3 SECTORAL DESCRIPTION (10) [Equations are included in
3.4 Aggregate Supply .1 CANDIDE 2.0
CANDIDE 2.0 is built upon an input/output framework with a 48 industry level of
disaggregation. Input/output models are based on a Leontief technology with fixed coefficients of production and one primary input, labour. CANDIDE does not specify potential output. Output is not subject to any long-run production function constraints. Discrepencies can exist between expenditure and production.
The investment equations of CANDIDE are based on Jorgenson's neoclassical model and thus implicitly assume Cobb-Douglas technology. The man-hours equations are based on either Cobb-Douglas or CES technology. Consistency is not imposed on the various implicit production functions by any framework of interrelated factor demands. This would be a very difficult task in practice, but not impossible in principle, in a model based on an input/output structure.
Private investment in CANDIDE is disaggregated into 38 industries and for each industry into non-residential construction and machinery and equipment. The specification of the equations follows that of Jorgenson and is derived from neoclassical investment theory assuming profit maximization and lagged adjustment of actual to desired capital stocks. The key explanatory variables are all industry specific. They include: 1) real output; 2) price; 3) the user cost of capital; and 4) capital stock. The form of the equation is:
Ii = a0 + JW(J1D(Pi * Xi/IUCi)) + JW(IKi)
where Ii is investment in industry i, Pi is the price of industry i, Xi is the output of industry i, IUCi is the user cost of capital in industry i, and IKi is the capital stock in industry i.
Sometimes the relative cost and output terms are entered in the investment equations separately.
The user cost of capital in CANDIDE is industry specific and provides a useful way to
incorporate industry specific information on depreciation, the corporate tax rate, the investment tax credit, and capital consumption allowances. The user cost equations are of the form:
IUCi = ((1/(1 - IETi)) * PFi * (FRATE + IEDi)) * (1 - IZi * IETi) * (1 - ITCi)
where IETi is the effective tax rate on industry i, PFi is the final demand deflator of the investment category, FRATE is the nominal yield on long-term industrial bonds, IEDi is the economic depreciation rate in industry i, IZi is discounted capital cost allowances in industry i, and ITC is the effective tax rate in industry i.
Note that the nominal interest rate is utilized in the user cost calculation.
Private inventory demand in CANDIDE 2.0 is disaggregated into seven holding industries: 1) agriculture; 2) forestry; 3) mining; 4) retail and wholesale trade; 5) durable manufacturing; 6) non-durable manufacturing; and 7) other. Equations are included for all of the industries except agriculture which is exogenous. Inventory change equations follow the accelerator model and are a function of: 1) activity levels in the holding industry; 2) the lagged inventory stock of the holding industry; and 3) the rate of change of prices relevant to the holding industry.
Employment demand in CANDIDE 2.0 is broken down into 37 industries and expressed in terms of man-hours. The man-hours equations are eithe:1) renormalized Cobb-Douglas production functions with lagged adjustment; or 2) labour demand functions derived from the first order equilibrium conditions of CES production functions. In the first case the explanatory variables are industry specific output and capital stock; in the second industry specific output and the real wage. A time trend is also often included.
Average weekly hours equations are provided in CANDIDE 2.0 to translate man-hours into employment. They are a function of the industry specific after-tax real wage, the unemployment rate and in some cases a time trend.
3.4.2 TIM
TIM like CANDIDE embodies a detailed input/output production sector. There is no overall production function. Potential output is not defined. Output is not subject to any long-run
production function constraints, but is primarily demand driven. Short-term productivity ensures that output plus inventories and net exports equals sales.
The investment equations of TIM are based on Jorgenson's neoclassical model with its assumed Cobb-Douglas production function. The employment equations are also mostly based on inverted Cobb-Douglas production functions. The explicit or implicit parameters of the production
functions, however, are not necessarily the same in the investment and employment equations.
The level of disaggregation is different between investment and employment in most cases, precluding constraints on parameters across equations.
Investment in TIM is modelled for over 45 sectors and for both machinery and equipment and non-residential construction. The investment equations are generally based on the Jorgenson neoclassical model. The functional form of the estimated equations is:
Ii = a0 + a1 * J1D(Yi * Pi/Ci) + a2 * Ki(-1)
where Ii is investment in industry i, Yi is output of industry i, Pi is the price of output of industry i, Ci is the user cost of industry i, and Ki is the stock of capital of industry i.
