An econometric model of the US economy structural analysis in 56 equations

1.3 The 56-Equation Model: 30 Behavioral Equations, 15 Identities Product Side ofNational Income and Product Accounts NIPA, and 8 Behavioral Equations, 3 Identities Income Side of NIPA 1

John J Heim

An Econometric Model of the US Economy

Structural Analysis in 56 Equations

John J Heim

University at Albany-SUNY, Albany, New York, USA

ISBN 978-3-319-50680-7 e-ISBN 978-3-319-50681-4

https://doi.org/10.1007/978-3-319-50681-4

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This book is dedicated to Susan who has given me so much

I left academic life in 1972, after getting my Ph.D At that time large-scale econometric modeling ofthe economy was the rage; everyone thought it would be just a matter of time before we had “doneenough science” to allow economists to discuss economics in the classroom, not in terms of the

alphas and betas of theoretical models, but in terms of the real-world coefficients they represent.Economics would become the next branch of engineering, or so many thought

Much to my surprise, when I returned to academic life 25 years later things had not much

progressed Most economists were still using alphas and betas to describe how one variable affectsanother in economics For lack of vigorous, concerted effort over those 25 years to pursue the hardnumbers underlying the theories, and their statistical significance, economists were still just

discussing theories with the best “numbers” we had – the abstract alphas and betas of pure theoretical

discourse Because we hadn’t disciplined our presentation of theories to those scientifically proven

to work, even more theories abounded than was the case in 1972 Worse, the overriding emphasis ineconomic theory was not on “what works?”, but on “what’s new?”

My engineering students knew the difference When I tried to describe macroeconomics as real

science , and then described the coefficients that connect one variable to another in alphas and betas,

instead of real numbers, they just snickered “Yes, but what is the real relationship?” they would ask,meaning what are the real numbers? “And if you don’t have them, why do you call this science?” theywould ask Certainly in their engineering courses, where every equation describes what actuallyworks, they were getting real numbers

This book attempts to meet that very standard by focusing on what works It attempts to moveforward the empirical efforts of Tinbergen, Goldberger, Klein, Eckstein, and Fair the past 80 years to

determine what works That is, the effort to convert economics from just theory to hard (by which I

mean reliable) science Doing so requires three things

First, it requires that the postulates we test have some economic meaning, and not be just somecollection of variables we are “running up the flagpole,” to see what happens

Second, it requires that the theory-based postulates we test are structured loosely enough so that

the data determine what is real, i.e., the exact shape and content of the theory being tested It is not

for us to say a priori by how we structure the model we test, whether Keynes’ consumption function,

whose principal determinant is current income, is correct, or whether Freidman’s, whose principaldeterminant is average income (permanent income) is correct

Third, it is not for us to claim some empirical result proves some theory is correct, simply

because it explains some variation in the economy, in some time period, in some economic model To

be correct, it should explain most variance, in most or all time periods, in most or all models.

This book tries to adhere to these three rules, we think successfully To meet the first condition,its model is built around the theory that we found most consistent with the data To meet the second,the shape (and inclusion) of each equation in the model is data-determined, e.g., there are no

predetermined assumptions about what drives consumer or investment spending Third, a large-scaleeconometric model is needed to capture all the sources of economic variation, and that’s what isused Extensive robustness testing was used to prove that any initial statistical finding was real andnot just some spurious artifact of the time period or particular model tested

I hope the reader will agree that the models developed in this book adhere to these rules for goodengineering science

SUNY, AlbanyJohn J Heim

Most of all, I am indebted to Nobel Laureate Robert Solow for providing review comments and

suggestions on an earlier draft, as did David Colander and Ray Fair They were a source of

inspiration and without their involvement and support, especially Robert Solow’s, this book probablywould not have been finished

I am also indebted to distinguished econometrician, Kajal Lahiri, for bringing me to SUNY

Albany and providing a place where I could work on this book with a minimum of other distractions

He has provided a very supportive and intellectually stimulating atmosphere within which to work,and provided guidance on econometric issues through his careful review of an earlier draft

I would also be remiss if I did not mention the long line of earlier economists who toiled long andhard as both macroeconomists and econometricians to turn macroeconomics from philosophy intoscience These economists include Jan Tinbergen, Lawrence Klein, Frank deLeeuw, Arthur

Goldberger, and, more recently, Ray Fair Fair has had the doubly difficult job of keeping the stronglyscientific Cowles tradition alive during recent decades, when many economists turned to different,less scientific approaches We owe him much

