5. Empirical Results
5.1. Basic regressioil results
+
I I I
5.1. Basic regressioil results
-20 -1 0 0 10 20
Temperature (difference from mean, degrees F)
Figure 4 shows the raw association between annual mean temperature and real wages by county. The wide scatter in the figure indicates that there is more t o life than climate. There is great variability of real wages by mean temperature. A visual scan indicates that little of the wide variation in wages across climatic zones is determined by the variation in average temperature.
The raw association of climate and wages proves little, of course, because other factors may lie behind the variability and may confound any underly- ing relationship. Figures 5(a)-5(i) show a number of simple bivariate scatter plots of real wages and other important variables. These show how wages vary by precipitation, summer temperature, winter temperature, unemploy- ment, latitude, longitude, population density, port tonnage, and migration.
There is no obvious relationship for most of the variables. The outlier with respect t o high latitude is North Slope, Alaska. The summer temperature
Precipitation (difference from mean, inches per month) Figure 5(a). R.eal wa,ge and precipita.tion.
1.6
!
I I + I-20 -1 0 0 10 20
Summer temperature (degrees F, difference from mean)
Figure 5(b). Real wage and summer temperature.
Winter temperature (degrees F, difference from mean) Figure 5(c). Real wage aad winter temperature.
I I I
0.0 0.1 0.2 0.3 0.4
Unemployment rate Figure 5(d). Real wage and unemployment.
Figure 5(e). Real wage and latitude.
Figure 5(g). Real wa.ge and density.
2.8,
2.6 -
Q,
$
2.4--
51
2.2 -C
0
2
E 2.0-m cn
4 0
1.8 - 1.6,
Port tonnage (millions of tons per year) Figure 5(h). Real wage and port tonnage.
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+++* +
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Log density (difference from mean)
Migration rate (fraction per six years)
F i g u r e 5(i). Real wage and migration.
graph indicates a slight negative relatioilship of wages with summer temper- atures, suggesting a positive amenity. The only variable that comes through clea.rly is the clear associatioil of wages with population density - a result that has been docunlented for many years.
T h e next step is to estiinate the underlying hedonic wage function. T h e principal statistical results iilvolve the OLS and TSLS estimates of the basic hedonic wage regression in (1) above. Rewriting this in its general form, we have
The bold letters indicate vectors, and the j subscripts indicate that the observations are over the 3105 counties. The 25 are the exogenous variables affecting supply, while the c; are the disturbances t o the supply equation. In the OLS approach, we simply estimate (1'). In the TSLS approach, we treat the density variable, L;, as endogenous and use omitted exogenous variables from the demand equation as instruments for the endogenous variable. It will be useful t o present simple regressions. These are the log of real wages on temperature, temperature and log density, and these variables plus state
dummy variables. The first set is unweighted; the second group is wage- weighted.
coefficient ( x 100)
On temp. Std error t-statistic Variables: C, T E M P
(unweighted) 0.1626 0.0290 5.60
Variables: C, TEMP, LDENS
(unweighted) 0.0501 0.0278 1.80
Variables: C , TEMP, LDENS,
STATE DUMMIES (unweighted) -0.0456 0.0367 -1.24
Variables: C, T E M P
(wage weighted) -0.0368 0.0233 -1.58
Variables: C , TEMP, LDENS
(wage weighted) 0.2417 0.0203 11.89
Variables: C, TEMP, LDENS,
STATE DUNINIIES (wa,ge unweighted) -0.3901 0.0301 -13.00 None of the temperature coefficients is large. Although three are statis- tically significant, the signs are inconsistent. The temperature coefficient is a semi-elasticity. The first coefficient indicates that a 1°F change in temper- ature is associated with a 0.16% increase in wages, or a 0.16% disamenity premium. T h e semi-elasticities ra,ilge from minus 0.39% t o plus 0.24%.
