector per square mile, the logarithm of the share
of total non-farm employment in the leisure and hospitality sector, logarithm of personal income, five year
log change in personal income, five year log change in personal income per capita, and five year log change
in employment in the leisure and hospitality as well as year and segment fixed effects. In specification (d),
a Bartik type instrument is used for demand volatility. Specification (e) reports the coefficient when one
drops the segment-year observations that involve independently affiliated hotels. Specification (f) reports the
coefficient when one drops the segment-year observations that were in 2008. Specification (g) reports the
coefficient when one uses the annual coefficient of variation in employment in leisure and hospitality at the
metro area-year level as the instrument for demand volatility.
34
Assuming a value of η, I can substitute Dimts in for the quantity in both the measures of
demand volatility and the construction of the Bartik instrument given by equations (2) and
(4)-(5). This measure of demand while having more structure, also has several advantages
to the measure of demand volatility used in the main results. First, movements in Dimts
coincides with shifts in the demand curve by controlling for any movements in price. The
other advantage of this measure is that it does not suffer from any censoring from above.
In the event that any metro area-segment faces a capacity constraint, shifts in the demand
curve are reflected in movements in price given the binding capacity constraint.
Table (6) presents the regression results from the main estimating regression given by
equation (3) using a price elasticity of demand parameter of 1.85. I use the price elasticity of
demand of 1.85, because it is the average of the price elasticity of demands that rationalize
the average of the Lerner indices reported by Kalnins (2006) for economy and luxury hotels.39
To benchmark these results to the main empirical specification it is important to note that
the standard deviation of the demand volatility measure for this specification is almost twice
as large as the demand volatility measure used for the main results. Taking the difference of
variation in demand volatility into account, the results presented in table (6) are very similar
to the estimates presented in the main results. The estimated coefficient on demand volatility
is negative and statistically significant from zero across all the regression specifications. To
the extent that the price elasticity of demand is constant within the year, any issues with not
incorporating price or censoring from above do not seem to be driving the main empirical
results.
6.3
Linear Form of Main Regression Specification
In the main results, the estimating equation took a linear form. There are no characteristics of
the hotel industry or the relationship between demand volatility and measured productivity
to suggest such a specification. Here, I present results of a non-parametric form. To do this,
I assume that the relationship between measured productivity and demand volatility takes a
single-index form given by:
39
Kalnins (2006) reports that the marginal cost difference for a rented room and an unoccupied room is $20
for an economy hotel and $75 for a luxury hotel. At a similar period the average daily rate for an economy
hotel was $52, while for a luxury hotel it was $144. For regression results using a price elasticity of demand
parameter of 4, a price elasticity of demand used in Bloom (2009) to model the aggregate economy, see table
(20) in the appendix.
35
Table 6: Regression Results for Alternative Measure of Demand Volatility
(a)
(b)
(c)
(d)
(e)
(f)
(g)
ρ
-0.16 -0.17 -0.12
-0.11
-0.13
-0.09
-0.18
(0.02) (0.02) (0.01) (0.01) (0.02) (0.02) (0.02)
Dep. Variable: log(Yimt /Kimt )
Mean:
-0.50 -0.51 -0.51
-0.51
-0.50
-0.51
-0.51
Year/Segment FEs
yes
yes
yes
yes
yes
Indirect Controls
yes
yes
yes
yes
yes
yes
Full Controls
yes
yes
yes
yes
yes
Drop Independents
yes
Drop 2008
yes
Bartik Instrument
yes
yes
yes
Use Employment
yes
Hausman Endogeneity Test
no
no
no
yes
F -stat (1st stage)
378.17 291.21 281.23 101.98
2
R
0.03
0.45
0.71
0.71
0.71
0.72
0.71
N
2063
1837
1837
1837
1597
1327
1837
Regression results for several alternative versions of the regression specified in equation (3) with alternative
demand volatility measure and price elasticity of demand of 1.85. The estimated coefficient of demand
volatility is reported for all specifications in the first row, with the heteroskedasticity robust standard errors
reported in the second row within parenthesis. Additional statistics for each specification are given including
if the Hausman endogeneity test was significant at the 1 percent level (if applicable), the F -statistic of the
first stage regression (if applicable), the r-squared (R2 ) and the number of observations (N ) in the last rows.
Specification (a) reports the coefficient, absent any fixed effects or metro area-year controls. Specification
(b) reports the coefficient from a regression including controls for input prices, level of demand, and price
elasticity of demand including: hotel occupancy tax rate, logarithm of the average wage in the hotel industry,
logarithm of the U.S. Department of Housing and Urban Development’s fair market rent for a 3 bedroom,
logarithm of personal income per capita, logarithm of employment in the leisure and hospitality industry,
and the unemployment rate. Specification (c) adds a set of demographic controls at the metro area-year level
including: logarithm of employees in leisure and hospitality sector per square mile, the logarithm of the share
of total non-farm employment in the leisure and hospitality sector, logarithm of personal income, five year
log change in personal income, five year log change in personal income per capita, and five year log change
in employment in the leisure and hospitality as well as year and segment fixed effects. In specification (d),
a Bartik type instrument is used for demand volatility. Specification (e) reports the coefficient when one
drops the segment-year observations that involve independently affiliated hotels. Specification (f) reports the
coefficient when one drops the segment-year observations that were in 2008. Specification (g) reports the
coefficient when one uses the annual coefficient of variation in employment in leisure and hospitality at the
metro area-year level as the instrument for demand volatility.
36
Table 7: Non-parametric Specification Results
h=1
h=2
h=3
δ̂
(S.E.)
δ̂
(S.E.)
δ̂
(S.E.)
Demand Volatility
-0.75 (0.05) -0.74 (0.05) -0.74 (0.05)
log(Avg. Hotel Salary)
0.33 (0.36) 0.33 (0.36) 0.33 (0.36)
log(Avg. Electricity Price)
0.60 (0.21) 0.60 (0.20) 0.60 (0.20)
log(Avg. Rental Price)
1.35 (0.28) 1.35 (0.28) 1.35 (0.28)
log(Personal Income/capita)
-0.73 (0.34) -0.73 (0.34) -0.72 (0.34)
log(Occupancy Tax Rate)
-0.70 (0.36) -0.70 (0.36) -0.70 (0.36)
log(Emp in Leisure & Hospitality)
0.69 (0.09) 0.69 (0.09) 0.69 (0.09)
Unemployment Rate
-0.57 (0.02) -0.57 (0.02) -0.57 (0.02)
log(Emp in Leisure & Hospitality)/Sq. Mile 0.19 (0.03) 0.19 (0.03) 0.19 (0.03)
Non-parametric density weighted average derivative results for three different bandwidth selections. The estimated density weighted average derivative for each variable and its asymptotic standard error in parenthesis
are reported down each row, where each pair of columns corresponds to a separate estimate with a different
choice of bandwidth, h.
log(Measured Productivity)imt = f (Demand Volatilityimt , Xit ) + imt
(13)
where f (·) is some arbitrary smooth function. To evaluate the effect of demand volatility
on measured productivity, I use the methods of Powell et al. (1989) to estimate the density
weighted average derivative of f (·) with respect to Demand Volatilityimt .
