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A regional forecasting model for construction activity
Regional Science and Urban Economics 13 (1983) 557-577. North-Holland
A REGIONAL
FORECASTING MODEL ACTIVITY*
FOR CONSTRUCTION
R. William THOMAS Institute
for
Defense
Analyses,
Alexandria,
VA22311,
USA
H.O. STEKLER Industrial
College
of the Armed
Forces,
USA
Received September 1982, final version received January 1983 This paper presents a new, comprehensive and detailed model of construction activity. The model is intended primarily for forecasting applications. The model generates forecasts of new construction starts for each of the 50 states of the United States. Forecasts are made for 29 types of structures. The paper presents evidence that the structure of the determinants of construction activity varies across regions within the United States. Thus, prior models of construction, based only on national time-series data, may be subject to aggregation bias. Evaluation of the model’s forecasts indicates that the model outperforms simpler forecasting methods.
1. Introduction
1.1. Construction activity modeling Most of what economists know about the determinants of construction starts and activity has been derived from time series models based on aggregate data for the entire United States. Such models include, among others, the residential models of Muth (1960), Maisel (1963) and Jaffee and Rosen (1979). A non-business construction sector (including housing) was developed for the Brookings model [Maisel (1965)]. There are several studies which focused on the structures portion of business fixed investment. These include Bischoffs (1970) work on total non-residential construction, and the Bower (1965) and Hambor and Morgan (1971) studies of commercial construction. Finally, there have been a small number of articles which *The work reported here was conducted under Contract J-9-E-8-0031, the U.S. Department of Labor, as part of the development of the Construction Labor Demand System (CLDS). Publication does not indicate endorsement by the Department of Labor, nor should the contents be construed as reflecting the offtcial opinion of this agency or the Department of Defense. The authors gratefully acknowledge the support and comments of William F. Hahn and William R. Schriver of CLDS, as well as those of Robert E. Kuenne, Kenneth Ballard, Douglas Dacy, and Harry Williams. 01660462/83/$3.00
0 1983, Elsevier Science Publishers B.V. (North-Holland)
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analyzed the determinants of state and local government construction expenditures [Phelps (1969), Bolton, (1969) and Gramlich (1969)]. It should be emphasized that all these were national models. However, institutional analyses have stressed that the product and factor markets for construction are more localized [Dunlop and Mills (1960), and Burton (1972)]. It seems more appropriate, therefore, to attempt to model construction activity at the regional rather than the national level. This paper presents a new, comprehensive and detailed model of construction activity. The model is intended primarily for forecasting applications. In developing the model we also hoped to answer two questions which may have broader implications for future research in the field of regional science. First, would the theoretical model of investment behavior, yhich was developed and tested at the national level, be applicable at the state level? In particular, would it be possible to infer that regional construction activity data were generated by a model common to all regions? The second question involves the forecasting accuracy of this new model. Specifically, are the model’s forecasts superior to those provided by simpler and less expensive forecasting techniques? Our methodology and the conclusions drawn are presented below. 1.2. Description of the model The model generates annual forecasts of new construction starts for each of the fifty states and for the District of Columbia. Forecasts are made for twenty-nine types of structures (see table l), which are grouped into three classes: residential construction, non-residential buildings, and non-building construction. Separate forecasts are made for public and for private construction projects. Space considerations preclude a full description of the model [the model is described in detail in Thomas and Stekler (1980)], but a brief discussion of our procedures is warranted here. Our approach to the task of regional modeling follows the tradition of linking construction activity to expansion of the economic base of a region. Non-residential construction is related to growth of industrial output; residential construction, to growth in population. However, the methodology is more complex than that of the simple economic base multiplier. Rather, the demand for each type of structure is modeled as a function of local and national economic variables. The specific determinants used in each equation were originally specified theoretically; these specifications were later modified on the basis of statistical testing. The structure of the construction starts model is described in section 2. Section 3 describes the estimating procedures, the data, and the pooling technique which were used. Section 4 presents the results of estimating the model equations and hypothesis tests. Finally, section 5 presents an
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Table 1 Construction types forecast by the Construction Labor Demand System (CLDS). Residential construction
Non-residential buildings
Non-building construction
Single-family homes 24family homes Hotels and motels College housing 5 +-family homes
Manufacturing buildings Industrial buildings Retail trade and stores Service stations and repair garages Parking buildings Laboratories Warehouses Amusement, recreation and social Religious buildings Government administration buildings Public service buildings Misc. non-residential buildings Office buildings Schools Hospitals
Airports (excluding terminals) Bridges Communication systems Dams and reservoirs Sewers and waste disposals Water systems Streets and highways Civil works Misc. non-building construction
evaluation of the ex post forecasting results for both the sample period and for two years outside of the sample. 2. Structure of the construction model
The Construction Labor Demand System (CLDS) operates as a satellite model [Glickman and Klein (1977)] of a regional economic model, in this case the National Regional Impact Evaluation System (NRIES) [Ballard, Gustely and Wendling (1980)]. While industrial models have often been developed as satellites of national econometric models, our effort is the first instance of which we are aware that this approach has been taken at the state level. NRIES is a set of inter-related state economic models with a common theoretical structure but different estimated coefficients for each state. The equations of NRIES include state variables, common national variables, and weighted inter-regional variables. The latter are aggregates of state variables, the weights varying inversely with the distance between states. Thus, ‘neighborhood’ effects are transmitted in the model. NRIES may be viewed as combining the econometric and gravity model approaches of regional science to forecasting economic activity at the state level. NRIES’ forecasts of state output, employment, income, and other variables are the primary inputs to the CLDS model, which provides regional estimates of construction activity, and the labor requirements associated with
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that activity. Labor requirements are estimated for various crafts employed on the 29 construction types listed in table 1. We use a three-step methodology to estimate construction starts, construction activity, and construction employment. First starts are estimated using the model described in this paper. Then starts are used to estimate construction activity (value put in place). Finally, start estimates are used to determine labor requirements. Although our focus in this paper is on the model which explains starts, it is useful to describe the overall system briefly. Starts of particular types of construction are related to regional demographic and economic variables by (l),
(1)
St = L-m = Cf’wJl,
where S, refers to a p x 1 vector of starts occurring in period t for the p types of construction, and X, is a vector of economic and demographic variables. Starts are then translated into activity by applying a distributed lag which is estimated separately for each type of structure. This may be represented as
where dk is the proportion of total activity undertaken for structure type i in the Tth month of construction, and ni is the total time required to complete the construction of the ith structure type. Finally, craft employment is determined by applying a fixed coefficient labor requirements matrix to each type. Therefore,
1
E,=[lg]= c F St-TW;T) [ i T=O Etis an L x 1 vector of labor requirements
(3)
where for the L crafts, and WiT is an Lx n, matrix for type i. The columns of the W matrix are the labor requirements for each craft in the Tth month of construction. 3. Estimating procedures and data 3.1. Choice of dependent variable and use of weighted regressions
The dependent variable used in each of the three residential housing starts equations was the number of starts. In choosing to forecast the number of starts, we follow the standard practice for the residential sector, where it is possible to meaningfully aggregate in terms of physical units. All other equations were estimated with the value of construction starts as the
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dependent variables. The dollar data were deflated’ to remove the effect of purely inflationary increases on the values of these starts. In all cases, both the dependent and the independent variables included in a particular equation were deflated by the state’s population. Thus, all equations are estimated in per capita terms. This normalization procedure would be expected to remove the heteroscedasticity that could result from the disparate size of the states and the large variations in construction starts. For instance, in one year the number of single-family housing starts ranged from 150 in the District of Columbia to 165,000 in California. Given this disparity in size, an improvement in estimation accuracy can be obtained by weighting the larger states more heavily in the estimation procedure. The appropriate weighting factor is the square root of total population.’ Consequently, for each construction type the equation to be estimated is of the form (4)
where the Yi’s are the relevant dependent variables, D is a national construction deflator, Pi is the population of the ith state, and the Xj’S are the independent variables. In eq. (4), Vi, is assumed to be distributed normally with
Wt, Ku)= d
if
r=s
= 0 otherwise.
and
t=u,
(5)
3.2. Data
The construction starts data used to estimate all the equations were obtained from a service of the F. W. Dodge Company. This service, entitled Dodge Construction Potentials, provides data which are time series observations on individual construction projects which we aggregated to the state level by construction type. These aggregated variables are the dependent variables of the equations. The remaining variables were obtained from the NRIES data file. The Dodge data are available for 1972-1979. The ‘Individual deflators were chosen from the set of construction cost indices used by the Bureau of the Census. 2This procedure was also used by Houthakker (1980) in his recent study of electricity demand, which also used state data. Forecast values must be ‘deweigbted’.