The user cost variable (Ci) is defined as Ci = PGi * (r + di)
where Ci is the user cost of capital in industry i, PGi is the price of investment in industry i, r is the interest rate on industrial bonds, and di is the depreciation rate in industry i.
There are two things worthy of note here. First, a nominal interest rate is used as the measure of the cost of financing. Second, the rental cost is specified before tax and does not have
built-in tax parameters.
Other investment specifications utilized in TIM, but much less widely, relate investment to output and the interest rate or to output and the lagged capital stock.
Inventory change is modelled in TIM for eight categories: 1) wholesale trade; 2) grain; 3) other farm; 4) non-farm primary; 5) durable manufacturing; 6) non-durable manufacturing; 7) cars at the retail level; and 8) other retail trade. The equations are based on a stock adjustment model in which inventory change is related to the gap between desired and actual inventory stocks.
The desired stock is primarily a function of some activity variable such as real output, or consumption of relevant goods and services. The nominal interest rate on commercial paper is included as an additional explanatory variable in the two equations for the change in
manufacturing inventories. Dummy variables reflecting special factors are also in some of the equations.
Employment demand in TIM is disaggregated into 23 industries. Most of the equations are based on a stock adjustment model with the desired employment derived by inverting the
Cobb-Douglas
production function for the industry. The average age of the capital stock is introduced as a proxy for technological change and increased efficiency. A representative equation is that for non-durable manufacturing:
(1)
J1D(LOG(MANDET)) = a0 + a1 * D75 + a2 * MNDVMK (2)
+ a3 * LOG(((MNDCMK + MNDCCK ) * ((MANDY/
(MNDCMK + MNDCCK))**(1/.66)/MANDET(-1)) where MANDET is employment in non-durable manufacturing, D75 is a dummy variable equal to 1 in 1975, MNDVMK is the vintage of the capital stock of machinery and equipment in non-durable manufacturing, MNDCMK is the stock of machinery and equipment in non-durable manufacturing, MNDCCK is the stock of non-residential construction in non-durable manufacturing, and MANDY is real domestic product in non-durable manufacturing.
Term (1) measures the vintage of the capital stock. It is calculated as a distributed lag on a time trend with the weights given by the share of investment minus scrappage in the period to
the total stock of the particular type of capital. The coefficient on this term, which can be viewed as a time trend, is negative. Term (2) represents the gap between desired and actual
employment. A feature of this specification is that if output and capital stock grow at the same rate,employment will grow less rapidly due to the negative coefficient on the vintage of the capital stock. This allows for labour augmenting technical change and productivity growth.
In some industries other formulations are utilized. For instance, employment in pipelines is tied to capital stock and employment in agriculture is positively related to overall unemployment as well as to agricultural output.
Total annual hours worked by industry in TIM depends on employment in the industry and on trend and cyclical factors. The cyclical variables most commonly utilized are output and productivity.
3.4.3 RDX2
The key output concept in RDX2 is gross private business product excluding agriculture and commercial services (UGPP). The supply of output is based on a three factor Cobb-Douglas production function with the stock of machinery and equipment, the stock of non-residential construction, and the labour inputs in efficiency units. Labour input in efficiency units is defined as the product of employment in mining, manufacturing and other business and average weekly hours times a labour efficiency factor. The economy quite reasonably allows for variable operating rates and is not required to operate on its production function in the short-run. In the longer-run, however, it exhibits a tendency to gravitate back on its production function.
The RDX2 concept corresponding to potential output (UGPPD) is calculated using the same production function but with employment based on the average employment rate and with trended weekly hours. Another important output concept in RDX2 is private business product adjusted to remove unintended inventory changes (using the coefficient from the inventory change equation). This concept is called UGPPA. The ratio of UGPPA to UGPPD is the RDX2 measure of capacity utilization which appears in some of the price and import equations.
Investment in RDX2 is forward looking. Investment in machinery and equipment is specified to be a function of the gap between future output and preferred output according to the vintage stock
of capital and the desired capital output ratio calculated from the production function assuming cost minimization. A cash index influences the speed with which the gap is closed. Lagged investment is introduced as an additional explanatory variable.
Investment in non-residential construction also depends on a forward looking gap variable and the lagged capital stock. However, dependency is intermediated by an equation for commercial, industrial, and engineering contract awards. Investment in non-residential construction is a distributed lag on real contract awards.
The imputed rental prices for machinery and equipment and non-residential construction utilize a weighted sum of the real supply price of capital in Canada and the U.S. based on ownership of the domestic capital stock as the interest rate variable. They incorporate the weighted corporate tax rate, and the present value of capital consumption allowances for each category.