Table (7) provides the results for this procedure. In table (7), I provide the density
weighted average derivatives for demand volatility as well as the other factors contained in
Xit that were used in the main results. I present the results for three different bandwidth
specifications, given by h. For each of the bandwidth specifications, the density weighted
derivative of demand volatility is negative and statistically significant. The robustness of the
effect of demand volatility across the different bandwidth specifications suggest that the linear specification chosen in the previous section does not drive the results. Furthermore, the
estimated signs of the density weighted derivatives for the other variables are broadly consistent with the hypothesized signs given by table (22), and most are statistically significant
from zero.
37
6.4
Constant Returns to Scale
In the previous section, measured productivity was constructed by assuming constant returns
to scale. Several methods exist to estimate the returns to scale of a production function.
Two such methods include the panel data approach and the structural approach developed
by Olley and Pakes (1996) and Levinsohn and Petrin (2003). While the constant returns to
scale assumption seems reasonable in the hotel industry, both the panel data and structural
approaches provide an opportunity to empirically test the validity of this assumption in
the sample. Both methods use orthogonality conditions to estimate input elasticities of the
production function.40 For a production function with an elasticity of substitution between
capital and labor of one (see section (6.1)), the returns to scale are estimated using the
following regression equation:
yimt = β 0 + β k kimt + β [rit − wit ] + ωimt + imt .
(14)
Table (8) provides the results for several alternative specifications of the regression given
by equation (14) using the panel data approach. Specifications (a)-(c) report the regression
coefficients assuming no technical substitution between capital and labor. Explicitly, specifications (a)-(c), fix β = 0, and consequently the estimate of β k corresponds to the returns to
scale. Specifications (d)-(f) report the regression coefficients assuming an elasticity of substitution between capital and labor of one. Thus, specifications (d)-(f) allow for an arbitrary
output elasticity on labor and the estimate of β k corresponds to the returns to scale as the
sum of output elasticities of capital and labor. Within both (a)-(c) and (d)-(f), are varying
treatments of fixed effects and the instrument for kimt .
Across all specifications the resulting estimate of β k remains close to one with a high level
of statistical precision.41 These results provide justification for the constant returns to scale
assumption.42 The results for hotels do not seem to be driven by the constant returns to
40
The effect of demand volatility on factor demand I document offers a justification for the identification
result of Bond and Söderbom (2005) of productivity estimates from panel data methods.
41
It should be noted that the hypothesis of constant to returns to scale can be rejected in favor of an
alternative hypothesis of increasing returns to scale. To ensure that the results are not sensitive to an
assumption regarding increasing returns to scale, I provide a similar regression table using (1.04) instead of
1 when constructing my measure of productivity; see table (19).
42
Furthermore, these results also suggest that each of the traditional methods are likely to have their
estimates of annual metro-segment productivity be largely driven by the annual occupancy level of a metro
area-segment. The data requirements of the structural approach of Olley and Pakes (1996) prohibit this
38
Table 8: Regression Results for Estimating the Returns to Scale
(a)
(b)
(c)
(d)
(e)
(f)
βk
1.03
1.04
1.04
1.04
1.04
1.04
(0.00) (0.00)
(0.00)
(0.00) (0.00)
(0.00)
β
0.01
0.08
0.11
(0.02) (0.01)
(0.02)
Dep. Variable: log(Yimt )
Mean:
13.60 13.60
13.60
13.61 13.61
13.60
Lag of kimt instrument
yes
yes
Year FEs
yes
yes
yes
yes
Segment FEs
yes
yes
yes
yes
Hausman Endogeneity Test
yes
yes
F-stat (1st Stage)
22676.28
20508.43
R2
0.97
0.98
0.98
0.97
0.99
0.98
N
2063
2063
1530
1837
1837
1518
Regression results for several alternative specifications of the regression in equation (14). The estimated
coefficient for the returns to scale is reported for all specifications in the first row, with the heteroskedasticity
robust standard errors reported within parenthesis. Additional statistics for each specification are given
including if the Hausman endogeneity test was significant at the 1 percent level (if applicable), the F -statistic
of the first stage regression (if applicable), the r-squared (R2 ) and the number of observations (N ) in the
last rows. Specifications (a)-(c) report the regression coefficients assuming no technical substitution between
capital and labor. Specifications (d)-(f) report the regression coefficients assuming a Cobb-Douglas form for
the value added component of the production function. Specifications within each of the those two forms of
the production function include various fixed effects components and instruments for the kimt .
scale assumption.
method from being used with the data on hotels. Despite not being able to provide an estimate using this
approach, any effect of demand volatility and temporal aggregation present using the panel data method is
likely to be present in any application of the more structural approaches. The orthogonality conditions that
would identify the coefficient on capital are likely to be very similar in both the panel data methods and
the structural approaches. As a result, the estimate of β k is likely to be similar and thus result in similar
estimates of productivity for hotels. Furthermore, structural approaches could be problematic in this set up
given that they require the unobservable (to the econometrician) to be a scalar. In my setting, not only is the
metro area-segment level productivity an unobservable, but the level of demand volatility is an unobservable,
causing the scalar assumption to be violated.
39
6.5
Cross sectional Aggregation
The last critical modeling choice I use is the level of cross sectional aggregation. In the
results of the previous section, I use measured productivity at the metro area-segment level.
This level of aggregation included at minimum four hotels, and on average as many as 43
hotels. A potential concern is at this level of aggregation, the effect of demand volatility and
adjustment costs on measured productivity does not match the effect when examined at the
individual level. Unfortunately, there does not exist individual level information of hotels at
the requisite level of disaggregation to replicate the analysis I perform here.
Alternatively, I examine the effect of demand volatility with adjustment costs and temporal aggregation on measured productivity using the individual hotel tax records for all hotels
in the state of Texas. This source provides detailed information for each individual hotel
including the address, number of rooms and sales at a quarterly frequency. Unfortunately,
the tax records of Texas hotels does not require reporting total number of room-nights sold,
making sales the only related observation of output reported. In order to construct measured
productivity for an individual hotel, I use the methods of Klette and Griliches (1996) and
Loecker (2011) in order to accommodate unobserved variation in prices that observations of
sales might contain.43
Table (9) presents the results of the main estimating regression equation (3) for a set of
Texas hotels. While the estimates are considerably less precise, the estimated coefficient on
demand volatility is negative and statistically significant across all specifications. The results
involving individual hotels in Texas suggest that the broader patterns found in the national
sample are not likely to be driven by the level of cross sectional aggregation in that sample.
7
An Alternative Estimator
The results involving the hotel industry suggest that demand volatility has a strong effect
on measured productivity. Temporal aggregation and varying levels of input use due to
adjustment costs generate this effect of demand volatility on measured productivity. In this
section, I offer an alternative measure of productivity that accommodates variation in the
43
For a more detailed explanation on the data used and the methods see the section (A.4) in the appendix.
For a more detailed depiction of the raw correlation in the STR sample of the annual occupancy rates with
demand volatility as well as the annual revenue per room with demand volatility see figure (12) in the
appendix.
40
Table 9: Regression Results for Sample of Individual Hotels in Texas
(a)
(b)
(c)
(d)
ρ
-4.33 -9.61 -7.33 -7.91
(1.38) (2.36) (2.65) (3.47)
Dep. Variable: Equation (19)
Mean:
0.00
0.00
0.00
0.00
Year FEs
X
Brand FEs
X
X
City FEs
X
X
X
R2
0.01
0.03
0.06
0.07
N
1000
1000
1000
1000
Regression results for several alternative versions of the regression specified in equation (3) for the sample of
individual hotels in Texas. The estimated coefficient for the coefficient of variation on demand is reported
for all specifications in the first row, with the standard errors as calculated by 1000 bootstrap replications
reported in the second row within parenthesis. Additional statistics for each specification are given including
the r-squared (R2 ) and the number of observations (N ) in the last rows. Specification (a) reports the
coefficient, absent any fixed effects. Specification (b) reports the coefficient from a regression including metro
area fixed effects. Specification (c) adds a set of hotel brand fixed effects, and specification (d) includes a set
of year fixed effects.