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data for 1972-1977 were used to estimate the model; those for the last two years are used to test it. 3.3. Estimating technique Data restrictions influenced our choice of estimating technique. There were an insufficient number of observations to permit the use of a pure time series approach for each state. On the other hand, a pure cross-sectional approach was also rejected because of our desire to test for regional variability. Thus to capture both the regional and cyclical variability, the data were pooled, yielding 306 (51 x 6) observations for each type when national estimates are made. Maddala (1979) has described the techniques most commonly applied in estimating pooled relationships. The least square dummy variables’ regression (LSDV’) technique was chosen for our model because it assumes that each region has certain (unexplained) unique characteristics which are fixed over time.
3.4. Hypothesis regarding model structure There are good reasons to test the hypothesis that the same underlying model holds in all regions. It is possible that the same model might not be appropriate for both high and low (or negative) population growth regions. In particular, theory suggests the potential for asymmetric behavior with respect to adjustment rates for long-lived assets such as housing. That is, the housing stock can be adjusted upward rapidly, if excess demand prevails, but depreciates slowly in the presence of excess supply. We tested the composite hypothesis that all parameter values are identical in the four regions. The test procedure involved estimating the equation nationally, then estimating separate equations using data pooled regionally. The difference in explained variance can be used to form a test statistic which is distributed as F. To illustrate our approach, the results for the single-family home equation are presented in the next section. 4. The estimated model and tests of the pooling hypothesis This section describes the results obtained from estimating the model equations using the F. W. Dodge data. The first section describes the results for the housing sector in some detail. Because of space limitations, we must present the results for the other sectors in condensed form. A more complete description of and rationale for the specifications chosen is presented in Thomas and Stekler (1980).
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4.1. Residential construction 4.1.1. Theoretical specification
The specification of the residential construction equations draws on the work of Muth (1960), Maisel (1965) and Jaffee and Rosen (1979). The major finding of the Muth and Maisel studies was that housing demand was fundamentally based on permanent income, the number of households formed, and the price of housing. Short-term variations in new housing units started are induced by financial factors, chiefly periods of monetary stringency associated with rapid increases in interest rates. Jaffee and Rosen’s contribution was to elaborate on how the demands of different age-specific demographic factors especially affect the mix of single- and multi-unit housing demanded. Our specifications for the single-family and live-or-more-unit housing starts equations are consistent with these models.3 A standard stock adjustment model is used, since annual housing stock estimates (KSFI) could be developed from benchmark data. 4 The single-unit equation [appendix eq. (A.l)] includes disposable income (DPI), the interest rate (INT), the rate of new immigration (PMN) and the proportion of the population over 65 (P6.5) as determinants. Other demographic subgroups were included in alternative specifications. The variables included in the multi-unit equation [appendix eq. (A.3)] were income, the population aged 65 and over, interest rates, price of housing and relative prices of renting versus home ownership.
4.1.2. Results: Single-family housing starts
Table 2 presents the estimates for the single-family home equation. In the national equation, all the variables except the interest rate are significant, but the stock variable has the wrong sign. In the regional equations the interest rate has the expected sign and is only insignificant in the equation explaining starts in the Northeast region. The coefficients of other variables vary in an unsystematic way among the regional equations. Given the variation of coefficients, we tested whether the data should be pooled nationally. The hypothesis was that the regions shared a common model. Using the standard F-test, this hypothesis was rejected. The value of the F-statistic was 4.91 with 15 and 184 degrees of freedom.
3However, data limitations at the state level required us to substitute for some of demographic variables used. 4The 1970 Census of Housing (1973) and the 1976 Annual Housing Survey (1978) provided two bench mark estimates. Annual values for 19691977 were constructed from annual new construction series using the perpetual inventory method.
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Table 2 National and regional equations for single-family housing starts, 1973-1977 (t-statistics in parentheses). Estimated using data for region Variable
National
INT” PMNd P65’ KSF” RZ
Standard error Deesees of
N. Central
South
West
Dependent variable
SFSI” DPIb
Northeast
0.389 (7.00) -0.0173 (- 1.85) 3.28 (4.40) -4.87 (3.42) 0.133 (5.38) 0.943 4.19
0.212 (1.56) -0.0347 (- 1.89) 0.134 (0.12) 5.72 (1.W -0.096 ( - 2.53) 0.913 1.82
199.0
31.0
-9.67 x 1O-3 0.639 ( - 0.26) (6.57) -0.102 -0.124 (- 10.72) ( - 9.05) 2.23 7.44 x 1o-3 (5.5 x 10-3) (2.W 20.58 1.71 (2.24) 0.37 0.023 - 0.022 (0.45) ( - 0.090) 0.960 0.968 2.07 3.41 43.0
63.0
0.499 (2.97) -0.141 (-5.80) 6.83 (2.32) 11.3 (1.09) 0.120 (1.43) 0.928 5.59 47.0
*Units per 100 people. “Thousands of dollars per capita. =Percent. dNet immigrants as a ratio to total population. ‘Persons over 65 as a ratio to total population.
4.2. Other construction sectors 4.2.1. Theoretical specljkations The equation estimates for the other construction sectors are shown in the appendix. The theoretical specifications used in estimating these equations closely followed the classic theory of investment. For example, it was assumed that new industrial buildings would be started when additional capacity was desired. This in turn suggested that changes in expected output or sales and the cost of capital relative to the price of output were the relevant explanatory variables. In the non-commercial building sector, basic indicators of the need for new facilities are used. Thus, religious buildings, amusement and recreational buildings, and schools are all related to the level of new housing starts. The most difficult problem of specifications arose in modeling the non-
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building structures sector. Most construction in this sector is public and includes sectors related to general growth of population (water and sewer systems, streets and highways) and a second group related to geography (airports, bridges, dams and civil works). An examination of the equations in the appendix shows that better results were achieved in modeling the sectors where population growth was the dominant factor, as compared to those where geographic factors dominate.
4.2.2. Results
Our approach in modeling all these sectors was to formulate an appropriate theoretical specification and estimate it with data pooled nationally. Then the identical equation was again re-estimated for each of the four Census Regions, and the hypothesis that the same model held for all regions was tested. Construction sectors where regional equations’ parameters differed significantly from national parameters included multi-family housing, manufacturing buildings, warehouses, schools and offices. Regions where we could not reject the null hypothesis that the national model applied in all regions included religious buildings, hospitals, water and sewer systems, and streets. We observe a pattern here. The latter group consists of basic infrastructure elements, which are required in proportion to population and/or housing units. Given knowledge of the level of housing starts, there is no reason to expect major regional differences in these relationships. In contrast, most of the first group of structures evidence considerable regional variability in response to the differences in economic variables among the regions.
4.3. Regional variability: An assessment
Overall, our results tend to reject rather conclusively the hypothesis that regional construction demand can be described by the same theoretical model nationwide. The F-test for the pooling of regional data was rejected for the housing starts equations and for a majority of the non-residential construction equations of the model. The only equations where we could not reject the hypothesis of a common model were those which included housing starts as an explanatory variable. This conclusion calls into question the process of creating regional and state economic forecasts by allocating national forecasts among the states according to population or more sophisticated ‘share-down’ rules.
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5. Model forecasting accuracy Since the primary goal of the model development effort was the generation of forecasts of new construction activity, it is important that the model be evaluated primarily by this criterion. Several measures of forecasting accuracy are commonly used - mean absolute error (MAE) and mean square error (MSE) being the most frequent choices. We focus on Thiel’s U coefficient, expressed as the ratio of the RMSE to the root mean square change in the actual series,
= RMSE (forecast)/RMSE
(actual).
