It is impossible to ascertain the steady state properties of a model without extensive simulation analysis. However, it is possible to gain some understanding of the tendencies that these models might exhibit by an analysis of their structure. For SAM this understanding can be very good because the steady state properties are built into the model. For other models, the understanding is necessarily much more incomplete and tentative.
The concepts of interest are: the natural rate of unemployment; trend productivity; potential output; the structural deficit; the marginal propensity to consume; real interest rates; inflation expectations; and desired factors of production.
The natural rate of unemployment is not defined in CANDIDE and TIM. It is also not defined in MTFM which also takes an industry and age-sex approach to the labour market. The natural rate of unemployment also was not a concept utilized in RDX2 since it only gained acceptance in the early 1970s after the RDX2 wage sector was already specified.
A natural rate is found in all of the quarterly models except for MTFM. The natural rate
corresponds to an average rate adjusted for changes in the composition of the labour force and for other developments such as the Unemployment Insurance regime. The natural rates in the
FOCUS and DRI models are based on the work of Dungan and Wilson (9). The natural rates in the CHASE, RDXF and QFS models follow a similar approach. The natural rate in SAM is based on that in RDXF. The MACE model also has a natural rate.
Trend productivity is not defined in the CANDIDE and TIM models. In CHASE, DRI, FOCUS, QFS, and RDXF there is a total factor productivity variable. In the DRI model total factor
productivity grows by 1 per cent per year. In FOCUS it shifts downward after 1973. In QFS it grows 1 per cent per year up to 1973 and .2 per cent per year commencing in 1974. The total factor productivity trend in RDXF is 1.9 per cent before 1970 declining to .16 per cent in 1974 and subsequent years. MACE has a labour productivity index for its production which grows at a steady 1.86 per cent per year. SAM has a kink in its productivity growth after 1973, dropping from 2.1 per cent to 1.6 per cent. The rest of the slowdown can be attributed to factor price changes and cyclical factors. RDX2 had a constant labour efficiency factor.
Aggregate potential output is not defined for CANDIDE or TIM. The quarterly models, except for MTFM which has no production function, have all followed RDX2 in having a trend, full employment or potential output based on the natural rate (or in RDX2's case, an average rate) of unemployment. The DRI and FOCUS models have even gone a bit further using capital stock at a peak or natural rate of capacity utilization in the production function in the place of the actual capital stock. The ratio of actual to potential output is used as an aggregate capacity
utilization rate in CHASE, QFS, and RDXF as it was in RDX2.
The MACE model does not have a potential output, but one could easily be defined using the natural rate and production function that are in the model. Instead MACE has a concept called vintage-based synthetic supply that is calculated from the production function using actual inputs. The ratio of output to vintage-based synthetic supply is a capacity variable in the model.
The SAM model has steady state output based on steady state labour supply and the
output/labour ratio based on an optimizing decision given factor prices. This corresponds to potential output. The SAM model has very strong mechanisms which cause it to gravitate to steady state output in the long-run. None of the models calculate a structural government deficit.
It is difficult to tell the long-run marginal propensity to consume from an inspection of the consumption sectors of the models. The only evidence available is from the simulations done for the Bank of Canada and Department of Finance comparative models seminar in June, 1982. This evidence is not definitive for the models currently being studied for a number of reasons. RDX2 was already defunct. MTFM did not participate. Some of the models such as SAM and RDXF have been significantly modified since the seminar. Other models have been modified to a less significant extent. Also the simulations presented at the seminar were managed to a certain extent to generate what model builders considered reasonable results and thus may not have reflected model properties.
For what it is worth, the long-run (10 year) marginal propensities to consume resulting from a $1 billion personal income tax cut were associated with an MPC of .773 in CANDIDE, .8 in TIM, .71 in CHASE, .75 in DRI, .84 in FOCUS, and .817 in MACE. The QFS MPC is estimated to be in the .6 to .7 range. For purposes of comparison, the MPC for RDX2 cited in the documentation was .66, rising from .76 if an adjustment were made to endogenize input and paid rent. This is in the same range as those calculated for the other models. In all cases, the MPCs are significantly less than the average propensity to consume and could cause problems in long-run growth
simulations.
Various definitions of real interest rates are utilized in the models in different places. This is discussed in more detail in the sectoral descriptions below. FOCUS is the only quarterly model with consistent definitions of real interest rates, based on its synthetic expected inflation series.
In most of the models inflation expectations are adaptive. In some of the models such as TIM and MACE expectations are determined by distributed lags on prices and can vary from one equation to another. In others such as CHASE, QFS, and RDXF an attempt has been made to follow RDX2 with its PCPICE and calculate a price expectations variable with fixed lag weights to be used where appropriate. QFS even has two such price expectations series. This approach, however, is not always consistently pursued in the models and estimated distributed lags to capture expectations can also quite often be found.
Other more novel approaches to modelling inflation expectations have also been utilized in some of the models. CANDIDE has an inflation expectation variable based on past money growth as well as past inflation (weight .27 on money and .73 on past prices).FOCUS has a synthetic expectations series calculated using reduced form forecasting equations for 90 day, 1 year and 2 year ahead price expectations. The expectations variables are utilized consistently in the model.
In SAM expected inflation is a function of current and long-run expected inflation, with long-run expected inflation being dependent on the difference between the expected money supply growth and steady state output growth.