For similar reasons, we owe Greg Mankiw much His 2006 article in the Journal of Economic

Perspectives convinced many that the detour in the 1980s away from Cowles modeling and toward

DSGE has proven unproductive, and helped resurrect interest in Cowles modeling again Solow’s(2010) testimony to Congress reached the same conclusion about DSGE and helped in the same way

Nor could the book have been written without the strong support of my wife Sue This book

required 2 years full-time work, and before that, considerable part-time work The problems to beresolved required endless long hours at work, and endlessly preoccupied my mind, even at home Suewas always willing to make the sacrifices necessary to cope with all that

Finally, I must acknowledge the secretarial assistance provided by Annemarie Hebert She hashelped pull together, duplicate, and send out endless drafts of this work

The book has two parts: Part I contains 45 equations describing in detail the “product side” of the

National Income and Product Accounts (NIPA) It contains tested models of the GDP and its majorcomponents, and the determinants of their level of production (Chapters 4 – 19 ) Part II provides 11additional equations describing how the value of the product generated producing the GDP is

distributed among the factors of production For each factor of production there are two equations

The first describes the variables that were found to determine each factor’s percentage share of

national income The second describes the variables found to determine the total amount (the level )

of each factor’s total income These models describe the variables whose own changes cause thedistribution of income among factors to shift from one factor to another over time ( Chapter 20 )

Chapter 19 provides a summary of the substantive findings as to the determinants of GDP and itscomponents Chapter 20 , Section 20.​5 , summarizes the determinants of factor shares and levels ofincome

The Production Side Model

Production is treated as a response to aggregate demand (AD) Hence the key determinants of GDPproduction are expressed as determinants of AD Supply shortages can also affect the level of

production, but the empirical evidence indicates that demand is far more commonly the driving factor.Fully 85–95% of the variation of GDP over the 50-year period 1960–2010 appears to stem fromvariation in AD Demand-driven models are commonly thought of as Keynesian models, and to thatextent this is a Keynesian model However, when a variable to measure “crowd out” is added tostandard Keynesian consumption and investment equations, this model’s conclusions about the

effectiveness of fiscal policy in stimulating the economy are just the opposite of Keynes’ Its

conclusions about monetary policy conclusions are also not the same The model indicates the

stimulus effects of changes in the money supply to be modest at best

The 45-equation first part (the production side) includes 30 behavioral equations and 15

identities The identities connect the behavioral equations into a comprehensive model of the realU.S economy The behavioral equations were generally estimated applying strong instrument 2SLS to1960–2010 data The model includes eight consumption and nine investment equations, includingthree for personal, corporate, and depreciation allowance savings Two interest rate determinationmodels based on the Taylor rule or the Keynesian LM curve are included Also included are twounemployment determination models, a Phillips curve model, one export function, and two “IS” curvefunctions determining GDP Other behavioral models are provided for taxes and government

spending, recognizing that part of these variables levels is endogenously determined by the state ofthe economy Two functions describe the determinants of M1 and M2 velocity These are included toshow mathematically how fiscal policy can shift the AD curve Extensive efforts were made to ensurethat all identification issues were resolved by replacing Hausman-endogenous variables with Wald-strong instruments which were Sargan-tested to ensure they also were not endogenously determined.There are 75 variables (or different lags of the same variables) in the 45 equations Robustnesstesting, a non-negotiable requirement of good science, was exhaustive All models were tested in fourdifferent time periods to ensure estimated effects were consistent over time, i.e., immune to Lucascritique All coefficients were also tested for robustness to changes in the model being tested, i.e., to

see how additions and subtractions of variables from the model affected the remaining variablesestimated effects Because of the pervasiveness of the multicollinearity problem, this type of

robustness testing is also a non-negotiable requirement of good science Finally, almost all weretested using OLS as well as 2SLS techniques to allow comparisons with literature of an earlier day,which sometimes used OLS

DSGE and VAR methodologies are currently more popular methodologies for macroeconomicmodeling Therefore, a lengthy section is included in Chapter 2 discussing the advantages of the olderCowles methodology and why it is used here Chapter 2 is literally a paper within a paper It dealswith what may be the most pressing unresolved methodological issue facing macroeconomic

modelers today: how to successfully model the macroeconomy the way it actually works , so that

models can be reliably used by policy makers to predict consequences of decision-making Earlymodels designed to do this were referred to as Cowles Commission models and were very good atexplaining the data, though not always 100% successful Cowles models dominated model buildingfrom the advent of the econometric revolution up to the mid-1980s However, in the last 30 years,many economists have turned away from Cowles types of modeling in favor of DSGE and VAR