(6)
The U coefficient is a relative measure which compares the errors of the forecasts to the errors of a naive forecast of no change.5 In using this statistic, we are following the procedures used in evaluating large macroeconometric models. The no-change naive model is a most appropriate standard to use in evaluating the forecasts of variables, such as construction expenditures, which are subject to wide annual fluctuations, but exhibit little secular trend. 5.1. Basis of evaluation The model generates annual forecasts for 29 construction types, two ownership classes, and 51 regions. Obviously, it is impossible to present a systematic evaluation of all forecasts. We focus here on the accuracy of (1) forecasts of total new construction value among states and (2) forecasts of national construction value for each of the 29 construction types. All forecasts are expressed in terms of predicted changes derived from a dynamic simulation of the model over 1973-1977. Using predicted changes rather than levels avoids a bias against the model which would result from the fact that the naive model standard has only a one-year forecast horizon. Thus, the error in period t is expressed as
while the error of the naive model is AA, [since the naive hypothesis is AA,=O]. ‘The use of a more sophisticated naive model, such as an ARIMA specification, was precluded by the limited number of time-series observations available for each variable.
R.W Thomas and H.O. Stekler, Regional forecasting model for construction activity
The U coefficients for the construction
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equations were computed by
where the i subscript denotes the construction type, j the state, and t the year of each observation. P represents forecast values and A actual values. Note that forecasts are summed across states before being compared to actual results. Thus, compensating errors in individual states cancel and reduce the national error. An alternative measure (UX) has been defined which does not have this property, 63)
The U” measure penalizes both the forecasting and naive model for generating compensating errors. The corresponding U and U” measures for states are defined similarly, (9) I
77
29
1
I
77
29
UT=J ,&, izl(APijt-AAijt)” Id f&, & (AAi.it)2.
(10)
5.2. Within-sample results
Table 3 displays the distribution of U and U” for construction equations and for states. A value of U less than one indicates that the forecasting model is superior to the naive model. This was true for 65 percent of the 29 construction equations. Actually, an unweighted comparison by type understates the performance of the model, since the construction ‘types for which the naive model was superior were the smaller construction types or those which involve large projects which are relatively sparsely distributed (such as airports, bridges, dams and reservoirs). Together these ten types accounted for only nine percent of 1979 construction outlays. When the alternative U” measure is used, a tendency toward a more compact distribution is observed. Most of the construction types recorded U values in the range 0.8-1.0. The number of types where U” is greater than one fell to seven. Results for states were even more encouraging. Only six states (D.C., Hawaii, Louisiana, Maine, Rhode Island, and West Virginia) recorded U RSUE-
E
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Table 3 Distribution of U and Ux coeffkients for 28 construction equations and 51 states (in percent) for period of iit, 1913-1911. Construction equations
States
Value of U, Ux
U
ux
u
ux
0.0 < 0.2 0.2<0.4 0.4<0.6 0.6 < 0.8 0.8< 1.0 l.O< 1.2 1.2< 1.4 1.4< 1.6 1.6 < 1.8 1.8<2.0 2.0 and greater
0.036 0 0.214 0.214 0.179 0.214 0.036 0.071 0.036 0 0
0 0.036 0 0.071 0.643 0.179 0.036 0.036 0 0 0
0 0.255 0.333 0.235 0.059 0.058 0.020 0 0.020 0 0.020
0 0 0.196 0.471 0.255 0.058 0 0.020 0 0 0
coefficients greater than 1.0. As column 3 of table 3 shows, three-fifths of the states had U values of 0.6 or less. Again, the distribution of U” was more compact, with nearly half the states in the range of 0.60.8.
5.3. Post-sample results Ex post forecasts were made for 1978 and 1979, years not included in the period of tit. The same evaluation procedures were applied to these forecasts. The results, however, are not totally comparable. Although the forecasts were generated ex post, data for many of the exogenous variables were unavailable and estimates were used in their place. Also, observations based on only two time periods obviously have higher variance than the 1973-1977 results. With these caveats, the distribution of U is shown in table 4. The results are consistent with those presented above. Approximately the same number of states and types had u’s below 1.0 as was true in the sample period. Deterioration is noticeable in the higher range of U values for the exceptions, and the higher mean values of U.
5.4. National results For the nation as a whole, the U value associated with the national forecast of total construction activity was 0.122. For the post-sample period, it was 0.51. We regard these results as encouraging indicators of progress,
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Table Distribution
Value
of U
0.0 < 0.2 0.2 < 0.4 0.4<0.6 0.6<0.8 0.8 < 1.0 1.0 < 1.2 1.2< 1.4 1.4< 1.6 1.6< 1.8 1.8 < 2.0 2.0
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4
of U coefficients (in 1978 and 1979 forecasts. State 0.059 0.137 0.176 0.314 0.137 0.137 0 0 0.020 0 0.020
U
percent)
Type 0 0.036 0.286 0.107 0.250 0.107 0.036 0 0.071 0.036 0.071
for
U
-
considering the difficulties associated with forecasting such a volatile component of economic activity as construction on a regional basis. 6. Summary and conclusions
This paper has presented some of the results obtained from a new regional forecasting model for construction activity. The analysis focused on two major issues. First, is the theoretical model of investment behavior the same for all regions? Second, are the model’s forecasts superior to those obtained from simpler forecasting techniques? On the basis of our analysis, we concluded that there was considerable regional variation in the structure of many construction starts equations. For many construction sectors, the same model did not apply to all regions. This suggests that most prior empirical work on construction may suffer from aggregation biases. Our evaluation of the model’s ex post forecasting performance indicated that, for most states and construction types, the model out-performs naive methods of forecasting. These results held for two years not included in the sample data as well as for the sample period. Appendix: Model equations
This appendix presents the major equations of the Regional Construction Forecasting Model. Excluded for reasons of space are the equations used to link average values per start to the construction deflators. Examples of these were presented in the text. Also excluded are the numerous identities of the model. Interested readers may purchase a report [Thomas and Stekler
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(1980)] presenting the model in detail through the National Technical Information Service. In this description, equations whose coefficients were estimated separately for each Census Region are indicated by a +. The coefficient values shown are those of the Southern region. Also the use of individual intercept terms for each state is indicated by including ‘a’ rather than a value for the intercept. ‘T-values appear in parentheses. A.1. Residential sector
(1)
Number of private single-unit housing starts+ (NHSl)’ PMN
NHSl
100. -=a+ p
2.66 -+ (1.38) p
P65A
12.73 (2.39) p
DPI
+ 0.203 __ -0.195 (1.81) p (-10.5)
FBYA
R2=0.928,
-0.0645 (100.~~, (-2.16)
s.e.e.=6.11. (A4
P PMN P65A DPI FBYA SHSl (2)
= total population, = net immigration, =population, ages 65 and over, = disposable personal income, = long-term interest rate, = stock of housing units, single-unit structures. Number of private housing starts, 2-4unit
SHS2
NHSZINHSI
In (1 + NHS2/NHSl)
iI2 = 0.473,
structures+ (NHS2)
=’ + ;$;;)
s.e.e.=0.785.
SHSl
64.2)
6This equation differs from the equation for the South presented in table 2. The one presented here also includes data for 1972.
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Number of private housing starts, 5-or-more-unit NHSS
loo.p=”
DCHR -377.6 ~ DCHH (14;;; (- 6.79) -0.0933
FBYA+
(-3.64)
R2 =0.953, DCHR DCHH PHSS SHS.5
(4)
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structures+ (NHSS) P65A P
0.0475 =
(0.70)
- 0.663 lOO*SHS5P,
(-10.4)
s.e.e.=6.44.
(4.3)
=rental component, consumer price index, = housing component, consumer price index, =rate of change, average value of multi-unit structures, = stock of housing units, Sor-more-unit structures.
Value of private hotel and motel starts (VHAM) VHAM = 2.57 + 0.00291DTCC. P
1’
(3.81)
R2 = 0.466,
s.e.e. = 0.33.
(A.4)
DTCC=Turner Construction Company cost index, XSER = output originating, services sector (1972 dollars).
(5)
Value of college housing starts (VCH, BCH)
R2=0.176,
s.e.e.=0.080.
DEFL =simple average of the Turner (DTCC) DSFH cost indices, P517 =population, ages 5 through 17.
(A.5) and single-family
residential
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A.2. Non-residential
(1)
forecasting
modelfor constructionactivity
buildings
Value of manufacturing buildings+ (VMFG) VMFG P.DTCC
=a+
2 ViAXM-i
0.136 c
(3.86) i=”
’
-0.00138 (-4.73) 82 =0.629,
~,=0.25,
vi =0.50,
~,=0.25,
s.e.e.= 0.740,
Wi =0.333,
64.6)
i=l,2,3.