41
volatility of demand when adjustment costs might affect temporally aggregated measures of
productivity.
The alternative approach augments the panel data methods with a random coefficient
component to the model.44 Specifically, I use the production function given by equations (9)
and (10) in section (6.1), but allow for varying output elasticity of capital. Formally, the log
production function will be given by:
yimt = α0 + (αitk + αl )kimt + αl [rit − wit ] + ωimt + yimt
αitk = γ0 + γ1 Dit + αit
(15)
(16)
where the random coefficient of the elasticity of capital is given by αitk and Dit corresponds to
a measure of demand volatility in market i and year t. In this application, I use the coefficient
of variation of quantity demanded at the metro area-year level as my measure of demand
volatility. Equation (15) corresponds to the “structural” description of the production function under the Leontief gross output and Cobb-Douglas value added formulation described
in section (6.1). Instead of modeling the dynamics of capital use explicitly, equation (16)
describes how the elasticity of capital responds to demand volatility, adjustment costs, and
temporal aggregation in a reduced form sense. Combining equations (15) and (16) produces
the estimating equation:
yimt = δ0 + δ1 kimt + δ2 kimt Dit + δ [rit − wit ] + ωimt + νimt
(17)
where δ1 = γ0 + αl , δ2 = γ1 , and δ = αl .
Table (10) reports the regression results of equation (17). Specifications (a)-(c) report the
regression coefficients assuming no technical substitution between capital and labor. Explicitly, specifications (a)-(c), fix δ = αl = 0, and consequently the estimate of δ1 corresponds to
the structural parameter γ0 . Specifications (d)-(f) report the regression coefficients assuming a Cobb-Douglas form for the value added component of the production function. Thus,
specifications (d)-(f) allow for an arbitrary αl and the estimate of δ1 corresponds to the sum
44
Several examples of papers utilizing panel data methods include Arellano and Bond (1991), Griliches and
Mairesse (1995), Blundell and Bond (1998, 2000). The random coefficient model is used routinely in demand
estimation (Nevo (2001)), and has been used to estimate productivity by Mairesse and Griliches (1988) and
Klette (1999) but not in the context of adjusting for differences in demand volatility.
42
Table 10: Regression Results for Random Coefficient Model Estimator
(a)
(b)
(c)
(d)
(e)
(f)
δ1
1.03
1.03
1.04
1.03
1.04
1.04
(0.00) (0.00)
(0.00)
(0.00) (0.00)
(0.00)
δ2
-0.07 -0.05
-0.05
-0.07 -0.05
-0.05
(0.00) (0.00)
(0.00)
(0.00) (0.00)
(0.00)
δ
0.02
0.09
0.11
(0.02) (0.01)
(0.01)
Dep. Variable: log(Yimt )
Mean:
13.60 13.60
13.60
13.60 13.61
13.60
Lag of kimt instrument
yes
yes
Year FEs
yes
yes
yes
yes
Segment FEs
yes
yes
yes
yes
Hausman Endogeneity Test
yes
yes
F-stat (1st Stage)
20406.28
18648.66
R2
0.97
0.99
0.99
0.97
0.99
0.99
N
2063
2063
1530
1837
1837
1518
Regression results for several alternative specifications of the regression in equation (17). The estimated
coefficient for the δ1 parameter is reported for all specifications in the first row, while the estimated coefficient
for δ2 and δ are reported all specifications in the second and third rows with the heteroskedasticity robust
standard errors reported within parenthesis. Additional statistics for each specification are given including
if the Hausman endogeneity test was significant at the 1 percent level (if applicable), the F -statistic of the
first stage regression (if applicable), the r-squared (R2 ) and the number of observations (N ) in the last rows.
Specifications (a)-(c) report the regression coefficients assuming no technical substitution between capital
and labor. Specifications (d)-(f) report the regression coefficients assuming a Cobb-Douglas form for the
value added component of the production function. Specifications within each of the those two forms of the
production function include various fixed effects components and instruments for the kimt .
43
of γ0 and αl . Within both (a)-(c) and (d)-(f), are varying treatments of fixed effects and the
instrument for kimt .
Not surprisingly, the estimate of the average return to scale δ1 across all specifications is
close to one. This result holds for both forms of the production function. Furthermore, the
estimate of δ2 corresponding to the sensitivity of the capital elasticity to demand volatility
is negative and statistically significant from zero at all common confidence levels across all
specifications. Similar to the results in section (6.1), the estimate of αl in the last three
specifications all are very close to zero. The results here suggest that with observations
of demand volatility a random coefficient variant of the standard panel data method to
estimating productivity might provide superior results.
8
Conclusion
In this paper, I demonstrate that (i) demand volatility, (ii) adjustment costs, and (iii) temporal aggregation together affect measured productivity. I document this effect empirically by
comparing the hotel and airline industries. In the hotel application, I find demand volatility
with adjustment costs and temporal aggregation explains as much as 35 percent of the variation in measured productivity at the metro area-segment-year level. The effect of demand
volatility and temporal aggregation is robust to the choice of functional form and the level of
technical substitution assumed between capital and labor. In contrast, demand volatility has
no effect on the measured productivity of airlines at the destination-airline-year level. The
difference in the results highlights the role of adjustment costs on the influence of demand
volatility and temporal aggregation on measured productivity.
These results lay the groundwork for several paths for further research. One path involves reevaluating the relationship of some factors, including the propensity to export and
produce multiple products, with productivity in the context of how these factors might relate
to smoothing fluctuations in demand. Next, efforts to gather or match higher frequency information to the annual observations on producers would allow one to disentangle how much
of what is observed as measured productivity differences is coming from demand volatility
and temporal aggregation. Finally, exploring how demand volatility interacts with industry
structure and how the interaction affects productivity outcomes would create a much deeper
understanding of what drives the widely different outcomes across producers.
44
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48
A
Appendix
A.1
Additional Control Variables
The list of metro area (destination)-year level information includes: personal income, personal
income per capita, the average wage in hotels (for hotel application only), the unemployment
rate, the local hotel occupancy tax rate (for hotel application only), the passenger facility
charge (for airline application only), the number of employees in the leisure and hospitality sector (for hotel application only), the number of employees in the non-farm sector (for
airline application only), the state-wide average commercial price of electricity, the number
of employees in leisure and hospitality sector per square mile (for hotel application only),
the share of non-farm employees in the leisure and hospitality sector (for hotel application
only), and the U.S. Department of Housing and Urban Development’s (HUD) fair market
rent for 3 bedroom units. These observations were gathered from a variety of sources including the Bureau of Economic Analysis (BEA), the Bureau of Labor Statistics (BLS), the
County Business Patterns (CBP), the Energy Information Administration (EIA), the State
and Metropolitan Area Data Book, the County and City Data Book, and various trade press
articles.45 Finally, in order to ensure my results are robust to longer-run trends, I also construct a set of five-year log differences of several of the variables including personal income,
personal income per capita, number of employees in the leisure and hospitality sector (for hotel application only), and number of employees in the non-farm sector (for airline application
only).