Which of these three methods for discerning economic reality is to be preferred? To shed somelight on this question, the statistical performance of several VAR and DSGE models are comparedwith Cowles-type structural models Comparisons are made, or reported from other studies, andinclude comparisons with a Sims (1980) VAR model, the Smets-Wouters model, FRB/US, and asimplified version of the FRB/NY model These tests overwhelmingly indicate the more Keynesian(Cowles) structural models outperform the others in accurately modeling the actual year-to-yearfluctuations of the economy Therefore, they should become the models of choice in future

macroeconomic studies analyzing the consequences of changes in economic variables

Nobel Laureate economist Robert Solow (2016) concurs; he has said Cowles models far betterexplain the data than DSGE or VAR models: after reviewing this paper’s analysis of the three

methods, Solow wrote

… Your arguments in favor of Cowles-type models as against VAR and DSGE models have realweight … I think that you get across that whatever can be said for DSGE models … they are

inferior at explaining the facts … You do the same for general VAR models

After Keynes himself, Solow is arguably the greatest economist of the twentieth century

The Income Shares Model

Part II of this book ( Chapter 20 ) describes how the income generated producing the GDP is

distributed Four equations describe the variables found to determine the level of income received aslabor, profit rent, and interest income An additional four equations describe the variables found to

affect the percentage share of national income received by each of these factors, that causes factor

shares to vary from decade to decade A summary of findings is presented at the beginning of Chapter

20 The econometric methodology used, including exhaustive robustness testing, was the same asused in Part I of the book

Methodology

Good science requires replicability of results This chapter’s goal was to provide, to the best extentpossible, models whose results meet the replicability standard Largely, this goal appears to be

achieved, though in some areas more remains to be done Hopefully, future generations of researcherswill find it worthwhile to take up where this study leaves off In particular, in some equations wewere not able to fully resolve the “left out” variables and multicollinearity problems that affects thecredibility of parameter estimates in any economic model

In most models 85–95% of the variance is explained However, in some models, there are

definitely some “left out” explanatory variables remaining to be found Less of the total variance inthe model than we would like is explained by the variables Models with this problem are identified

estimates For most of our parameter estimates we are able to show these techniques achieved thedesired level of stability, but not for all For some models, parameter estimates are still sensitive toexactly what other variables are included in the model (these models are identified in the text)

Economists needs to develop better scientific methods for dealing with this problem

1.3 The 56-Equation Model: 30 Behavioral Equations, 15 Identities (Product Side of

National Income and Product Accounts (NIPA)), and 8 Behavioral Equations, 3 Identities (Income Side of NIPA)

1.4 The 38 Behavioral Equations: Coefficients, Significance, R 2 , and Durbin Watson Tests: (Summary of Results: Detailed Explanations of Findings Presented in Chapters 4-20)

Part I Production of the GDP

2 Methodology

2.​1 General Methodological Issues

2.​2 Choosing Between VAR, DSGE, and Cowles Commission Models

3 Literature Review

3.1 Lawrence Klein and Michael Evans (1968): The Wharton Econometric Forecasting

Model

3.2 Otto Eckstein’s (1983) The DRI Model of the U.S Economy

3.3 Ray Fair’s Estimating How the Macroeconomy Works (2004)

3.​4 Federal Reserve Board/​U.​S.​ Model (1996)

3.​5 Literature Review Summary

4 The Consumption Models

4.​1 Total Consumer Spending on Both Domestically Produced and Imported Consumer

Goods

4.​2 Spending on Imported Consumer Goods – OLS Estimates

4.​3 Spending on Imported Consumer Goods – 2SLS Estimates

4.​4 Consumer Spending on Domestically Produced Consumer Goods (OLS)

4.​5 Determinants of Consumer Borrowing – OLS Estimates

4.​6 Determinants of Consumer Borrowing – 2SLS Estimates

4.​7 Modeling the Major Components of Total Consumption

4.​8 Determinants of Spending on Consumer Durables (OLS)

4.​9 Determinants of Spending on Consumer Durables (2SLS)

4.​10 Determinants of Spending on Consumer Nondurables (OLS)

4.​11 Determinants of Spending on Consumer Nondurables (2SLS)

4.​12 Determinants of Spending on Consumer Services (OLS)

4.​13 Determinants of Spending on Consumer Services (2SLS)