A&M = change in output originating in manufacturing (1972 dollars), DQM =rate of change, manufacturing output deflator, TAX = total state and local tax receipts. (2)
Value of retail trade buildings (VRT) VRT A(RS/DPCE) = 2.45 + 0.0226 -+ 0.790 DTCC. P P (8.37) (29.2)
R2 =0.712,
s.e.e. =0.36.
.l
(A-7)
RS =value of retail sales (current dollars), DPCE =personal consumption expenditures deflator. (3)
Value of service stations and repair garages (VSSG) VSSG A(RSGS/DPCE) = - 0.239 + 0.00246 DEFL . P P (3.50)
+000395?+ (8.82)
R2=0.626,
s.e.e.=0.014.
0.360 (8.47) 64.8)
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RSGE =retail sales of gasoline stations, (current dollars) MVR = motor vehicle registrations. (4)
Value of parking buildings (VPB, BPB) VPB f BPB = 1.62 + 0.0193 DTCC. P (3.91)
R2=0.135, (5)
s.e.e.=O.llO.
(A.9)
Value of warehouses? ( V WHS) VWHS =a+ 00164W’PCE) DCEN. P (lb.1) p
R2=0.908, DCEN= (6)
s.e.e.=0.13.
(A.10)
Bureau of the Census construction industrial and commercial buildings.
cost index for non-residential
Value of amusement, recreation and social buildings? (VARS, BARS) VARS + BARS DEFL . P
R2 =0.595,
s.e.e. = 0.145
(A.ll)
NHS = total new housing starts (NH% + NHS2 + NHSS). (7)
Value of religious buildings (VREL) VREL =0.62+(,,8~)+,8~(~)~; DSFH * P
R2=0.798, (8)
s.e.e.=0.055.
(A.12)
Value of government administration BGOV =a+ DTCC. P
AXG
0.135(1.91) p ’
AXG =change in output originating
and public service+ buildings (BGOV)
R2=0.302,
s.e.e.=0.713.
in government (1972 dollars).
(A.13)
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Value offreight
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terminals+ (VTER)
VTER =a+ DCEN . P
0.0146 (4.33)
AXTCU
p
-
, R2=0.727,
s.e.e.=0.0355.
AX TCU = change in output
originating in the transportation, cation, and utility sector (1972 dollars).
(10)
activity
(A.14)
communi-
Value @private school buildings+ (VSCH) VSCH DEFL. P
R2=0.474,
s.e.e.=0.0645.
(A.15)
(11) Value of public school buildings+ (BSCH) BSCH DEFL . P
R2 =0.631,
s.e.e.=0.463.
(A.16)
(12) Value of ofice buildings+ (VOFF) VOFF -----=a+ DTCC.
0.571 x 10-3XNM-1-0.147 x 10-4(FPCP-FBYA) (5.23) (- 3.22)
-0.00974$$ (-3.71) XNM
=output
s.e.e.=0.005.
(A.17)
originating in the non-manufacturing sector (in 1972 dollars), interest rate; FPCP minus FBYA is the spread between the short-term and long-term rate, =local government tax receipts.
FPCP =short-term TXL
i?2=0.803,
R.W Thomas and H.O. Stekler, Regional forecasting
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(13) Value of private hospitals and nursing home starts (VHOS) VHOS =2.16+ DTCC. P
P65A
0.0041p+ (2.52)
7.05x lo(1.72)
4 DPI
p
+;;$(D~:~P)-I’
R2=0.442,
s.e.e.=0.310.
(A.18)
(14) Value of public hospital starts (BHOS) VHOS + BHOS =5.75+ P
+ 0.110 (2.03) R2 =0.464, N.B.,
DPI
1.24x 1O-3p (2.49)
VHOS + BHOS DTCC. P >
s.e.e.=0.380,
BHOS = (VHOS + BHOS) - VHOS).
A.3. Non-building
(1)
P65A
0.0567p+ (2.92)
(A.19)
structure starts
Value of sewer systems (BSEW)
R2 =0.466,
s.e.e.=0.004.
(A.20)
DSE W= EPA construction cost index for sewers, VHS =value of housing starts. (2)
Value of water systems (BWAT)
R2 = 0.284,
s.e.e.= 0.002.
D WAT = Bureau of the Census construction
(A.21) cost index for water systems.
576
(3)
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Value of street and highway construction (BSTR) BSTR DFHA.P
=5.67+0.131~+0.0020DFG;; (2.50) (3.61)
p *
R2=0.518,
;~:;$D:~P)-l
s.e.e.=0.566. (A.22)
l?FHA=
P GRF
(4)
FHA index of highway construction =rate of change of total population, = Federal grants-in-aid.
cost,
Value of civil works .(BCIV) BCIV = 0.00282 DREC. P
(2.77)
R2=0.567,
s.e.e.=0.121.
DREC = Bureau of Reclamation
(A.23) construction cost index.
References Ballard, Kenneth P., Richard D. Gustely and Robert M. Wendling, 1980, NRIES - Structure, performance, and application of a bottom-up interregional econometric model (U.S. Department of Commerce, Washington, DC). Bischoff, C., 1970, A model of non-residential construction in the U.S., American Economic Review 60, l&17. Bolton, Roger E., 1969, Predictive models for state and local government purchases, in: James S. Duesenberry et al., eds., The Brookings model: Some further results (Rand McNally, Chicago, IL) 223-267. Bower, Joseph L., 1965, Investment in commercial construction, Review of Economics and Statistics 47, 268-277. Burton, Foster M., A regional model of the construction industry, Unpublished Ph.D. dissertation (University of Pennsylvania, Pittsburgh, PA). Dunlop, John T. and D. Quinn Mills, 1968, Manpower in construction: A profile of the industry and projections to 1975, in: Report of the President’s Commission on Urban Housing (U.S. Government Printing Office, Washington, DC). Glickman, Norman J. and Lawrence R. Klein, 1977, Econometric model-building at the regional level, Regional Science and Urban Economics 7,3-23. Gramlich, E.M., 1969, State and local governments and their budget constraints, International Economic Review 10,168-182. Hambor, John C. and W. Douglas Morgan, 1971, The determinants of commercial construction, Western Economic Journal 9, 172-183. Hausman, J.A., 1978, Specification tests in econometrics, Econometrica 46, 1261-1264. Houthakker, H.S., 1980, Residential energy demand revisited, The Energy Journal 1, 2942. Jaffee, Dwight M. and Kenneth T. Rosen, 1979, Mortgage credit availability and residential construction, Brookings Papers on Economic Activity, 333-376.
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571
Maddala, G.S., 1979, Econometrics (McGraw-Hill, New York). Maisel, Sherman J., 1963, A theory of fluctuations in residential construction starts, American Economic Review 53,359-383. Maisel, Sherman J., 1965, Nonbusiness consumption, in: James S. Duesenberry et al., eds., The Brookings quarterly econometric model of the United States (Rand McNally, Chicago, IL) 179-202. Muth, Richard F., 1960, The demand for non-farm housing, in: Arnold E. Harberger, ed., Demand for durable goods (University of Chicago Press, Chicago, IL). Phelps, Charlotte, 1969, Real and monetary determinants of state and local highway investment, 1951-1966, American Economic Review 59, 507-621. Thomas, R. William and H.O. Stekler, 1980, A regional forecasting model for construction activity, IDA report R-252, PBSl-162380 (National Technical Information Services, Springfield, VA). Thomas, R. William and H.O. Stekler, 1979, Forecasts of construction activity for states, Economics Letters 4, 195-199. U.S. Bureau of the Census, 1973, 1970 Census of housing, Vol. I (U.S. Government Printing Office, Washington, DC). U.S. Bureau of the Census, 1978, Annual housing survey, 1976, Series H50-76A (U.S. Government Printing Oflice, Washington, DC). U.S. Bureau of the Census, Current construction reports, Series C40, Housing units authorized by building permits and public contracts, Monthly publication (Bureau of the Census, Washington, DC). U.S. Department of Labor, Construction Labor Demand System, 1979, Projections of cost, duration, and on-site labor requirements for constructing electric generating plants, 1979-83, DoL/CLDS/PP2 (U.S. Department of Labor, Washington, DC).