They also allow for the deductibility of interest payments on the debt financed portion of investment.
Employment in mining,manufacturing, and other business in RDX2 can be viewed as the residual factor of production. It is modelled as a function of the gap between desired employment
calculated by inverting the production function given output, capital stocks, and long-run hours.
The desired level of employment is constrained by a non-linear relationship to the potential labour force. The gap between desired quantity of labour and labour supply is utilized in the wage equation as the labour market tightness variable.
The gap between average weekly hours worked in mining and manufacturing and trend hours as a per cent of trend hours is explained as a function of the gap between constrained desired employment and actual employment divided by actual.
The RDX2 inventory change equation is fairly simple. Intended inventory change depends on the gap between the desired and actual inventory stocks. The desired stock is defined as a
distributed lag on sales and a separate lag on imports. The unintended component is represented by the difference between the supply of output calculated from the production function and real private business product excluding inventory change. It is the coefficient on this term that is utilized to adjust private business product for unintended inventory accumulation.
The use of the production function rather than "expected sales" to define the buffer change in inventories is a crucial difference between RDX2 and any other Canadian models prior to MACE and SAM (15).
Factor demands in RDX2 are consistently estimated within aframework of interrelated factor demands. There is a hierarchy of demands running from short-run productivity, hours,
employment, machinery and equipment, and non-residential construction. In RDX2 there is no powerful mechanism to ensure that the economy returns to the production function within a short period of time, although the model exhibits a tendency in this direction. Short-run productivity changes can persist for fairly long periods of time. Whether or not this is an accurate description of the real world is an empirical question. There is much empirical evidence that variable
operating rates are an important characteristic of the economy which can not be ignored. There is less reliable evidence about the duration of variable operating rates.
3.4.4 CHASE
The key output variable in the CHASE model is for real private, business output which is defined as real GNE excluding capital consumption allowances, external interest and dividends, output of the farm and government sectors, and gross rent. The production function utilized in the CHASE model to calculate aggregate supply is:
XGPPSCA = (KMEXCA(-1)**EKMECA(-1)) * (KNRCXECA(-1)**EKNRCA(-1)) * ((NICCA * NAWMMCA * .052)**ELCA) * ETFPCA
where XGPPSCA is aggregate supply, KMEXCA is the stock of non-farm machinery and equipment excluding energy,EKMECA is the
production function coefficient on M&E, KNRCXECA is the stock of non-farm non-residential construction excluding energy, EKNRCA is the coefficient on non-residential construction, NICCA is industrial composite employment, NAWMMCA is average weekly hours worked in manufacturing, ELCA is the coefficient on labour, and ETFPCA is total
factor productivity in the private business sector.
There is no requirement that demand and supply as defined by the production function be equilibrated in the long-run.
The same production function is used with the substitution of trend hours and trend labour demand to define trend private business product. It is the ratio of private business product to trend private business product that serves as the capacity utilization variable in the CHASE model which appears most importantly in the import equations.
The investment sector has equations for non-energy investment in business non-residential construction, and machinery and equipment. They are basically accelerator equations with a cash flow variable added. There are no cost of capital variables embodying tax parameters. Energy investment is treated as exogenous.
The investment in non-residential construction (INRCCA) equation is:
(1)
LOG(INRCCA - INRCNRCA) = .70520 - .98071 * LOG(KNRCXECA(-1) (2)
+ .13440 * (LOG(YCCA(-1) - TCCFCA(-1) + CCACZCA(-1)) (3) (4)
- LOG(XGPPZCA)) + .26989 * LOG(INRCNRCA) (5)
+ JW(LOG(XGPPCA(-1))
where INRCNRCA is energy investment in non-residential construction, KNRXECA is the stock of non-farm nonresidential construction excluding energy, YCCA is corporate profits before tax,
TCCFCA is federal corporate income tax collections,
CCACZCA is capital consumption allowances of corporations, XGPPZCA is gross private business product in current dollars, and XGPPCA is real gross private business product.
Term (2) is the cash flow variable. RDX2, the DRI model and FOCUS also have cash flow terms in their investment equations, but cash flow has a larger role in CHASE than in the other models.
The sum of the lag weights on gross private business product (term (5)) is 1.098.