A.2
Additional Empirical Results
In this section I identify if the size of the demand volatility effect might be large enough to
alter the inferences of other factors role in explaining productivity. I explore the sensitivity
of results examining the role of Right to Work legislation and the share of chain affiliated
hotels on the measured productivity of hotels. For each application, I estimate the change in
the conditional expectation of measured productivity as a result of either being in a Right
to Work state or having a larger share of chain affiliated hotels. For each application, I then
estimate the same effect controlling for the demand volatility experienced in that market
that year. The main estimating equations are as follows:
Measured Productivityimt = βRight to Workit + Demand Volatilityimt γ + imt
Measured Productivityimt = βChain Affiliated Shareimt + Demand Volatilityimt γ + imt .
Table (11) presents the results of the regressions given by the equations above. In both
cases the estimated effect of the factor of interest is not robust to the role of demand volatility.
45
For a detailed list of all sources and additional variable information see table (16).
49
Table 11: Regression Results for the Effect of Right to Work and Chain Affiliation on Hotel
Productivity
(a)
(b)
(c)
(d)
β(Right to Work)
-0.02 -0.00
(0.00) (0.01)
β(Chain Share)
-0.10 -0.01
(0.02) (0.02)
Dep. Variable: log(Yimt /Kimt )
Mean:
-0.51 -0.51 -0.50 -0.50
Demand Volatility Controls
yes
yes
Year FEs
yes
yes
yes
yes
Segment FEs
yes
yes
yes
yes
2
R
0.49
0.69
0.51
0.69
N
1837
1837
1597
1597
Regression results for several alternative versions of the regression specified in equation (11). The estimated
coefficient of the explanatory factor, market in a Right to Work state or share of chain affiliated hotels,
with the heteroskedasticity robust standard errors reported within parenthesis. Additional statistics for each
specification are given including the r-squared (R2 ) and the number of observations (N ) in the last rows and
the use of various fixed effects.
Put differently, in both settings the omitted variable bias generated by the role of demand
volatility is large enough to alter the interpretations of the effect of each explanatory factor.
A.3
Derivation of Lower Bound Argument
This section derives formally the argument that the measure of productivity used in the
main empirical results lead to a lower bound for the effect of demand volatility on measures
of productivity. Ultimately, the argument requires four conditions:
1. The production function is constant returns to scale
2. The technical substitution between all other inputs Iimt and capital is zero
3. The other inputs are flexible
ι
4. The covariance between the idiosyncratic use of the other inputs (1 + νimt
) and demand
ι
volatility is positive: E [Demand Volatilityimt (1 + νimt )] = γ > 0
The traditional measure of total factor productivity will be given by:
ωimt = log (Yimt ) − 1 − cI log (Kimt ) − cI log (Iimt )
50
where cI is the cost share of all the other inputs, and ωimt is the traditional measure of total
factor productivity.
Given the assumptions of cost minimization, constant returns to scale, the technical
substitution between all other inputs Iimt and capital being zero, and that the other inputs
are flexible, the input demand Iimt can be defined as a function of output Yimt , the true level
ι
of productivity ωimt , a scale factor ι, and idiosyncratic input use νimt
ωimt = log (Yimt ) − 1 − c
=
I
Yimt
ι
(1 + νimt )
log (Kimt ) − c log ι
ωimt
I
ι
)
1 − cI [log (Yimt ) − log (Kimt )] + cI ωimt − cI log(ι) − cI log(1 + νimt
= log(Measured Productivity)imt − Constant − Measurement Errorimt
where the last equation follows from the fact that log(Measured Productivity)imt = log(Yimt )−
log(Kimt ).
Now, note the assumption of the expected covariance between demand volatility and the
idiosyncratic use of the other inputs is positive and that the expected variance of demand
volatility, c, must be greater than zero.
Furthermore, abstract from the other exogenous controls in the main regression specification and define the true empirical relationship between total factor productivity ωimt and
demand volatility is given by:
ωimt = ρDemand Volatilityimt + εimt .
This formulation results in an estimating equation, inclusive of the measurement error
associated with productivity, given by:
log(Measured Productivity)imt = Constant + ρDemand Volatilityimt
+Measurement Errorimt + εimt .
Using the standard results for measurement error of a dependent variable leads me to the
usual characterization of the bias of ordinary least squares (OLS) estimate of the demand
volatility coefficient:
ρb(OLS) = ρ + γ/c >> ρ.
This completes the argument that the measurement of productivity used in the main
empirical results leads to a lower bound estimate of the effect of demand volatility on more
51
traditional measures of productivity.
A.4
Estimating Productivity of Individual Hotels in Texas
To explore the sensitivity of my main results to the level of cross sectional aggregation, I
investigate whether the demand volatility effect exists in an alternative sample of individual
hotels in Texas. The data set I use comes from the Texas Comptroller of Public Accounts.46
For any given hotel the Texas Comptroller reports the quarterly sales, number of rooms,
tax payer identification, as well as the address and name of the hotel. Unfortunately, actual
quantities sold are not reported. For this reason, in order to estimate total factor productivity
and not revenue productivity I must use the methods of Klette and Griliches (1996) and
Loecker (2011).
In order to implement the methods of Klette and Griliches (1996) and Loecker (2011), I
supplement the individual hotel data from Texas with the metro level aggregates of average
price and total quantity demanded from the STR data set. Because I am required to match
the individual level hotel data to the STR market aggregates, I am restricted to only use
hotels found in the six major metro markets covered by the STR reports over the period of
2006–2009.47 Furthermore, for the purposes of using hotels that are broadly similar across
locations, I restrict the sample to hotels within eleven major chains as well as limiting my
sample to hotels that operated for a full year.48
Following the methods of Klette and Griliches (1996) and Loecker (2011), I estimate a
revenue production function by modeling demand as a constant elasticity of substitution, η
with respect to price. With sales Sjimt and capacity Kjimt at the individual hotel j in market
i, segment m, and year t I estimate the following production function:
sjimt − pimt = α0 + α1 kjimt + α2 [rit − wit ] + α3 qimt + ωjimt + ηjimt
(18)
where qimt denotes the aggregate log quantity demanded and pimt denotes the log average price
in that market i, segment m at year t reported by STR. The reduced form parameters
of the
η+1
k
α + αl ,
main estimating equation map to the structural parameters as follows: α1 = η
−1
l
α2 = η+1
α
,
and
α
=
. Finally, with estimates of the coefficients from the previous
3
η
η
equation, a measure of productivity for the individual hotel is the following:
ω
bjimt = sjimt − pimt − α
b0 − α
b1 kjimt − α
b2 [rit − wit ] + α
b3 qimt .
46
(19)
The individual hotel sales data can be acquired at: http://www.window.state.tx.us/taxinfo/taxfiles.html.
The six major metro markets in Texas include: Fort Worth/Arlington, Austin, McAllen/Brownsville,
Dallas, Houston, and San Antonio.
48
The eleven major chains include: Holiday Inn, Best Western, La Quinta, Super 8 Motel, Motel 6, Days
Inn, Courtyard, Hampton Inn, Baymont Inn, Springhill Suites, and Red Roof Inn.