A REGIONAL
FORECASTING MODEL ACTIVITY*
FOR CONSTRUCTION
R. William THOMAS Institute
for
Defense
Analyses,
Alexandria,
VA22311,
USA
H.O. STEKLER Industrial
College
of the Armed
Forces,
USA
Received September 1982, final version received January 1983 This paper presents a new, comprehensive and detailed model of construction activity. The model is intended primarily for forecasting applications. The model generates forecasts of new construction starts for each of the 50 states of the United States. Forecasts are made for 29 types of structures. The paper presents evidence that the structure of the determinants of construction activity varies across regions within the United States. Thus, prior models of construction, based only on national time-series data, may be subject to aggregation bias. Evaluation of the model’s forecasts indicates that the model outperforms simpler forecasting methods.
1. Introduction
1.1. Construction activity modeling Most of what economists know about the determinants of construction starts and activity has been derived from time series models based on aggregate data for the entire United States. Such models include, among others, the residential models of Muth (1960), Maisel (1963) and Jaffee and Rosen (1979). A non-business construction sector (including housing) was developed for the Brookings model [Maisel (1965)]. There are several studies which focused on the structures portion of business fixed investment. These include Bischoffs (1970) work on total non-residential construction, and the Bower (1965) and Hambor and Morgan (1971) studies of commercial construction. Finally, there have been a small number of articles which *The work reported here was conducted under Contract J-9-E-8-0031, the U.S. Department of Labor, as part of the development of the Construction Labor Demand System (CLDS). Publication does not indicate endorsement by the Department of Labor, nor should the contents be construed as reflecting the offtcial opinion of this agency or the Department of Defense. The authors gratefully acknowledge the support and comments of William F. Hahn and William R. Schriver of CLDS, as well as those of Robert E. Kuenne, Kenneth Ballard, Douglas Dacy, and Harry Williams. 01660462/83/$3.00
0 1983, Elsevier Science Publishers B.V. (North-Holland)
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analyzed the determinants of state and local government construction expenditures [Phelps (1969), Bolton, (1969) and Gramlich (1969)]. It should be emphasized that all these were national models. However, institutional analyses have stressed that the product and factor markets for construction are more localized [Dunlop and Mills (1960), and Burton (1972)]. It seems more appropriate, therefore, to attempt to model construction activity at the regional rather than the national level. This paper presents a new, comprehensive and detailed model of construction activity. The model is intended primarily for forecasting applications. In developing the model we also hoped to answer two questions which may have broader implications for future research in the field of regional science. First, would the theoretical model of investment behavior, yhich was developed and tested at the national level, be applicable at the state level? In particular, would it be possible to infer that regional construction activity data were generated by a model common to all regions? The second question involves the forecasting accuracy of this new model. Specifically, are the model’s forecasts superior to those provided by simpler and less expensive forecasting techniques? Our methodology and the conclusions drawn are presented below. 1.2. Description of the model The model generates annual forecasts of new construction starts for each of the fifty states and for the District of Columbia. Forecasts are made for twenty-nine types of structures (see table l), which are grouped into three classes: residential construction, non-residential buildings, and non-building construction. Separate forecasts are made for public and for private construction projects. Space considerations preclude a full description of the model [the model is described in detail in Thomas and Stekler (1980)], but a brief discussion of our procedures is warranted here. Our approach to the task of regional modeling follows the tradition of linking construction activity to expansion of the economic base of a region. Non-residential construction is related to growth of industrial output; residential construction, to growth in population. However, the methodology is more complex than that of the simple economic base multiplier. Rather, the demand for each type of structure is modeled as a function of local and national economic variables. The specific determinants used in each equation were originally specified theoretically; these specifications were later modified on the basis of statistical testing. The structure of the construction starts model is described in section 2. Section 3 describes the estimating procedures, the data, and the pooling technique which were used. Section 4 presents the results of estimating the model equations and hypothesis tests. Finally, section 5 presents an
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Table 1 Construction types forecast by the Construction Labor Demand System (CLDS). Residential construction
Non-residential buildings
Non-building construction
Single-family homes 24family homes Hotels and motels College housing 5 +-family homes
Manufacturing buildings Industrial buildings Retail trade and stores Service stations and repair garages Parking buildings Laboratories Warehouses Amusement, recreation and social Religious buildings Government administration buildings Public service buildings Misc. non-residential buildings Office buildings Schools Hospitals
Airports (excluding terminals) Bridges Communication systems Dams and reservoirs Sewers and waste disposals Water systems Streets and highways Civil works Misc. non-building construction
evaluation of the ex post forecasting results for both the sample period and for two years outside of the sample. 2. Structure of the construction model
The Construction Labor Demand System (CLDS) operates as a satellite model [Glickman and Klein (1977)] of a regional economic model, in this case the National Regional Impact Evaluation System (NRIES) [Ballard, Gustely and Wendling (1980)]. While industrial models have often been developed as satellites of national econometric models, our effort is the first instance of which we are aware that this approach has been taken at the state level. NRIES is a set of inter-related state economic models with a common theoretical structure but different estimated coefficients for each state. The equations of NRIES include state variables, common national variables, and weighted inter-regional variables. The latter are aggregates of state variables, the weights varying inversely with the distance between states. Thus, ‘neighborhood’ effects are transmitted in the model. NRIES may be viewed as combining the econometric and gravity model approaches of regional science to forecasting economic activity at the state level. NRIES’ forecasts of state output, employment, income, and other variables are the primary inputs to the CLDS model, which provides regional estimates of construction activity, and the labor requirements associated with
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that activity. Labor requirements are estimated for various crafts employed on the 29 construction types listed in table 1. We use a three-step methodology to estimate construction starts, construction activity, and construction employment. First starts are estimated using the model described in this paper. Then starts are used to estimate construction activity (value put in place). Finally, start estimates are used to determine labor requirements. Although our focus in this paper is on the model which explains starts, it is useful to describe the overall system briefly. Starts of particular types of construction are related to regional demographic and economic variables by (l),
(1)
St = L-m = Cf’wJl,
where S, refers to a p x 1 vector of starts occurring in period t for the p types of construction, and X, is a vector of economic and demographic variables. Starts are then translated into activity by applying a distributed lag which is estimated separately for each type of structure. This may be represented as
where dk is the proportion of total activity undertaken for structure type i in the Tth month of construction, and ni is the total time required to complete the construction of the ith structure type. Finally, craft employment is determined by applying a fixed coefficient labor requirements matrix to each type. Therefore,
1
E,=[lg]= c F St-TW;T) [ i T=O Etis an L x 1 vector of labor requirements
(3)
where for the L crafts, and WiT is an Lx n, matrix for type i. The columns of the W matrix are the labor requirements for each craft in the Tth month of construction. 3. Estimating procedures and data 3.1. Choice of dependent variable and use of weighted regressions
The dependent variable used in each of the three residential housing starts equations was the number of starts. In choosing to forecast the number of starts, we follow the standard practice for the residential sector, where it is possible to meaningfully aggregate in terms of physical units. All other equations were estimated with the value of construction starts as the
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561
dependent variables. The dollar data were deflated’ to remove the effect of purely inflationary increases on the values of these starts. In all cases, both the dependent and the independent variables included in a particular equation were deflated by the state’s population. Thus, all equations are estimated in per capita terms. This normalization procedure would be expected to remove the heteroscedasticity that could result from the disparate size of the states and the large variations in construction starts. For instance, in one year the number of single-family housing starts ranged from 150 in the District of Columbia to 165,000 in California. Given this disparity in size, an improvement in estimation accuracy can be obtained by weighting the larger states more heavily in the estimation procedure. The appropriate weighting factor is the square root of total population.’ Consequently, for each construction type the equation to be estimated is of the form (4)
where the Yi’s are the relevant dependent variables, D is a national construction deflator, Pi is the population of the ith state, and the Xj’S are the independent variables. In eq. (4), Vi, is assumed to be distributed normally with
Wt, Ku)= d
if
r=s
= 0 otherwise.
and
t=u,
(5)
3.2. Data
The construction starts data used to estimate all the equations were obtained from a service of the F. W. Dodge Company. This service, entitled Dodge Construction Potentials, provides data which are time series observations on individual construction projects which we aggregated to the state level by construction type. These aggregated variables are the dependent variables of the equations. The remaining variables were obtained from the NRIES data file. The Dodge data are available for 1972-1979. The ‘Individual deflators were chosen from the set of construction cost indices used by the Bureau of the Census. 2This procedure was also used by Houthakker (1980) in his recent study of electricity demand, which also used state data. Forecast values must be ‘deweigbted’.