5 Models Identifying the Determinants of Investment Spending and Borrowing

5.​1 OLS Estimates of the Determinants of Total Investment Spending

5.​2 2SLS Estimates of the Determinants of Total Investment

5.​3 OLS Estimates of the Determinants of Domestically Produced Investment Goods 5.​4 2SLS Estimates of the Determinants of Domestically Produced Investment Goods 5.​5 OLS Estimates of the Determinants of Imported Investment Goods

5.​6 2SLS Estimates of the Determinants of Imported Investment Goods

5.​7 An Alternative Method of Calculating Coefficients in the Investment Imports Model 5.​8 OLS Estimates of the Determinants of Investment Borrowing

5.​9 Determinants of Spending on Fixed Plant and Equipment Investment (OLS)

5.​10 Determinants of Spending on Fixed Plant and Equipment Investment (2SLS)

5.​11 Determinants of Spending on Residential Investment (OLS)

5.​12 Determinants of Spending on Residential Investment (2SLS)

5.​13 Determinants of Spending on Inventory Investment (OLS)

6 The Exports Demand Equation

6.​1 OLS Model of Export Demand

7 Statistically Estimated Real GDP Determination Functions (#x201C;IS” Curves)

7.1 The GDP as a Function of the Determinants of Domestically Produced Consumer and Investment Goods and Services, Government Spending and Exports (GDP = C D + I D + G + X)

7.2 The GDP as a Function of the Determinants of Total Consumer and Investment Goods and Services, Government Spending, and Exports Minus Imports (GDP = C T + I T + G + X – M)

8 Real GDP Determination Function (#x201C;IS#x201D; Curve) Coefficients Aggregated from Parameter Estimates Obtained by Statistically Estimating the Subcomponent Functions

Comprising the GDP

8.1 Using the GDP Determination Model (GDP = C D + I D + G + X)

8.2 Using the GDP Determination Model (GDP = C T + I T + G + X – M)

9 Determinants of the Prime Interest Rate:​ Taylor Rule Method

9.​1 OLS Estimates

10 Determinants of the Prime Interest Rate – LM Curve Method

10.​1 OLS Models of the LM Curve

11 Determinants of Inflation – The Phillips Curve Model

11.​1 Reconciling the Money Supply Variable in the Taylor Rule and LM Equation Interest Rate Models with the Money Supply Variable in the Inflation (Phillips Curve) Equation

12 Determinants of Unemployment

12.​1 A Simple OLS Model Based on Okun’s Law

12.​2 The 2SLS Okun Model

12.​3 The OLS Technological Change Model

12.​4 The 2SLS Technological Change Model

13 The Savings Functions

13.​1 The Corporate Savings Function

13.​2 The Depreciation Allowances Savings Function

13.​3 Personal Savings

14 Determinants of Government Receipts

14.​1 Contributions to Explained Variance

14.​2 Robustness Over Time

14.​3 Robustness to Model Specification Changes (1960–2010 Data Set)

15 Endogeneity of Government Spending Levels

15.​1 The Model for Total Government Spending for All Purposes:​ Goods, Services, and Transfers

15.​2 The Model for Government Spending on Goods and Services Only

16 Capacity of the Model to Explain Behavior of the Macroeconomy Beyond the Period Used to Estimate the Model

16.​1 Model #1 Treating All Determinants of C, I, and X as Exogenous

16.​2 Model 2:​ Treating C, I, and X Model Determinants for Which We Have Explanatory Functions as Endogenous

17 Converting the Older Keynesian IS-LM Model to the More Modern AS-AD Interpretation of the Keynesian Model

17.​1 Short– and Long-Run Aggregate Supply Curves

17.​2 The Aggregate Demand Curve and the Role of Velocity In Aggregate Demand

17.​3 OLS Tests of M1 Velocity’s Determinants

17.​5 OLS Tests of M2 Velocity’s Determinants

17.​6 Which Determinants of GDP Are Also Determinants of Velocity

17.​7 Stationarity Issues

17.​8 Alternative Method:​ Calculating Impact of Determinants of GDP on Velocity Using Regression Coefficients Obtained Estimating Consumption, Investment, and Export

Functions

18 Dynamics

18.​1 Introduction

19 Summary and Conclusions (Production Side of the NIPA Accounts)

19.​1 Other Major Findings

Part II Income Side of the NIPA Accounts

20 Determinants of Factor Shares

20.​1 Introduction, Theory of Factor Shares, and Summary of Findings

20.​2 Literature on Factor Shares

List of Figures

Fig 4.1.1 Actual consumption compared to levels calculated from Model 4.1.T 1960–2010