The investment in machinery and equipment (IMECA) equation is similar:
LOG(IMECA - IMENRGCA)/KMEXECA(-1)) = -.51047 - .28077 * LOG(KMEXECA(-1)/XGPPCA(-1)) + .65756
* LOG((IMECA(-1) - IMENRGCA(-1))/KMEXECA(-2)) + .16822 * (LOG(YCCA(-1) - TCCFCA(-1)
+ CCACZCA(-1)) - LOG(XGPPZCA(-1)))
where IMECA is investment in machinery and equipment,
IMENRGCA is energy investment in machinery and equipment, KMEXECA is the stock of non-farm machinery and equipment excluding energy, and the other variables are as defined above.
The main employment variable in the CHASE model is employment in the industrial composite.
It is the variable that appears in the production function. Other employment categories such as non-commercial services and public administration are also modelled. As are categories for paid and unpaid, part-time and full-time employment and by age and sex.
Employment in the industrial composite depends on nominal private business product divided by the hourly labour cost, a proxy for the marginal product of labour. The equation is:
LOG(NICCA/NICCA(-1) = -.19083 + .17124 * (LOG(XGPPZCA/WNICCA * (1 + RYWSLPCA/NAWMMCA)) - LOG(NICCA(-1))) where NICCA is employment in the industrial composite,
XGPPZCA is gross private business product, WNICCA is average weekly wages and salaries for the industrial composite,
RYWSLPCA is the proportion of supplementary income in total labour income, and NAWMMCA is average weekly hours worked in manufacturing.
The change in non-farm business inventories is modelled as the percentage change in the stock.
This is a function of a distributed lag on the percentage change in the sales of private
business and the four quarter percentage change in the ratio of corporate profits before tax to private business product.
Although the CHASE model has a Cobb-Douglas production function, factor demands are not modelled consistently with the production function. There is no hierarchy of factor demand response to a demand shock. There are no mechanisms to make sure that the economy operates on the production function in the long run. The model is mainly demand driven.
3.4.5 DRI
The main output concept in the DRI model is real GNP. Potential output is defined as full employment GNP which is generated by a Cobb-Douglas production function relating real GNP to labour, capital and energy inputs. Potential GNP is thus expressed as a function of the
full-employment labour force (contribution = .637), the fully utilized capital stock at the peak level of capacity utilization in manufacturing (contribution = .296), an implicit energy demand term based on relative energy prices (contribution = .0677), and a time trend for total factor productivity. The function can be summarized:
GNP71FE = f(EFE, "K", "ENERGY", TIME)
where GNP71FE is full employment GNP, EFE is full-employment employment,calculated using the full employment labour force and unemployment rates, "K" is fully utilized capital stock equal to the peak level of capacity utilization in manufacturing times the capital stock, "ENERGY" is a weighted sum of the price of natural gas, petroleum and coal, and electricity to the GNP deflator, and TIME is the time trend for total factor productivity.
There is no requirement that supply as defined by the production function and demand be equilibrated in the long-run.
The investment equations in the DRI model are for investment in non-residential construction and machinery and equipment excluding pipelines, electricity and mining. The equations are characterized in the model documentation as reflecting a "cash flow-augmented neoclassical stock-adjustment model embodying a replacement investment hypothesis". Investment is specified to depend on the gap between the desired and actual capital stock and on the
depreciation of the capital stock. The desired capital stock is specified to be a function of real final sales, the user
cost of capital, and real cash flow.
The equation for non-residential construction (ICERNE71) can be summarized as follows:
ICERNE71 = f(SF71(-i), PGNP71/ICERCOST(-j), CASH71(-k),
KNCERNE71(-l), d * KNCERNE71(-l), DMYEXPO, DMYOLYM) where i = 1,16; j = 4,11; k = 1,8; d = .021799, and
SF71 is real final sales, PGNP71 is the GNP deflator, ICERCOST is the user cost for non-residential construction, CASH71 is real cash flow, KNCERNE71 is the stock of
non-residential construction, and DMYEXPO and DMYOLYM are dummy variables for Expo 67 and the 1976 Olympics.
The equation for machinery and equipment (IPDENE71) can be similarly summarized:
IPDENE71 = f(SF71(-i), PGNP71/IPDECOST(-j), CASH71(-k), KNPDENE71(-l), d * KNPDENE71(-l), DMEXPO)
where i = 1,12; j = 4,11; k = 1,8; d = .0844909, and
IPDECOST is the user cost for machinery and equipment, KNPDENE71 is the stock of machinery and equipment, and all other variables are as defined above.
The user cost variables in the DRI model for both non-residential construction and machinery
The user cost variables in the DRI model for both non-residential construction and machinery