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data for 1972-1977 were used to estimate the model; those for the last two years are used to test it. 3.3. Estimating technique Data restrictions influenced our choice of estimating technique. There were an insufficient number of observations to permit the use of a pure time series approach for each state. On the other hand, a pure cross-sectional approach was also rejected because of our desire to test for regional variability. Thus to capture both the regional and cyclical variability, the data were pooled, yielding 306 (51 x 6) observations for each type when national estimates are made. Maddala (1979) has described the techniques most commonly applied in estimating pooled relationships. The least square dummy variables’ regression (LSDV’) technique was chosen for our model because it assumes that each region has certain (unexplained) unique characteristics which are fixed over time.
3.4. Hypothesis regarding model structure There are good reasons to test the hypothesis that the same underlying model holds in all regions. It is possible that the same model might not be appropriate for both high and low (or negative) population growth regions. In particular, theory suggests the potential for asymmetric behavior with respect to adjustment rates for long-lived assets such as housing. That is, the housing stock can be adjusted upward rapidly, if excess demand prevails, but depreciates slowly in the presence of excess supply. We tested the composite hypothesis that all parameter values are identical in the four regions. The test procedure involved estimating the equation nationally, then estimating separate equations using data pooled regionally. The difference in explained variance can be used to form a test statistic which is distributed as F. To illustrate our approach, the results for the single-family home equation are presented in the next section. 4. The estimated model and tests of the pooling hypothesis This section describes the results obtained from estimating the model equations using the F. W. Dodge data. The first section describes the results for the housing sector in some detail. Because of space limitations, we must present the results for the other sectors in condensed form. A more complete description of and rationale for the specifications chosen is presented in Thomas and Stekler (1980).
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4.1. Residential construction 4.1.1. Theoretical specification
The specification of the residential construction equations draws on the work of Muth (1960), Maisel (1965) and Jaffee and Rosen (1979). The major finding of the Muth and Maisel studies was that housing demand was fundamentally based on permanent income, the number of households formed, and the price of housing. Short-term variations in new housing units started are induced by financial factors, chiefly periods of monetary stringency associated with rapid increases in interest rates. Jaffee and Rosen’s contribution was to elaborate on how the demands of different age-specific demographic factors especially affect the mix of single- and multi-unit housing demanded. Our specifications for the single-family and live-or-more-unit housing starts equations are consistent with these models.3 A standard stock adjustment model is used, since annual housing stock estimates (KSFI) could be developed from benchmark data. 4 The single-unit equation [appendix eq. (A.l)] includes disposable income (DPI), the interest rate (INT), the rate of new immigration (PMN) and the proportion of the population over 65 (P6.5) as determinants. Other demographic subgroups were included in alternative specifications. The variables included in the multi-unit equation [appendix eq. (A.3)] were income, the population aged 65 and over, interest rates, price of housing and relative prices of renting versus home ownership.
4.1.2. Results: Single-family housing starts
Table 2 presents the estimates for the single-family home equation. In the national equation, all the variables except the interest rate are significant, but the stock variable has the wrong sign. In the regional equations the interest rate has the expected sign and is only insignificant in the equation explaining starts in the Northeast region. The coefficients of other variables vary in an unsystematic way among the regional equations. Given the variation of coefficients, we tested whether the data should be pooled nationally. The hypothesis was that the regions shared a common model. Using the standard F-test, this hypothesis was rejected. The value of the F-statistic was 4.91 with 15 and 184 degrees of freedom.
3However, data limitations at the state level required us to substitute for some of demographic variables used. 4The 1970 Census of Housing (1973) and the 1976 Annual Housing Survey (1978) provided two bench mark estimates. Annual values for 19691977 were constructed from annual new construction series using the perpetual inventory method.
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Table 2 National and regional equations for single-family housing starts, 1973-1977 (t-statistics in parentheses). Estimated using data for region Variable
National
INT” PMNd P65’ KSF” RZ
Standard error Deesees of
N. Central
South
West
Dependent variable
SFSI” DPIb
Northeast
0.389 (7.00) -0.0173 (- 1.85) 3.28 (4.40) -4.87 (3.42) 0.133 (5.38) 0.943 4.19
0.212 (1.56) -0.0347 (- 1.89) 0.134 (0.12) 5.72 (1.W -0.096 ( - 2.53) 0.913 1.82
199.0
31.0
-9.67 x 1O-3 0.639 ( - 0.26) (6.57) -0.102 -0.124 (- 10.72) ( - 9.05) 2.23 7.44 x 1o-3 (5.5 x 10-3) (2.W 20.58 1.71 (2.24) 0.37 0.023 - 0.022 (0.45) ( - 0.090) 0.960 0.968 2.07 3.41 43.0
63.0
0.499 (2.97) -0.141 (-5.80) 6.83 (2.32) 11.3 (1.09) 0.120 (1.43) 0.928 5.59 47.0
*Units per 100 people. “Thousands of dollars per capita. =Percent. dNet immigrants as a ratio to total population. ‘Persons over 65 as a ratio to total population.
4.2. Other construction sectors 4.2.1. Theoretical specljkations The equation estimates for the other construction sectors are shown in the appendix. The theoretical specifications used in estimating these equations closely followed the classic theory of investment. For example, it was assumed that new industrial buildings would be started when additional capacity was desired. This in turn suggested that changes in expected output or sales and the cost of capital relative to the price of output were the relevant explanatory variables. In the non-commercial building sector, basic indicators of the need for new facilities are used. Thus, religious buildings, amusement and recreational buildings, and schools are all related to the level of new housing starts. The most difficult problem of specifications arose in modeling the non-
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565
building structures sector. Most construction in this sector is public and includes sectors related to general growth of population (water and sewer systems, streets and highways) and a second group related to geography (airports, bridges, dams and civil works). An examination of the equations in the appendix shows that better results were achieved in modeling the sectors where population growth was the dominant factor, as compared to those where geographic factors dominate.
4.2.2. Results
Our approach in modeling all these sectors was to formulate an appropriate theoretical specification and estimate it with data pooled nationally. Then the identical equation was again re-estimated for each of the four Census Regions, and the hypothesis that the same model held for all regions was tested. Construction sectors where regional equations’ parameters differed significantly from national parameters included multi-family housing, manufacturing buildings, warehouses, schools and offices. Regions where we could not reject the null hypothesis that the national model applied in all regions included religious buildings, hospitals, water and sewer systems, and streets. We observe a pattern here. The latter group consists of basic infrastructure elements, which are required in proportion to population and/or housing units. Given knowledge of the level of housing starts, there is no reason to expect major regional differences in these relationships. In contrast, most of the first group of structures evidence considerable regional variability in response to the differences in economic variables among the regions.
4.3. Regional variability: An assessment
Overall, our results tend to reject rather conclusively the hypothesis that regional construction demand can be described by the same theoretical model nationwide. The F-test for the pooling of regional data was rejected for the housing starts equations and for a majority of the non-residential construction equations of the model. The only equations where we could not reject the hypothesis of a common model were those which included housing starts as an explanatory variable. This conclusion calls into question the process of creating regional and state economic forecasts by allocating national forecasts among the states according to population or more sophisticated ‘share-down’ rules.
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5. Model forecasting accuracy Since the primary goal of the model development effort was the generation of forecasts of new construction activity, it is important that the model be evaluated primarily by this criterion. Several measures of forecasting accuracy are commonly used - mean absolute error (MAE) and mean square error (MSE) being the most frequent choices. We focus on Thiel’s U coefficient, expressed as the ratio of the RMSE to the root mean square change in the actual series,
= RMSE (forecast)/RMSE
(actual).
(6)
The U coefficient is a relative measure which compares the errors of the forecasts to the errors of a naive forecast of no change.5 In using this statistic, we are following the procedures used in evaluating large macroeconometric models. The no-change naive model is a most appropriate standard to use in evaluating the forecasts of variables, such as construction expenditures, which are subject to wide annual fluctuations, but exhibit little secular trend. 5.1. Basis of evaluation The model generates annual forecasts for 29 construction types, two ownership classes, and 51 regions. Obviously, it is impossible to present a systematic evaluation of all forecasts. We focus here on the accuracy of (1) forecasts of total new construction value among states and (2) forecasts of national construction value for each of the 29 construction types. All forecasts are expressed in terms of predicted changes derived from a dynamic simulation of the model over 1973-1977. Using predicted changes rather than levels avoids a bias against the model which would result from the fact that the naive model standard has only a one-year forecast horizon. Thus, the error in period t is expressed as
while the error of the naive model is AA, [since the naive hypothesis is AA,=O]. ‘The use of a more sophisticated naive model, such as an ARIMA specification, was precluded by the limited number of time-series observations available for each variable.
