### Stability of the Jobs to Sales Ratio by Capacity

### Utilization in the Input-Output Model

### Ya-Yen Sun

### Assistant Professor

### Department of Kinesiology, Health, and Leisure Studies (DKHL)

### National University of Kaohsiung, Taiwan

### September 3, 2007

Presentation for the Advances in Forest and Natural Resource Management Symposium

### Input-Output (I-O) Analysis in

### Recreation & Tourism

###

_{Estimate economic changes resulting from spending }

### associated with recreation/ tourism activities

###

### Total economic impacts

### = demand changes * multipliers * economic ratios = Ê(I-A)

-1### Y

### Total jobs = spending * sales multipliers * jobs to sales ratio

###

_{Assumptions}

### constant multipliers and economic ratios

### Factors that influence the stability of

### multipliers and economic ratios

### technological changes

### price changes

### returns to scale

### trade patterns

(Rose & Miernyk, 1989; West, 1995).

### capacity utilization (CU)

### “the ratio of actual used

### (consumed) products to the

### total available products”

(Nelson, 1989)

¾

### Lodging

¾

### Transportation

¾### Entertainment

¾

### Food and beverage

### Purposes of this study

### Study subject: Taiwan Tourist Hotel

### 1.

### Jobs to sales ratio:

### Empirically test the stability of the jobs to sales ratio in relation

### to capacity utilization (occupancy rates)

### 2.

### Direct job estimation

### Compare job estimates (direct effect) based on the standard I-O

### analysis and predicted job ratio by occupancy rates

### Data

### Panel data:

### Monthly Taiwan tourist hotels operational data from

### 1999 to 2005 (84 data points)

### Analytical framework

### P

### 1

### *

### X

### J

### price

### 1

### *

### efficiency

### labor

### price

### room

### 1

### *

### rooms

### occupied

### jobs

### sales

### jobs

### (JR)

### ratio

### sales

### to

### jobs

### The

### =

### =

### =

### =

### T

### X

### capacity

### total

### rooms

### occupied

### (OR)

### rate

### Occupancy

### =

### =

OR = occupancy rate JR = jobs to sales ratio J: jobs X: occupied rooms P: room price T: hotel capacity### )

### (

### OR

### 1

### *

### T

### *

### P

### J

### JR

### =

### =

*f*

*OR*

### Analytical framework

### Because

### lnJR = lnJ – lnP – lnT – lnOR

*Hypothesis 1: ln (jobs to sales ratio) = f [ln(occupancy rate)]*

*Hypothesis 2: ln (jobs) = f [ln(occupancy rate)]*

*Hypothesis 3: ln (room price) = f [ln(occupancy rate)]*

*Hypothesis 4: ln (hotel capacity) = f [ln(occupancy rate)]*

### Analytical framework

### I: Standard I-O analysis

### Direct jobs = sales at t

_{2}

### * jobs to sales ratio at t

_{1}

### = Number of units sold at t

_{2 }

### * price ratio between t

_{1}

### & t

_{2 }

### * labor efficiency at t

_{1}

### II: Our approach for the estimation of jobs

### Direct jobs

### = Number of units (services) sold at t

_{2}

### * labor efficiency at t

_{2}

1 1 1 2 2 1 1 1 2 2 Xt Jt * Pt Pt * Xt Pt * Xt Jt * ) Pt * Xt ( = =

### Result

### Table 1. Descriptive statistics of monthly tourist hotel operation in Taiwan

### (1999~2005)

**Monthly data** **Min.** **Max. ** **Mean** **Std. **

**Deviation**

**Coeff. of **
**variation **
**(CV)**

Total available rooms 18,724 20,977 20,117 617 3%

Occupied rooms / month 136,814 485,271 386,600 57,682 15%

Occupancy rate 22% 78% 63% 9% 14%

Average room price (NT$) 2,301 3,152 2,903 130 4%

Total employees 6,013 7,694 7,198 295 4%

Jobs to NT$ million sales

### Objective 1:

### Jobs to sales ratio and occupancy rate

**B**

**Std. **

**Error Std. Coeff. ** **t** **Sig.**

(Constant) 1.324 0.013 98.250 0.000

log of occupancy rate **-1.041** 0.029 -0.915 -36.508 0.000

1999 0.119 0.015 0.213 8.177 0.000

2000 0.089 0.014 0.159 6.257 0.000

2001 0.090 0.014 0.160 6.211 0.000

2002 0.061 0.015 0.109 4.226 0.000

2003 0.039 0.016 0.069 2.442 0.017

Dependent Variable: log of jobs to sales ratio ; F = 323.8173 (p = 0.000), Adjusted R2 _{= }

0.959

### Objective 1:

### Room price and occupancy rate

**B**

**Std. **

**Error Std. Coeff.** **t** **Sig.**

(Constant) 8.044 0.010 779.348 0.000

log of occupancy rate **0.137** 0.022 0.507 6.346 0.000

2003 -0.051 0.011 -0.388 -4.846 0.000

Dependent Variable: log of room price ; F = 49.5920 (p = 0.000), Adjusted R2 _{= 0.539}

### Objective 1:

### Room employees and occupancy rate

**B**

**Std. **

**Error Std. Coeff.** **t** **Sig.**

(Constant) 8.905 0.008 1,131.088 0.000

log of occupancy rate **0.122** 0.015 0.501 8.180 0.000

1999 0.050 0.008 0.415 6.356 0.000

2000 0.046 0.008 0.387 5.944 0.000

2001 0.072 0.008 0.605 9.287 0.000

2002 0.065 0.008 0.541 8.298 0.000

Dependent Variable: log of employees ; F = 38.4502 (p = 0.000) , Adjusted R2 _{= 0.693}

### Objective 2:

### Job estimates by scenario 1

### 50%

### 60%

(base level)### 70%

Pct change from 60% to 50% Pct change from 60% to 70%**Scenario 1: Per million dollar spending in the accommodation sector**

Jobs to sales ratio 7.73 6.40 5.45 21% -15%

Room price $2,835 $2,906 $2,968 -3% 2%

Employee number 6,771 6,923 7,055 -2% 2%

Labor efficiency1

(J/X) 0.022 0.018 0.016 18% -13%

6.4 5.5 5.9 7.0 7.7 4 5 6 7 8 9 50% 55% 60% 65% 70% Occupancy rate Jo b s p er N T $ m illio n sp en d in g

### Objective 2:

### Job estimates by scenario 2

**Occupancy rate**

**50%** **60%**

**(base level)**

**70%**

**Scenario 2: Per 1,000 occupied rooms (e.g., a special event)**

Room sales ( NT$ million’s) $2.84 $2.91 $2.97

Direct jobs using fixed ratio (standard I-O) 18.1 18.6 19.0

Direct jobs using predicted ratio 21.9 18.6 16.2

18.1 18.4 18.6 18.8 19.0 21.9 20.1 18.6 17.3 16.2 12 14 16 18 20 22 24 50% 55% 60% 65% 70%

### occupancy rates

### Jobs

### pe

### r 1,000 oc

### c

### upi

### e

### d room

### s

### Conclusion

###

### Jobs to sales ratio is influenced by capacity utilization

### Employee number does not increase/ decrease in direct proportion to

### sales.

###

### Standard I-O model will give biased estimates for

### scenarios involving variation in CU

### Overestimate jobs when CU is high

### Underestimate jobs when CU is low