47
52
53
Albany/Schenectady, NY
Albuquerque, NM
Allentown/Reading, PA
Anaheim/Santa Ana, CA
Atlanta, GA
Augusta, GA-SC
Austin, TX
Baltimore, MD
Bergen/Passaic, NJ
Birmingham, AL
Boston, MA
Buffalo, NY
Charleston, SC
Charlotte, NC-SC
Chattanooga, TN-GA
Chicago, IL
Cincinnati, OH-KY-IN
Cleveland, OH
Colorado Springs, CO
Columbia, SC
Columbus, OH
Dallas, TX
Dayton/Springfield, OH
Daytona Beach, FL
Denver, CO
Des Moines, IA
Detroit, MI
Fort Lauderdale, FL
Fort Myers, FL
Fort Worth/Arlington, TX
Grand Rapids, MI
Greensboro/Winston Salem, NC
Greenville/Spartanburg, SC
Harrisburg, PA
Hartford, CT
Houston, TX
Indianapolis, IN
Jackson, MS
Jacksonville, FL
Kansas City, MO-KS
Knoxville, TN
Las Vegas, NV
Lexington, KY
Little Rock, AR
Los Angeles/Long Beach, CA
Louisville, KY-IN
Macon/Warner Robbins, GA
Madison, WI
Maui Island, HI
McAllen/Brownsville, TX
Melbourne/Titusville, FL
Memphis, TN-AR-MS
Miami/Hialeah, FL
Milwaukee, WI
Minneapolis/St Paul, MN-WI
Mobile, AL
Myrtle Beach, SC
Nashville, TN
New Orleans, LA
New York, NY
Newark, NJ
Norfolk/Virginia Beach, VA
Oahu Island, HI
Oakland, CA
Oklahoma City, OK
Omaha, NE
Orlando, FL
Philadelphia, PA-NJ
Phoenix, AZ
Pittsburgh, PA
Portland, OR
Raleigh/Durham/Chapel Hill, NC
Richmond/Petersburg, VA
Riverside/San Bernardino, CA
Rochester, NY
Sacramento, CA
Salt Lake City/Ogden, UT
San Antonio, TX
San Diego, CA
San Francisco/San Mateo, CA
San Jose/Santa Cruz, CA
Sarasota/Bradenton, FL
Savannah, GA
Scranton/Wilkes-Barre, PA
Seattle, WA
St Louis, MO-IL
Syracuse, NY
Tampa/St Petersburg, FL
Tucson, AZ
Tulsa, OK
Washington, DC-MD-VA
West Palm Beach/Boca Raton, FL
Table 12: List of STR Metro Markets Included in the Hotel Sample
Table 13: List of STR Metro Markets and Census MSA or Metro Division Equivalent
STR Market
Birmingham, AL
Mobile, AL
Phoenix, AZ
Tucson, AZ
Little Rock, AR
Anaheim/Santa Ana, CA
Los Angeles/Long Beach, CA
Oakland, CA
Riverside/San Bernardino, CA
Sacramento, CA
San Diego, CA
San Francisco/San Mateo, CA
San Jose/Santa Cruz, CA
Denver, CO
Colorado Springs, CO
Hartford, CT
Washington, DC-MD-VA
Fort Lauderdale, FL
Jacksonville, FL
Miami/Hialeah, FL
Orlando, FL
Tampa/St Petersburg, FL
West Palm Beach/Boca Raton, FL
Fort Myers, FL
Daytona Beach, FL
Melbourne/Titusville, FL
Sarasota/Bradenton, FL
Atlanta, GA
Macon/Warner Robbins, GA
Augusta, GA-SC
Savannah, GA
Oahu Island, HI
Maui Island, HI
Chicago, IL
Indianapolis, IN
Des Moines, IA
Louisville, KY-IN
Lexington, KY
New Orleans, LA
Baltimore, MD
Boston, MA
Detroit, MI
Grand Rapids, MI
Minneapolis/St Paul, MN-WI
Jackson, MS
Kansas City, MO-KS
MSA or Metro Division Equivalent
Birmingham-Hoover
Mobile
Phoenix-Mesa-Scottsdale
Tuscon
Little Rock-North Little Rock
Santa Ana-Anaheim-Irvine CA Metro Div
Los Angeles-Long Beach-Glendale Metro Div
Oakland-Fremont-Hayward Metro Div
Riverside-San Bernardino-Ontario PMSA
Sacramento-Arden-Arcade-Roseville
San Diego-Carlsbad-San Marcos
San Francisco-San Mateo-Redwood City Metro Div
San Jose-Sunnyvale-Santa Clara + Santa Cruz-Watsonville
Denver-Aurora
Colorado Springs
Hartford-West Hartford-East Hartford
Washington DC PMSA
Fort Lauderdale-Pampano Beach-Deerfield Beach Metro Div
Jacksonville
Miami-Miami Beach-Kendall Metro Div
Orlando
Tampa - St. Petersburg - Clearwater
West Palm Beach - Boca Raton - Boynton Metro Div
Cape Coral - Fort Myers
Deltona - Daytona Beach - Ormond Beach
Palm Bay - Melbourne -Titusville
North Port - Bradenton - Sarasota
Atlanta - Sandy Springs - Marietta
Macon + Warner Robins
Augusta - Richmond
Savannah
Honolulu
Maui
Chicago - Naperville - Joliet Met Div
Indianapolis
Des Moines
Louisville
Lexington-Fayette
New Orleans - Metairie - Kenner
Baltimore - Towson
Boston - Cambridge - Quincy Div
Detroit - Livonia - Dearborn Metro Div
Grand Rapids - Wyoming
Minneapolis - St Paul - Bloomington
Jackson
Kansas City MO-KS
54
Table 14: List of STR Metro Markets and Census MSA or Metro Division Equivalent (Cont’d)
STR Market
St Louis, MO-IL
Omaha, NE
Las Vegas, NV
Bergen/Passaic, NJ
Newark, NJ
Albuquerque, NM
New York, NY
Syracuse, NY
Albany/Schenectady, NY
Buffalo, NY
Rochester, NY
Charlotte, NC-SC
Greensboro/Winston Salem, NC
Raleigh/Durham/Chapel Hill, NC
Cincinnati, OH-KY-IN
Cleveland, OH
Columbus, OH
Dayton/Springfield, OH
Oklahoma City, OK
Tulsa, OK
Portland, OR
Philadelphia, PA-NJ
Pittsburgh, PA
Scranton/Wilkes-Barre, PA
Harrisburg, PA
Allentown/Reading, PA
Greenville/Spartanburg, SC
Columbia, SC
Charleston, SC
Myrtle Beach, SC
Knoxville, TN
Memphis, TN-AR-MS
Nashville, TN
Chattanooga, TN-GA
Austin, TX
Dallas, TX
Fort Worth/Arlington, TX
Houston, TX
San Antonio, TX
McAllen/Brownsville, TX
Salt Lake City/Ogden, UT
Norfolk/Virginia Beach, VA
Richmond/Petersburg, VA
Seattle, WA
Milwaukee, WI
Madison, WI
MSA or Metro Division Equivalent
St Louis
Omaha - Council Bluffs
Las Vegas - Paradise
Bergen - Hudson - Passaic
Newark - Union Metro Div
Albuquerque
NY - Wayne - White Plains Metro Div
Syracuse
Albany - Schenectady - Troy
Buffalo - Niagara Falls
Rochester
Charlotte - Gastonia - Rock Hill
Greensboro - High Point + Winston-Salem
Raleigh-Cary + Durham
Cincinnati - Middletown
Cleveland - Elyria - Mentor
Columbus
Dayton + Springfield
Oklahoma City
Tulsa
Portland - Vancouver - Beaverton
Philadelphia Metro Div
Pittsburgh
Scranton - Wilkes - Barre - Hazleton
Harrisburg - Carlisle
Allentown - Bethlehem - Easton + Reading
Greenville + Spartanburg
Columbia
Charleston - North Charleston
Myrtle Beach - Conway - North Myrtle Beach
Knoxville
Memphis
Nashville - Davidson - Murfreesboro
Chattanooga
Austin - Round Rock
Dallas - Plano - Irving Metro Div
Fort Worth - Arlington Metro Div
Houston - Sugar Land - Baytown
San Antonio
McAllen - Edinburg - Pharr + Brownsville - Harlingen - San Benito