R.W Thomas and H.O. Stekler, Regional forecasting model for construction activity
The U coefficients for the construction
561
equations were computed by
where the i subscript denotes the construction type, j the state, and t the year of each observation. P represents forecast values and A actual values. Note that forecasts are summed across states before being compared to actual results. Thus, compensating errors in individual states cancel and reduce the national error. An alternative measure (UX) has been defined which does not have this property, 63)
The U” measure penalizes both the forecasting and naive model for generating compensating errors. The corresponding U and U” measures for states are defined similarly, (9) I
77
29
1
I
77
29
UT=J ,&, izl(APijt-AAijt)” Id f&, & (AAi.it)2.
(10)
5.2. Within-sample results
Table 3 displays the distribution of U and U” for construction equations and for states. A value of U less than one indicates that the forecasting model is superior to the naive model. This was true for 65 percent of the 29 construction equations. Actually, an unweighted comparison by type understates the performance of the model, since the construction ‘types for which the naive model was superior were the smaller construction types or those which involve large projects which are relatively sparsely distributed (such as airports, bridges, dams and reservoirs). Together these ten types accounted for only nine percent of 1979 construction outlays. When the alternative U” measure is used, a tendency toward a more compact distribution is observed. Most of the construction types recorded U values in the range 0.8-1.0. The number of types where U” is greater than one fell to seven. Results for states were even more encouraging. Only six states (D.C., Hawaii, Louisiana, Maine, Rhode Island, and West Virginia) recorded U RSUE-
E
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Table 3 Distribution of U and Ux coeffkients for 28 construction equations and 51 states (in percent) for period of iit, 1913-1911. Construction equations
States
Value of U, Ux
U
ux
u
ux
0.0 < 0.2 0.2<0.4 0.4<0.6 0.6 < 0.8 0.8< 1.0 l.O< 1.2 1.2< 1.4 1.4< 1.6 1.6 < 1.8 1.8<2.0 2.0 and greater
0.036 0 0.214 0.214 0.179 0.214 0.036 0.071 0.036 0 0
0 0.036 0 0.071 0.643 0.179 0.036 0.036 0 0 0
0 0.255 0.333 0.235 0.059 0.058 0.020 0 0.020 0 0.020
0 0 0.196 0.471 0.255 0.058 0 0.020 0 0 0
coefficients greater than 1.0. As column 3 of table 3 shows, three-fifths of the states had U values of 0.6 or less. Again, the distribution of U” was more compact, with nearly half the states in the range of 0.60.8.
5.3. Post-sample results Ex post forecasts were made for 1978 and 1979, years not included in the period of tit. The same evaluation procedures were applied to these forecasts. The results, however, are not totally comparable. Although the forecasts were generated ex post, data for many of the exogenous variables were unavailable and estimates were used in their place. Also, observations based on only two time periods obviously have higher variance than the 1973-1977 results. With these caveats, the distribution of U is shown in table 4. The results are consistent with those presented above. Approximately the same number of states and types had u’s below 1.0 as was true in the sample period. Deterioration is noticeable in the higher range of U values for the exceptions, and the higher mean values of U.
5.4. National results For the nation as a whole, the U value associated with the national forecast of total construction activity was 0.122. For the post-sample period, it was 0.51. We regard these results as encouraging indicators of progress,
R.W! Thomas
and H.O.
Stekler,
Regional
forecasting
Table Distribution
Value
of U
0.0 < 0.2 0.2 < 0.4 0.4<0.6 0.6<0.8 0.8 < 1.0 1.0 < 1.2 1.2< 1.4 1.4< 1.6 1.6< 1.8 1.8 < 2.0 2.0
model for
construction
activity
569
4
of U coefficients (in 1978 and 1979 forecasts. State 0.059 0.137 0.176 0.314 0.137 0.137 0 0 0.020 0 0.020
U
percent)
Type 0 0.036 0.286 0.107 0.250 0.107 0.036 0 0.071 0.036 0.071
for
U
-
considering the difficulties associated with forecasting such a volatile component of economic activity as construction on a regional basis. 6. Summary and conclusions
This paper has presented some of the results obtained from a new regional forecasting model for construction activity. The analysis focused on two major issues. First, is the theoretical model of investment behavior the same for all regions? Second, are the model’s forecasts superior to those obtained from simpler forecasting techniques? On the basis of our analysis, we concluded that there was considerable regional variation in the structure of many construction starts equations. For many construction sectors, the same model did not apply to all regions. This suggests that most prior empirical work on construction may suffer from aggregation biases. Our evaluation of the model’s ex post forecasting performance indicated that, for most states and construction types, the model out-performs naive methods of forecasting. These results held for two years not included in the sample data as well as for the sample period. Appendix: Model equations
This appendix presents the major equations of the Regional Construction Forecasting Model. Excluded for reasons of space are the equations used to link average values per start to the construction deflators. Examples of these were presented in the text. Also excluded are the numerous identities of the model. Interested readers may purchase a report [Thomas and Stekler
570
R.W
Thomas
and H.O.
Stekler,
Regional
forecasting
model for
activity
construction
(1980)] presenting the model in detail through the National Technical Information Service. In this description, equations whose coefficients were estimated separately for each Census Region are indicated by a +. The coefficient values shown are those of the Southern region. Also the use of individual intercept terms for each state is indicated by including ‘a’ rather than a value for the intercept. ‘T-values appear in parentheses. A.1. Residential sector
(1)
Number of private single-unit housing starts+ (NHSl)’ PMN
NHSl
100. -=a+ p
2.66 -+ (1.38) p
P65A
12.73 (2.39) p
DPI
+ 0.203 __ -0.195 (1.81) p (-10.5)
FBYA
R2=0.928,
-0.0645 (100.~~, (-2.16)
s.e.e.=6.11. (A4
P PMN P65A DPI FBYA SHSl (2)
= total population, = net immigration, =population, ages 65 and over, = disposable personal income, = long-term interest rate, = stock of housing units, single-unit structures. Number of private housing starts, 2-4unit
SHS2
NHSZINHSI
In (1 + NHS2/NHSl)
iI2 = 0.473,
structures+ (NHS2)
=’ + ;$;;)
s.e.e.=0.785.
SHSl
64.2)
6This equation differs from the equation for the South presented in table 2. The one presented here also includes data for 1972.
R.W? Thomas
(3)
and H.O.
Stekler,
Regional
model for
Number of private housing starts, 5-or-more-unit NHSS
loo.p=”
DCHR -377.6 ~ DCHH (14;;; (- 6.79) -0.0933
FBYA+
(-3.64)
R2 =0.953, DCHR DCHH PHSS SHS.5
(4)
forecasting
construction
activity
571
structures+ (NHSS) P65A P
0.0475 =
(0.70)
- 0.663 lOO*SHS5P,
(-10.4)
s.e.e.=6.44.
(4.3)
=rental component, consumer price index, = housing component, consumer price index, =rate of change, average value of multi-unit structures, = stock of housing units, Sor-more-unit structures.
Value of private hotel and motel starts (VHAM) VHAM = 2.57 + 0.00291DTCC. P
1’
(3.81)
R2 = 0.466,
s.e.e. = 0.33.
(A.4)
DTCC=Turner Construction Company cost index, XSER = output originating, services sector (1972 dollars).
(5)
Value of college housing starts (VCH, BCH)
R2=0.176,
s.e.e.=0.080.
DEFL =simple average of the Turner (DTCC) DSFH cost indices, P517 =population, ages 5 through 17.
(A.5) and single-family
residential
512
R. W. 7homasand H.O. Stekler, Regional
A.2. Non-residential
(1)
forecasting
modelfor constructionactivity
buildings
Value of manufacturing buildings+ (VMFG) VMFG P.DTCC
=a+
2 ViAXM-i
0.136 c
(3.86) i=”
’
-0.00138 (-4.73) 82 =0.629,
~,=0.25,
vi =0.50,
~,=0.25,
s.e.e.= 0.740,
Wi =0.333,
64.6)
i=l,2,3.
A&M = change in output originating in manufacturing (1972 dollars), DQM =rate of change, manufacturing output deflator, TAX = total state and local tax receipts. (2)
Value of retail trade buildings (VRT) VRT A(RS/DPCE) = 2.45 + 0.0226 -+ 0.790 DTCC. P P (8.37) (29.2)
R2 =0.712,
s.e.e. =0.36.