We now turn t o the full regressiou analysis. Begin with the standard version of the hedonic equation (1'). This equation has the real wage rate on the left-hand side a,nd a group of climatic, geographic, and socioeconomic variables on the right-hand side. The climatic variables are a cubic function of temperature, a. quadratic fullction of precipitation, and interaction terms.
The geographic va,riables include la.titude, longitude, contiguous bodies of water (such as ocean, the Great La,l<es, and navigable rivers), and interaction terms. The socioecoi~omic variables include the unemployment rate, the density of the population, education, and ethllic
variable^.^
To deal with simultaneous-equation bias, we treat wages and popula- tion density as endogenous and use TSLS. As an instrument for population
'We originally intended to include other demographic variables such as the crime rate, pollution, and d a t a on other demographic groups. These were, however, not available on a comprehensive basis. Tests of t,he relationship with these variables for counties where the d a t a were available did not illdicate ally economically significant difference in the outcome.
density, we used a variable we call BROADS, which is roughly equal to em- ploynlent in exogenous or "esports" industries in a county per unit of area.
BROADX begins with "broad export employment," which includes employ- ment in those industries in a county that we reckon t o be relatively inde- pendent of the climate and other excluded labor-supply variables. Mining is a good example. The presence of mining output in a county is determined by geological considerations and is unlikely t o be affected by variables af- fecting the supply of labor. (One of the largest observations for BROADX is the county containing North Slope, Alaska.) Other industries composing the broad instrument are manufacturing, fisheries, water transportation, and military. We then take total eillployillent in these industries, divide it by the area, and define this t o be BROADX, which is then assumed to be an instrument for populatioil density.
Table 1 shows the definitions of the variables, and Table 2 shows the results of the basic OLS regression. It will be useful t o focus on the coefficient of TEMP. Because we have removed the means from the variables, this coefficient gives the impact of a 1°F iilcrease in temperature on the log of average wages at the illeail of the sample. The semi-elasticity of 0.0075 indicates that a t the llleail of the sainple, a 1°F iilcrease in temperature (other things being equal) is associated with a 0.75% iilcrease in wages.
The hedonic interpretation of this coefficieilt is that higher temperatures are undesirable and require a compeilsatiilg wage differential of slightly less than 1% per OF increase.
T h e TSLS regressioil in Table 3 shows that simultaneous-equation bias is a significant problem. The semi-elasticity on mean temperature is reduced by approximately half, as would be expected if the warm climates are associated with higher productivity. Other variables are relatively less affected.
In both the OLS and the TSLS equations, density is an extremely pow- erful variable. This relatioilsllip was interpreted long ago in Nordhaus and Tobin as an "urban disameility premium" (Nordhaus and Tobin, 1973). This study shows that the premium is also apparent when extended t o all US perature. Conditional wages are calculated as wages after removing the pre- dicted impact of the non-temperature variables on wages. This figure allows us t o get a visual i~llpressioil of the partial relationship between wages and
Table 1. Variable list in regression analysis.
TEMP = Temperature by county (degrees F, deviation from national average).
TEMP2 = TEMP
'
= temperature squared TEMP2 = TEMP' = temperature cubedPREC = Precipitation by county (inches per month, deviation from national average).
PREC2 = PREC
'
= precipitation squaredTEMPREC = TEMP x PREC = interaction of precipitation and temperature
XTI, XT4. XT7, XTlO = Temperature by county for January, April, July, October (degrees F, deviation from national average annual average).
XPI. XP4, XP7, XPlO = Precipitation by county for January, April, July, October (inches per month, deviation from national average annual average).