Graph 6.1.1 Equation 6.1 Graphed

Graph 12.2.1 The augmented Okun model (Eq 12.4) model for explaining variation in unemployment1960–2010

Graph 12.4.1 Technological change model of determinants of unemployment (Eq.12.4.1)

Graph 13.1.1 Fifty years annual variation in corporate saving (calculated from Eq 13.1.1, then

compared to actual)

Graph 13.2.1 Explained and actual depreciation allowance savings the past 50 years

Graph 13.3.1 The explanatory power of the Eq 13.3.1 model

Graph 17.4.1 Actual and fitted V1 values 1960–2010 (taken from Eq 17.4.1.TR)

Graph 17.5.1 Actual and fitted V2 values 1960–2010 (taken from Eq 17.5.2.TR)

Graph 20.1.2.1 MPK and MPL curves – constant slopes

Graph 20.1.2.2 MPK and MPL curves – varying slopes

Graph 20.1.2.3 MPK and MPL curves – non – market wages

Graph 20.4.1.1 Model of only variables robust in at least three of four sample periods (Eq

20.4.1.2.TR)

Graph 20.4.3.1 Graph of the initial profit's share model (Eq 20.4.3.1)

List of Tables

Table.1.4.1 Determinants of consumption

Table.1.4.2 Determinants of investment

Table.1.4.3 Determinants of GDP (Cptr.8; arithmetically calculated from IS curve components)

Table.1.4.4 Is the prime interest rate determined by the Taylor rule?

Table.1.4.5 Is the prime interest rate determined by traditional Keynesian “LM” theory?

Table.1.4.6 Determinants of savings

Table.1.4.7 Determinants of government receipts and spending

Table.1.4.8 Determinants of unemployment and inflation

Table.1.4.9 Determinants of export demand

Table.1.4.10 Determinants of velocity robust models only (where V 1or2 = Y(P/M 1or2 )

Table.1.4.11 Determinants of labor's total income and percentage share of NI

Table.1.4.12 Determinants of profits' total income and percentage share of NI

Table.1.4.13 Determinants of rent's total income and percentage share of NI

Table.1.4.14 Determinants of interest total income and percentage share of NI

Table.2.2.3.1.1 DSGE model inflation forecast accuracy

Table.2.2.3.1.2 DSGE model GDP growth forecast accuracy

Table 2.2.3.2.1 (1) Current and four future year annual changes in income (real GDP) (Billions of

2005 Dollars)

Table 2.2.3.2.2 (1) Yearly variation in consumer spending 1960–2010 Explained by yearly variation

in TFP compared to other determinants of consumption

Table 2.2.3.2.3 (1) Robustness over time: (2SLS detrended model; subsamples of 1960–2010 dataset)

Table 2.2.3.2.3 (2) Robustness over time: (2SLS model 5.2, 1960–2010 data)

Table 2.2.3.2.4 (1) Forecasts of observable variables

Table 2.2.3.2.5 (1) Error of fit of a model similar to FRB/US'S nondurables and nonhousing servicesconsumption model compared to Cowles model (yearly change in ND&S consumption

Table.2.2.4.3.1 Comparison of % error of GDP estimates of VAR with structural models for the 10years after their 1960–2000 estimation period (absolute value of error % used)

Table.2.2.4.4.1 Time period robustness of SVAR model results

Table.2.2.4.4.2 Out–of–sample fit comparisons: Structural models vs SVARs

Table.4.0.1 Determinants of consumption assumed endogenous when applying endogeneity tests

Table.4.0.2 Determinants of consumption or investment initially assumed exogenous or lagged, and

used as regressors in the first–stage regression in Hausman of endogeneity tests (subscripts denotelags)

Table.4.1.1 Explained variance – total consumption

Table.4.1.2 Robustness over time – (2SLS detrended model, Eq 4.1.T)

Table.4.2.1 Explained variance – consumer imports

Table.4.2.2 Robustness over time – consumer imports

Table.4.4.1 Explained variance – domestically produced consumer goods

Table.4.4.2 Robustness over time – domestically produced consumer goods

Table.4.6.1 Explained variance – consumer borrowing

Table.4.6.2 Robustness over time – consumer borrowing, 2SLS Model 4.6

Table.4.9.1 Explained variance – consumer durables

Table.4.9.2 Robustness over time – consumer durables, 2SLS Model (4.9)