.l
(A-7)
RS =value of retail sales (current dollars), DPCE =personal consumption expenditures deflator. (3)
Value of service stations and repair garages (VSSG) VSSG A(RSGS/DPCE) = - 0.239 + 0.00246 DEFL . P P (3.50)
+000395?+ (8.82)
R2=0.626,
s.e.e.=0.014.
0.360 (8.47) 64.8)
R.W
Thomas
and H.O.
Stekler,
regional
forecasting
model
for
construction
activity
573
RSGE =retail sales of gasoline stations, (current dollars) MVR = motor vehicle registrations. (4)
Value of parking buildings (VPB, BPB) VPB f BPB = 1.62 + 0.0193 DTCC. P (3.91)
R2=0.135, (5)
s.e.e.=O.llO.
(A.9)
Value of warehouses? ( V WHS) VWHS =a+ 00164W’PCE) DCEN. P (lb.1) p
R2=0.908, DCEN= (6)
s.e.e.=0.13.
(A.10)
Bureau of the Census construction industrial and commercial buildings.
cost index for non-residential
Value of amusement, recreation and social buildings? (VARS, BARS) VARS + BARS DEFL . P
R2 =0.595,
s.e.e. = 0.145
(A.ll)
NHS = total new housing starts (NH% + NHS2 + NHSS). (7)
Value of religious buildings (VREL) VREL =0.62+(,,8~)+,8~(~)~; DSFH * P
R2=0.798, (8)
s.e.e.=0.055.
(A.12)
Value of government administration BGOV =a+ DTCC. P
AXG
0.135(1.91) p ’
AXG =change in output originating
and public service+ buildings (BGOV)
R2=0.302,
s.e.e.=0.713.
in government (1972 dollars).
(A.13)
574
R.W
Thomas
and H.O.
(9)
Value offreight
Stekler,
Regional
forecasting
model for
construction
terminals+ (VTER)
VTER =a+ DCEN . P
0.0146 (4.33)
AXTCU
p
-
, R2=0.727,
s.e.e.=0.0355.
AX TCU = change in output
originating in the transportation, cation, and utility sector (1972 dollars).
(10)
activity
(A.14)
communi-
Value @private school buildings+ (VSCH) VSCH DEFL. P
R2=0.474,
s.e.e.=0.0645.
(A.15)
(11) Value of public school buildings+ (BSCH) BSCH DEFL . P
R2 =0.631,
s.e.e.=0.463.
(A.16)
(12) Value of ofice buildings+ (VOFF) VOFF -----=a+ DTCC.
0.571 x 10-3XNM-1-0.147 x 10-4(FPCP-FBYA) (5.23) (- 3.22)
-0.00974$$ (-3.71) XNM
=output
s.e.e.=0.005.
(A.17)
originating in the non-manufacturing sector (in 1972 dollars), interest rate; FPCP minus FBYA is the spread between the short-term and long-term rate, =local government tax receipts.
FPCP =short-term TXL
i?2=0.803,
R.W Thomas and H.O. Stekler, Regional forecasting
model for construction activity
515
(13) Value of private hospitals and nursing home starts (VHOS) VHOS =2.16+ DTCC. P
P65A
0.0041p+ (2.52)
7.05x lo(1.72)
4 DPI
p
+;;$(D~:~P)-I’
R2=0.442,
s.e.e.=0.310.
(A.18)
(14) Value of public hospital starts (BHOS) VHOS + BHOS =5.75+ P
+ 0.110 (2.03) R2 =0.464, N.B.,
DPI
1.24x 1O-3p (2.49)
VHOS + BHOS DTCC. P >
s.e.e.=0.380,
BHOS = (VHOS + BHOS) - VHOS).
A.3. Non-building
(1)
P65A
0.0567p+ (2.92)
(A.19)
structure starts
Value of sewer systems (BSEW)
R2 =0.466,
s.e.e.=0.004.
(A.20)
DSE W= EPA construction cost index for sewers, VHS =value of housing starts. (2)
Value of water systems (BWAT)
R2 = 0.284,
s.e.e.= 0.002.
D WAT = Bureau of the Census construction
(A.21) cost index for water systems.
576
(3)
R.W
Thomas
and H.O.
Stekler,
Regional
forecasting
model for
construction
activity
Value of street and highway construction (BSTR) BSTR DFHA.P
=5.67+0.131~+0.0020DFG;; (2.50) (3.61)
p *
R2=0.518,
;~:;$D:~P)-l
s.e.e.=0.566. (A.22)
l?FHA=
P GRF
(4)
FHA index of highway construction =rate of change of total population, = Federal grants-in-aid.
cost,
Value of civil works .(BCIV) BCIV = 0.00282 DREC. P
(2.77)
R2=0.567,
s.e.e.=0.121.
DREC = Bureau of Reclamation
(A.23) construction cost index.
References Ballard, Kenneth P., Richard D. Gustely and Robert M. Wendling, 1980, NRIES - Structure, performance, and application of a bottom-up interregional econometric model (U.S. Department of Commerce, Washington, DC). Bischoff, C., 1970, A model of non-residential construction in the U.S., American Economic Review 60, l&17. Bolton, Roger E., 1969, Predictive models for state and local government purchases, in: James S. Duesenberry et al., eds., The Brookings model: Some further results (Rand McNally, Chicago, IL) 223-267. Bower, Joseph L., 1965, Investment in commercial construction, Review of Economics and Statistics 47, 268-277. Burton, Foster M., A regional model of the construction industry, Unpublished Ph.D. dissertation (University of Pennsylvania, Pittsburgh, PA). Dunlop, John T. and D. Quinn Mills, 1968, Manpower in construction: A profile of the industry and projections to 1975, in: Report of the President’s Commission on Urban Housing (U.S. Government Printing Office, Washington, DC). Glickman, Norman J. and Lawrence R. Klein, 1977, Econometric model-building at the regional level, Regional Science and Urban Economics 7,3-23. Gramlich, E.M., 1969, State and local governments and their budget constraints, International Economic Review 10,168-182. Hambor, John C. and W. Douglas Morgan, 1971, The determinants of commercial construction, Western Economic Journal 9, 172-183. Hausman, J.A., 1978, Specification tests in econometrics, Econometrica 46, 1261-1264. Houthakker, H.S., 1980, Residential energy demand revisited, The Energy Journal 1, 2942. Jaffee, Dwight M. and Kenneth T. Rosen, 1979, Mortgage credit availability and residential construction, Brookings Papers on Economic Activity, 333-376.
R. W. Zhomas
and H.O.
Stekler,
Regional
forecasting
model for
construction
activity
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Maddala, G.S., 1979, Econometrics (McGraw-Hill, New York). Maisel, Sherman J., 1963, A theory of fluctuations in residential construction starts, American Economic Review 53,359-383. Maisel, Sherman J., 1965, Nonbusiness consumption, in: James S. Duesenberry et al., eds., The Brookings quarterly econometric model of the United States (Rand McNally, Chicago, IL) 179-202. Muth, Richard F., 1960, The demand for non-farm housing, in: Arnold E. Harberger, ed., Demand for durable goods (University of Chicago Press, Chicago, IL). Phelps, Charlotte, 1969, Real and monetary determinants of state and local highway investment, 1951-1966, American Economic Review 59, 507-621. Thomas, R. William and H.O. Stekler, 1980, A regional forecasting model for construction activity, IDA report R-252, PBSl-162380 (National Technical Information Services, Springfield, VA). Thomas, R. William and H.O. Stekler, 1979, Forecasts of construction activity for states, Economics Letters 4, 195-199. U.S. Bureau of the Census, 1973, 1970 Census of housing, Vol. I (U.S. Government Printing Office, Washington, DC). U.S. Bureau of the Census, 1978, Annual housing survey, 1976, Series H50-76A (U.S. Government Printing Oflice, Washington, DC). U.S. Bureau of the Census, Current construction reports, Series C40, Housing units authorized by building permits and public contracts, Monthly publication (Bureau of the Census, Washington, DC). U.S. Department of Labor, Construction Labor Demand System, 1979, Projections of cost, duration, and on-site labor requirements for constructing electric generating plants, 1979-83, DoL/CLDS/PP2 (U.S. Department of Labor, Washington, DC).