X(s,t)2 = X(s,t)
'.
where i = P and T, t = 1,4,7, 10 LDENS = log of density (persons per square mile) LDENS'
= square of LDENSCOLGRAD = Fraction of population with a college degree HSGRAD = Fraction of population with a high-school degree POPHISP = Fraction of population with Hispanic origin LAT = Latitude (deviation from national average) LONG = Longitude (deviation from national average) LAT2 = LAT1= latitude squared
LONG2 = LONG
'
= longitude squaredLATLONG = LAT x LONG = interaction of latitude and longitude OCEAN = I if county on ocean, 0 otherwise
OCEANLAT = OCEAN-x LAT = interaction of ocen and latitude OCEANLON =OCEAN x LONG = interaction of ocean and longitude
OCEANLL = OCEAN x LONG x LAT = interaction of ocean, latitude, and longitude TEMPOCEA = TEMP x OCEAN = interaction of temperature and ocean
PRECOCEA = PREC x OCEAN = interaction of precipitation and ocean MISRIVER = I if on Mississippi River, 0 otherwise
TONPORT = Annual tonnage transshipped in port county PORT = I if on a navigable waterway, 0 otherwise GL = I if on Great Lakes, 0 otherwise
UR = Unemployment rate in county, 1982
LBROADX = Logarithm of instrumental variable for density. instrument is equal to total employment in
"exogenous" sectors per square mile as an instrument for density. Exogenous sectors are mining, manufacturing. water transportation,and military.
LBROADXZ = LBROADX' = squared instrument.
26
Table 2. Ordinary least squares estimates of hedonic regression.
LS N Dependent Variable is LAVI4 Date: 07/16/96 Time: 15:Ol
Table 3. Two-stage least squares estimates of hedonic regression.
TSLS I1 Dependent Variable is LAW4 Date: 0711 61% Time: I5:M Weighting series: WrWAG Sample: 1 3105
Included observations: 3 105
Instrument li: C TEMP TEMP2 TEMP3 PREC PREC2 TEMPREC XPI XP7 XP12 XP72 XTI XT7 XT12 XT72 LAT LONG LATZ LONG2 LATLONG LBROADX LBROAD2 OCEAN OCEANLAT OCEANLON OCEANLL TEMPOCEA PRECOCEA COLGRAD HSGRAD POPHISP UR CAPITAL GL MISRIVER TONPORT PORT [plus state dummies]
Variable Coefficient Std. Error t-Statistic Rob.
C
Adjusted R-squared 0.999907 S.D. dependent var S.E. of regression 0.109773 Akaike info criterion Sum s q u a d m i d 36.69285 Schwarr criterion F-statistic 565933.9 Durbin-Watson stat Prob(F-statistic) 0.000000
-1.0
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Demeaned temperature (degrees F)
Figure 6. Conditional wages and temperature by county. Conditional wages are wages less estimated impact of non-temperature variables on wages. That is, if w = f ( T )
+
g ( Z )+
E is the estimated relationship, then stripped wa.ges= W* = w - g ( Z ) = f ( T )
+
E. This shows graphically the conditional relationship between wages and mean temperature.temperature after allowing for the estimated impact of density, unemploy- ment, precipitation, and other variables. (The top and bottom 10 counties have been trimmed t o fit the graph.) The overwhelming impression of this graph is the loud noise and weak temperature-on-wage signal.
We next show in Figures 7(a)-7(e) a number of conditional predictions of the hedonic value of climate. For each of these, we have taken the coefficients from the TSLS equation in Table 3 and changed the sign t o reflect the hedonic interpretation that lower wages are interpreted as higher amenity values. These figures indicate that the preferred climate is slightly below the national mean [see Figure 7(a)]. The premium on warmer climates is strongly positive for colder regions. Note as well the strong value of warm winters and warm summers in Figures 7(c) and 7(d). The density disamenity premium is shown in Figure 7(e).
Figure 7(a). Estimated hedonic value of mean temperature.
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k el
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c -0.05-.g .o c 3
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-0.15
Figure 7(b). Estimated hedonic value of mean precipitation.
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2b
30Mean temperature (degrees F)
Figure 7(c). Estimated hedonic value of summer temperature.
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Winter temperature (degrees F) +
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Figure 7(d). Estimated hedonic value of winter temperature.
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Summer temperature (degrees F)
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Log density (demeaned)
Figure 7 ( e ) . Estimated hedonic value of density.