Salt Lake City + Ogden - Clearfield
Virginia Bech - Norfolk - Newport News
Richmond
Seattle - Tacoma - Bellevue
Milwaukee - Waukesha - W Allis
Madison
55
Table 15: List of Airports Included in the Airline Sample
Birmingham, AL
Phoenix, AZ
Tucson, AZ
Little Rock, AR
Anaheim/Santa Ana, CA
Los Angeles/Long Beach, CA
Oakland, CA
Sacramento, CA
San Diego, CA
San Francisco/San Mateo, CA
San Jose/Santa Cruz, CA
Denver, CO
Colorado Springs, CO
Hartford, CT
Washington, DC-MD-VA
Fort Lauderdale, FL
Jacksonville, FL
Miami/Hialeah, FL
Orlando, FL
Tampa/St Petersburg, FL
West Palm Beach/Boca Raton, FL
Fort Myers, FL
Atlanta, GA
Oahu Island, HI
Chicago, IL
Indianapolis, IN
Louisville, KY-IN
New Orleans, LA
Baltimore, MD
Boston, MA
Detroit, MI
Minneapolis/St Paul, MN-WI
Kansas City, MO-KS
St Louis, MO-IL
Omaha, NE
Las Vegas, NV
Newark, NJ
Albuquerque, NM
New York, NY
Albany/Schenectady, NY
Buffalo, NY
Charlotte, NC-SC
Raleigh/Durham/Chapel Hill, NC
Cincinnati, OH-KY-IN
Cleveland, OH
Columbus, OH
Dayton/Springfield, OH
Oklahoma City, OK
Tulsa, OK
Portland, OR
Philadelphia, PA-NJ
Pittsburgh, PA
Memphis, TN-AR-MS
Nashville, TN
Austin, TX
Dallas, TX
Houston, TX
San Antonio, TX
Salt Lake City/Ogden, UT
Norfolk/Virginia Beach, VA
Richmond/Petersburg, VA
Seattle, WA
American Airlines
Shuttlesworth International
Sky Harbor International
Tucson International
Bill and Hillary Clinton
John Wayne Airport
Los Angeles International
Metropolitan Oakland International
Sacramento International
San Diego International
San Francisco International
Norman Y Mineta International
Denver International
City of Colorado Springs Municipal
Bradley International
Ronald Reagan Washington
Ft. Lauderdale-Hollywood
Jacksonville International
Miami International
Orlando International
Tampa International
Palm Beach International
Southwest Florida International
Hartsfield-Jackson International
Honolulu International
Ohare International
Indianapolis International
Louisville International-Standiford Field
Louis Armstrong
Baltimore/Washington International
Logan International
Detroit Metro Wayne County
Minneapolis International
Kansas City International
Lambert-St. Louis International
Eppley Airfield
McCarran International
Newark Liberty International
Albuquerque International Sunport
John F. Kennedy International
Albany International
Buffalo Niagara International
Charlotte Douglas International
Raleigh-Durham International
Cincinnati/Northern Kentucky International
Cleveland-Hopkins International
Port Columbus International
James M Cox/Dayton International
Will Rogers World
Tulsa International
Portland International
Philadelphia International
Pittsburgh International
Memphis International
Nashville International
Bergstrom International
Dallas/Fort Worth International
George Bush Intercontinental
San Antonio International
Salt Lake City International
Norfolk International
Richmond International
Seattle/Tacoma International
56
Delta
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Southwest
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Midway International
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Love Field
Hobby
x
x
x
x
x
United
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
US Airways
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
57
Units
# of Employees
# of Employees
% Rate
$ Dollars
$ Dollars/capita
$ Dollars
Cents/Kilowatt hour
$/year
% Rate
% Rate
# of Residents
Square Mile
Variable
Leisure/Hospitality Employment
Non-farm Employment
Unemployment Rate
Personal Income
Personal Income/Capita
Fair Market Rent (3 Bedroom)
Commerical Electricity Price
Hotel Employee Salary
Hotel Occupancy Tax
Passenger Facility Charge
Population
Land Area
Airline
Airline/Hotel
Hotel
Application
Hotel
Airline/Hotel
Airline/Hotel
Airline/Hotel
Airline/Hotel
Airline/Hotel
Airline/Hotel
Hotel
Hotel
Airport
MSA/Division/County
MSA/Division/County
Geographic Identifier
MSA/Division
MSA/Division
MSA/Division
MSA/Division
MSA/Division
County
State
MSA/County
City
Source
Bureau of Labor Statistics
Bureau of Labor Statistics
Bureau of Labor Statistics
Bureau of Economic Analysis
Bureau of Economic Analysis
Housing & Urban Development
Energy Information Administration
County Business Patterns
HVS (2012), AHLA (2013),
Author’s calculations
Bureau of Transportation Statistics
Census
State-Metropolitan Area Data Book,
County-City Data Book
Table 16: Summary of Sources for Data Included in the Hotel and Airline Analysis
58
Std
Min
0.24 1.02
2.91 6.15
0.27 6.13
0.17 9.96
1.90 9.40
0.81 2.15
2.26 2.41
0.06 -0.05
0.07 -0.35
0.20 -2.80
0.87 15.87
0.07 0.01
1.47 0.18
0.16 0.06
0.44 0.09
Max
2.13
29.72
7.77
11.20
17.50
6.03
16.13
0.44
0.29
-1.46
20.48
0.50
8.15
1.30
4.12
Source: CBP for the average hotel wage, HUD for the fair market 3-bedroom rent, BEA for the personal income and personal income per
capita as well as the five year growth rates in each variable, BLS for the unemployment rate and employment in the leisure and hospitality
sector, as well as the share of total non-farm employment in the leisure of hospitality sector and the five year growth rate, EIA for the
average commercial price of electricity, and industry trade papers for the effective occupancy tax rate.
Table 17: Summary of Data Included in the Hotel Regressions
Mean
log(Avg. Hotel Quarterly Salary) ($1000)
1.61
Avg. Commercial Electricity Price (cent/kwh)
9.94
log(Fair Market 3-br Rent) ($/sqft)
6.97
log(Personal Income per capita) (thous. $/capita)
10.61
Effective Occupancy Tax Rate
13.86
log Employment in Leisure & Hospitality (thous.)
4.14
Unemployment Rate (%)
5.85
Five year log diff Personal Income per capita (thous. $/capita)
0.18
Five year log diff Leisure & Hospitality Emp. (thous.)