Labour supply in the models is usually determined by the underlying demographics and participation rate equations. In CANDIDE the demographic block is detailed and the
participation rate equations by age and sex group are a function of the real after-tax wage, and Unemployment Insurance and pension variables. TIM also has detailed demographics and the real wage influences the part rate. CHASE part rates are based on trends and the percentage change in employment. The DRI model calculates the labour force by adding up employment and unemployment. Unemployment depends on capacity utilization and the percentage of the labour force between 25 and 54. The FOCUS part rate equations depend on the employment rate, the maximum unemployment insurance benefit, real OAS pensions and trend factors. The group part rate equations in MTFM depend on the employment rate for the group and for all other groups. In QFS the part rate is a function of the deviation of employment from trend, a UI dummy, the real wage relative to expectations, and a time trend. The RDXF part rate responds to the
employment/population ratio, the natural rate and a time trend. The RDX2 part rate equation included capacity utilization, net immigration relative to population and the population in secondary school as explanatory variables. The MACE part rate is a function of capacity utilization, the ratio of the natural to actual rate of unemployment, the real wage in efficiency units, and an AIB dummy. The labour supply decision in SAM results from an intertemporal labour-leisure optimization decision by households. Labour supply depends on the ratio of per capita real human and non-human wealth to the after-tax return from labour force participation.
An adjustment is made for differences between steady state and actual valuations.
Desired factors of production should in theory be derived from a production function. This was the approach of interrelated factor demands pioneered in RDX2. All of the models except TIM, CHASE, and MTFM have production functions. However, only in FOCUS, MACE, and SAM are desired factors of production rigourously derived from the production function. For the annual models with industrial disaggregation such as CANDIDE and TIM or even for the quarterly models such as MTFM with integrated industrial disaggregation, it would be a very difficult task to consistently apply an interrelated factor demand approach. For the other quarterly models, it would not be as hard.
Basically, all of the models but FOCUS (flexible price version) and SAM are primarily demand driven. Output will increase in response to a demand shock. Short-run productivity is the most important source of the output increase and can persist for a very long time. The models based on consistent interrelated factor demand frameworks such as FOCUS (fixed price version), RDX2, MACE and SAM should exhibit a tendency for supply to eventually catch up with demand provided the factor demands are gap-closing. For factor demands to be gap-closing there must be good links between the disequilibrium terms (abnormal inventories and utilization) and pricing and trade behaviour that bring the economy back to equilibrium. For the other models there is no mechanism to guarantee that supply will ever equal demand.
In the flexible price version of FOCUS prices equilibrate supply from the production function with demand so supply will always equal demand. In SAM there are a number of mechanisms that operate to bring the economy into a steady state where supply equals demand and
expectations are met.
FOCUS (flexible price version) MACE and SAM are also the only models that are likely to exhibit strong tendencies to bring the economy back to full capacity (or potential) output. Other models besides FOCUS, SAM, and MACE may exhibit tendencies to return to full capacity, but they will be very much weaker. Whether strong or weak tendencies are more characteristic of the actual economy is an empirical question, which must be answered before it is possible to decide which models more accurately describe the way the real world economy operates.
An accelerationist wage-price sector is the most obvious mechanism which might serve to bring the economy back to potential output and the natural rate. For a model to be accelerationist a number of conditions must be met. First, the wage equation must be an extended Phillips curve based on a gap between the actual and natural rate of unemployment with a coefficient of 1 on expected inflation. This condition is met in DRI, and RDXF among the quarterly models.
The second condition is that prices must be homogenous of degree one in costs. In the DRI and QFS quarterly models this constraint is imposed. In other models it is approximately met.
The third condition is that all costs must be endogenous and respond to labour costs. This condition is not met in many quarterly models including CHASE, FOCUS and QFS among the quarterly models because of exogenous food or energy components.
The fourth condition is that the exchange rate must adjust to ensure purchasing power parity so that foreign costs in Canadian dollars will remain in line with domestic costs. Among the quarterly models the CHASE model has a purchasing power parity term in its exchange rate equation. The QFS and RDXF exchange rate equations are also designed with long-run purchasing power parity in mind.
The only quarterly models satisfying all conditions to be accelerationist are QFS and RDXF.
Among annual models the MACE model is reported to have its own model specific natural rate of unemployment and to exhibit accelerationist behaviour. However, it results from a somewhat different process from that sketched out above. MACE has a capacity variable in its wage
equation that produces a similar effect to a labour market gap variable. It has homogeneity in costs with the key cost variable specified as the dual to the longer-run production function. It also has no exogenous costs. As an alternative its exchange rate can be set in accordance with
purchasing power parity.
The SAM model would exhibit accelerationist behaviour if monetary policy were utilized to lower the unemployment rate below the natural rate. However, it is difficult to see why the model should exhibit such behaviour in response to a fiscal shock.
Of all the models, SAM is the only one with built in steady state conditions which guarantee that the actual unemployment rate equals the natural rate, actual output equals expected output, and that actual inflation equals expected inflation at a non-accelerating rate.
Another steady state property which is of interest is whether or not real wage growth equals trend labour productivity growth. This depends primarily on the role of productivity in the model's wage equations.
CANDIDE and TIM do not have a productivity variable in their wage equation. In CHASE the percentage change in the wage bill for the industrial composite depends on the percentage change in current dollar gross private business product with a coefficient of .5307 and on the change in the gap between the actual and natural rate of unemployment. Such a specification does not ensure that real wages keep up with productivity.
In the DRI model the key average hourly earnings wage variable that enters in the price equation does not have a productivity term in it, but the national accounts average wage equation does.
FOCUS also has no productivity term
QFS has a productivity term in its wage equation.
RDXF has a twelve quarter average of the first difference of total factor productivity in its wage equation. Since its coefficient is 1.435 the real wage must rise more rapidly than productivity.
The RDX2 wage change equation has the gap between trend productivity of labour and the real wage as the key long-run explanatory variable. It also includes a short-run productivity measure.
MACE includes the labour productivity index in its wage equation and constrains the long-run coefficient to one. In SAM the wage also tends towards the wage trend based on productivity in the long-run.
3 SECTORAL DESCRIPTION (10)