0.09
log(Share of Employment in Leisure & Hospitality) (%)
-2.40
log(Personal Income) (thous. $)
17.84
Five year log diff Personal Income (thous. $)
0.25
log Employment in Leisure & Hospitality/per Square Mile (thous./sq mile)
1.73
Alternative Demand Volatility (η = 1.85, N = 2063)
0.30
Alternative Demand Volatility (η = 4, N = 2063)
0.52
59
Min
5.54
4.84
0.00
10.21
2.41
3.16
16.62
-0.08
-0.35
-0.01
Max
34.88
7.90
4.50
11.26
16.13
6.17
35.09
0.46
0.31
0.71
Source: BTS and author’s calculations for the load factor and coefficient of variation of demand, HUD for the fair market 3-bedroom
rent, BEA for the personal income and personal income per capita as well as the five year growth rates in each variable, BLS for the
unemployment rate and the five year growth rate in non-farm employment, and the BTS for the passenger facility charge.
Table 18: Summary of Data Included in the Airline Regressions
Mean Std
Avg. Commercial Electricity Price (cent/kwh)
9.60 3.00
log(Fair Market 3-br Rent) ($/sqft)
7.09 0.28
Passenger Facility Charge (%)
4.10 0.94
log(Personal Income per capita) (thous. $/capita)
10.62 0.17
Unemployment Rate (%)
6.49 2.41
Log Employment in Non-farm (thous.)
4.59 0.66
log(Personal Income) (thous. $)
19.30 3.93
Five year log diff Personal Income per capita (thous. $/capita)
0.15 0.07
Five year log diff Non-farm Emp. (thous.)
0.07 0.07
Five year log diff Personal Income (thous. $)
0.23 0.10
Table 19: Regression Results
(a)
ρ
-0.82
(0.05)
1.04
Dep. Variable: log(Yimt /Kimt )
Mean:
-1.07
Year/Segment FEs
Indirect Controls
Full Controls
Drop Independents
Drop 2008
Bartik Instrument
Use Employment
Hausman Endogeneity Test
F -stat (1st stage)
R2
0.10
N
2063
Allowing for Increasing Returns to Scale
(b)
(c)
(d)
(e)
(f)
(g)
-0.67 -0.48
-0.44
-0.47
-0.36
-0.52
(0.05) (0.04) (0.05) (0.06) (0.06) (0.07)
-1.07
yes
0.41
1837
-1.07
yes
yes
yes
0.68
1837
-1.07
yes
yes
yes
-1.06
yes
yes
yes
yes
-1.07
yes
yes
yes
yes
yes
yes
yes
no
239.43
0.68
1837
no
191.13
0.67
1597
no
176.13
0.70
1327
-1.07
yes
yes
yes
yes
no
86.05
0.68
1837
Regression results for several alternative versions of the regression specified in equation (3) with alternative
productivity measure assuming increasing returns to scale of 1.04. The estimated coefficient of demand
volatility is reported for all specifications in the first row, with the heteroskedasticity robust standard errors
reported in the second row within parenthesis. Additional statistics for each specification are given including
if the Hausman endogeneity test was significant at the 1 percent level (if applicable), the F -statistic of the
first stage regression (if applicable), the r-squared (R2 ) and the number of observations (N ) in the last rows.
Specification (a) reports the coefficient, absent any fixed effects or metro area-year controls. Specification
(b) reports the coefficient from a regression including controls for input prices, level of demand, and price
elasticity of demand including: hotel occupancy tax rate, logarithm of the average wage in the hotel industry,
logarithm of the U.S. Department of Housing and Urban Development’s fair market rent for a 3 bedroom,
logarithm of personal income per capita, logarithm of employment in the leisure and hospitality industry,
and the unemployment rate. Specification (c) adds a set of demographic controls at the metro area-year level
including: logarithm of employees in leisure and hospitality sector per square mile, the logarithm of the share
of total non-farm employment in the leisure and hospitality sector, logarithm of personal income, five year
log change in personal income, five year log change in personal income per capita, and five year log change
in employment in the leisure and hospitality as well as year and segment fixed effects. In specification (d),
a Bartik type instrument is used for demand volatility. Specification (e) reports the coefficient when one
drops the segment-year observations that involve independently affiliated hotels. Specification (f) reports the
coefficient when one drops the segment-year observations that were in 2008. Specification (g) reports the
coefficient when one uses the annual coefficient of variation in employment in leisure and hospitality at the
metro area-year level as the instrument for demand volatility.
60
Table 20: Regression Results for Alternative Measure of
(a)
(b)
(c)
(d)
ρ
-0.04 -0.04 -0.04
-0.04
(0.01) (0.01) (0.01) (0.01)
Dep. Variable: log(Yimt /Kimt )
Mean:
-0.50 -0.51 -0.51
-0.51
Year/Segment FEs
yes
yes
Indirect Controls
yes
yes
yes
Full Controls
yes
yes
Drop Independents
Drop 2008
Bartik Instrument
yes
Use Employment
Hausman Endogeneity Test
no
F -stat (1st stage)
351.35
2
R
0.01
0.43
0.70
0.70
N
2063
1837
1837
1837
Demand Volatility
(e)
(f)
(g)
-0.04
-0.03
-0.07
(0.01) (0.01) (0.01)
-0.50
yes
yes
yes
yes
-0.51
yes
yes
yes
yes
yes
yes
no
256.88
0.70
1597
no
259.43
0.72
1327
-0.51
yes
yes
yes
yes
yes
110.07
0.70
1837
Regression results for several alternative versions of the regression specified in equation (3) with alternative
demand volatility measure and price elasticity of demand of 4. The estimated coefficient of demand volatility
is reported for all specifications in the first row, with the heteroskedasticity robust standard errors reported
in the second row within parenthesis. Additional statistics for each specification are given including if the
Hausman endogeneity test was significant at the 1 percent level (if applicable), the F -statistic of the first
stage regression (if applicable), the r-squared (R2 ) and the number of observations (N ) in the last rows.
Specification (a) reports the coefficient, absent any fixed effects or metro area-year controls. Specification
(b) reports the coefficient from a regression including controls for input prices, level of demand, and price
elasticity of demand including: hotel occupancy tax rate, logarithm of the average wage in the hotel industry,
logarithm of the U.S. Department of Housing and Urban Development’s fair market rent for a 3 bedroom,
logarithm of personal income per capita, logarithm of employment in the leisure and hospitality industry,
and the unemployment rate. Specification (c) adds a set of demographic controls at the metro area-year level
including: logarithm of employees in leisure and hospitality sector per square mile, the logarithm of the share
of total non-farm employment in the leisure and hospitality sector, logarithm of personal income, five year
log change in personal income, five year log change in personal income per capita, and five year log change
in employment in the leisure and hospitality as well as year and segment fixed effects. In specification (d),
a Bartik type instrument is used for demand volatility. Specification (e) reports the coefficient when one
drops the segment-year observations that involve independently affiliated hotels. Specification (f) reports the
coefficient when one drops the segment-year observations that were in 2008. Specification (g) reports the
coefficient when one uses the annual coefficient of variation in employment in leisure and hospitality at the
metro area-year level as the instrument for demand volatility.
61
Table 21: Regression Results for Revenue Per Available Room
(a)
(b)
(c)
(d)
(e)
(f)
ρ
-1.72 -0.61
0.07
0.30
0.17
0.42
(0.20) (0.20) (0.09) (0.10) (0.10) (0.12)
Dep. Variable: log(Simt /Kimt )
Mean:
4.01
4.01
4.01
4.01
4.01
4.00
Year/Segment FEs
yes
yes
yes
yes
Indirect Controls
yes
yes
yes
yes
yes
Full Controls
yes
yes
yes
yes
Drop Independents
yes
Drop 2008
yes
Bartik Instrument
yes
yes
yes
Use Employment
Hausman Endogeneity Test
yes
yes
yes
F -stat (1st stage)
239.43 191.13 176.13
2
R
0.04
0.26
0.89
0.89
0.92
0.89
N
2063
1837
1837
1837
1597
1327
(g)
0.28
(0.14)
4.01
yes
yes
yes
yes
no
86.05
0.89
1837
Regression results for several alternative versions of the regression specified in equation (3) but with the
logarithm of revenue per available room as the independent variable. The estimated coefficient of demand
volatility is reported for all specifications in the first row, with the heteroskedasticity robust standard errors
reported in the second row within parenthesis. Additional statistics for each specification are given including
if the Hausman endogeneity test was significant at the 1 percent level (if applicable), the F -statistic of the
first stage regression (if applicable), the r-squared (R2 ) and the number of observations (N ) in the last rows.
Specification (a) reports the coefficient, absent any fixed effects or metro area-year controls. Specification
(b) reports the coefficient from a regression including controls for input prices, level of demand, and price
elasticity of demand including: hotel occupancy tax rate, logarithm of the average wage in the hotel industry,
logarithm of the U.S. Department of Housing and Urban Development’s fair market rent for a 3 bedroom,
logarithm of personal income per capita, logarithm of employment in the leisure and hospitality industry,
and the unemployment rate. Specification (c) adds a set of demographic controls at the metro area-year level
including: logarithm of employees in leisure and hospitality sector per square mile, the logarithm of the share
of total non-farm employment in the leisure and hospitality sector, logarithm of personal income, five year
log change in personal income, five year log change in personal income per capita, and five year log change
in employment in the leisure and hospitality as well as year and segment fixed effects. In specification (d),
a Bartik type instrument is used for demand volatility. Specification (e) reports the coefficient when one
drops the segment-year observations that involve independently affiliated hotels. Specification (f) reports the
coefficient when one drops the segment-year observations that were in 2008. Specification (g) reports the
coefficient when one uses the annual coefficient of variation in employment in leisure and hospitality at the
metro area-year level as the instrument for demand volatility.
62
Table 22: Summary of Expected Signs & Estimated Coefficient for Indirect Controls
Observable for Hotels
Expected Sign Coefficient Significant for (b)-(g)
Occupancy Tax
(–)
(+/–)
Personal Income per capita
(–)
(+/–)
Avg. Hotel Salary
(+)
(+)
Avg. Electricity Price
(+)
(+)
Fair Market Rent
(+)
(+)
X
Emp in Leisure & Hospitality
(+)
(+)
X
Unemployment Rate
(–)
(–)
X
This table summarizes the coefficient estimates of some of the variables included in the regressions as controls
in the hotel application. For each variable used, the expected sign of the estimated coefficient, the sign of the
estimated coefficient in all specifications, and if that coefficient was statistically significant from zero (at a 5
percent level) for all of the regressions specifications (b)-(g) in table (2), are reported across the columns.
63
64
0.01
0.02
0.03
0.04
0.05
0.06
Bartik Instrument
0.07
0.08
0.09
0.1
Scatter plot of the 2,063 metro area-segment-years. On the vertical axis is the measure of demand volatility given by equation (2), while
on the horizontal axis is the measure of the Bartik instrument given by equations (4)-(5). For an explicit summary of the data see section
(4).
Source: Smith Travel Research and author’s calculations
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 7: Demand Volatility and Bartik Instrument for all Metro area-Segment-Years
Demand Volatility (units)
65
0.01
0.02
0.03
0.04
0.05
0.06
Bartik Instrument
0.07
0.08
0.09
0.1
Scatter plot of the 2,020 destination-airline-years. On the vertical axis is the measure of demand volatility given by equation (2), while on
the horizontal axis is the measure of the Bartik instrument given by equations (4)-(5). For an explicit summary of the data see section
(4).
Source: Bureau of Transportation Statistics and author’s calculations
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 8: Demand Volatility and Bartik Instrument for all Airline-Destination-Years
Demand Volatiltiy (units)
66
10
20
30
40
50
60
70
80
Share of Rooms in Sample of Respondents (%)
90
100
This figure displays the histogram for the 2,063 metro area-segment-year observations of the respondent share as measured by number of
rooms in the STR sample. For an explicit summary of the data see section (4).
Source: Smith Travel Research and author’s calculations
0
200
400
600
800
1000
1200
Figure 9: Histogram of Share of Rooms Covered by STR Respondents for all Metro area-Segment-Years
Count (observations of 2063)
67
10
20
30
40
50
60
Market Share of Room−nights Sold (%)
70
80
This figure displays the histogram of the market shares as measured by the share of room-nights sold a segment sells of the total for the
metro area in a year. For an explicit summary of the data see section (4).
Source: Smith Travel Research and author’s calculations
0
50
100
150
200
250
300
350
400
450
Figure 10: Histogram of Market Shares (Room-nights Sold) for all Metro area-Segment-Years
Count (observations of 2063)
68
0.6
0.7
Occupancy (%)
0.8
0.9
1
0
0.3
0.5
0
0.3
4
6
8
10
12
2
0.4
Ratio of Top to Bottom Decile = 1.45
2
4
6
8
10
12
0.5
0.6
0.7
Alternative Occupancy (%)
0.9
1
In the left panel the density estimate of the annual productivity as measured by annual occupancy rate for all 2,063 metro area-segmentyears is plotted. In the right panel, the density estimate of an alternative measure of productivity is displayed where the variation in
productivity is driven entirely by differences in annual demand volatility across metro area-segment-years. Both densities are estimated
using a normal kernel function with bandwidth 0.015. For a more explicit summary of the data see section (4).
0.4
0.8
Alternative Annual Occupancy Rates
Ratio of Top to Bottom Decile = 1.21
Figure 11: Measures of Productivity of Hotels
Source: Smith Travel Research and author’s calculations
Frequency
Annual Occupancy Rates
Frequency
69
200
0
0.2
0.4
0
0.05
0.1
0.15
Demand Volatility (units)
400
600
800
1000
1200
1400
1600
1800
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.05
0.1
0.15
Demand Volatility (units)
0.2
For each panel the observations displayed involve the metro area-segment-year observations of Texas metro areas only. In the left panel
the scatter plot displays the annual occupancy rates and the measure of demand volatility. In the right panel, the scatter plot displays the
annual revenue per available room and the measure of demand volatility. For an explicit summary of the data see section (4).
Source: Smith Travel Research and author’s calculations
Annual Occupancy (%)
Figure 12: Annual Occupancy Levels and Annual Revenue per Room with Demand Volatility of Texas Metro areaSegment-Years
Annual Revenue per Room ($/room)
70
4.9
5
5.1
5.2
5.3
5.4
5.5
Logarithm of Relative Input Prices
5.6
5.7
5.8
This figure displays the capital-labor ratio and the relative input prices for all the metro area-year observation in the hotel sample. Along
the vertical axis is the measure of the capital-labor ratio, while along the horizontal axis is the measure of relative input prices (logarithm
of fair market rent for a 3 bedroom over average hotel employee salary). For an explicit summary of the data see section (4).
Source: Smith Travel Research, County Business Patterns, and author’s calculations
6.5
7
7.5
8
8.5
9
Figure 13: Capital-Labor Ratios and Relative Input Prices for All Metro area-Years in Hotel Sample
Logarithm of Capital−Labor Ratio