Table.4.11.1 Explained variance – nondurables

Table.4.11.2 Robustness over time – nondurables, 2SLS Model (Eq 4.11)

Table.4.13.1 Explained variance – consumer services (Eq 4.12)

Table.4.13.2 Robustness over time – consumer services, 2SLS model (Eq.4.12)

Table.5.0.1 Determinants of consumption and investment initially assumed endogenous when applyingendogeneity tests

Table.5.0.2 Determinants of consumption and investment initially assumed exogenous or lagged intheir effect when applying endogeneity tests

Table.5.2.1 Explained variance – total investment

Table.5.2.2 Robustness over time – total investment, 2SLS Model 5.2

Table.5.4.1 Explained variance – domestically produced investment goods

Table.5.4.2 Robustness over time: (domestically produced investment goods, 2SLS Model 5.4)

Table.5.6.1 Explained variance – imported investment goods

Table.5.6.2 Robustness over time: – investment imports, 2SLS

Table.5.8.1 Explained variance – business borrowing

Table.5.8.2 Robustness over time – business borrowing, 2SLS

Table.5.10.1 Explained variance – plant and equipment investment

Table.5.10.2 Robustness over time – plant and equipment, 2SLS Model 5.10

Table.5.11.1 Explained variance – residential investment

Table.5.11.2 Robustness over time – residential investment, OLS Model 5.11

Table.5.13.1 Explained variance – inventory investment

Table.5.13.2 Robustness over time – inventory investment 2SLS Model 5.13

Table.6.0.1 Import/export relationships among U.S trading partners

Table.6.1.1 Explained variance – exports

Table.6.1.2 Robustness over time – exports

Table.7.1.1 Comparison of PR –2 effects in GDP, C, I, G, and (X–M) functions (i.e., all components

of GDP)

Table.9.2.1 Explained variance – Taylor rule model, using 2SLS

Table.9.2.2 Robustness over time – Taylor rule model: 2SLS model 9.2

Table.10.2.1 Explained variance LM curve interest rate model

Table.10.2.2 Robustness over time: LM curve interest, 2SLS model

Table.11.1 Explained variance – Phillips curve

Table.11.2 Robustness over time: Phillips curve

Table.12.2.1 Explained variance – Okun unemployment model

Table.12.2.2 Robustness over time: (Okun unemployment 2SLS model)

Table.12.4.1 Explained variance – technological progress unemployment model

Table.12.4.2 Robustness over time: (tech progress unemployment, 2SLS model)

Table.13.1.1 Explained variance – corporate savings (as % of GDP)

Table.13.1.2 Robustness over time – corporate savings, 2SLS Model

Table.13.2.1 Explained variance depreciation allowance savings

Table.13.2.2 Robustness over time – depreciation allowance savings

Table.13.3.1 Explained variance – personal savings model

Table.13.3.2 Robustness over time – Personal savings model

Table.14.1 Explained variance – government receipts

Table.14.2 Robustness over time – government receipts (assumes 1993 tax increase repealed by

2001 tax cut)

Table.14.3 Alt robustness over time (assumes 1993 tax increase continues through 2010)

Table.15.1.1 Explained variance – total government spending

Table.15.1.2 Robustness over time – total government spending

Table.15.2.1 Explained variance – government spending model (goods and services only)

Table.15.2.2 Robustness over time – government spending (goods and services only)

Table.16.1.1 Model 1 How well the model fits the data for the 10 periods following the 1960–2000period used to estimate the model a (billions of 2005 dollars)

Table.16.2.1 How well models 1 and 2 fit the data for the 10 periods following the 1960–2000estimation period (billions of 2005 dollars)

Table.16.2.2 How well models 1 and 2 fit the data for the 10 periods following the 1960–2000estimation period (nine additional equations substituted for variables treated as exogenous in Model1)

Table.17.4.1 Explained variance – V1 velocity

Table.17.4.2 Robustness over time – M1 velocity, 2SLS Eq 17.4.1

Table.17.5.1 Explained variance – V2 velocity

Table.17.5.2 Robustness over time – M2 velocity, 2SLS Eq 17.5.1.2

Table.17.7.1 Variables significant in stepwise models

Table.18.1 Dynamic Effects of Stimulus Programs on the GDP

Table.18.2 Dynamic Effects of Stimulus Programs on the GDP (Detailed effects on other key

economic variables after 33 periods)

Table.19.1 Determinants of consumption, investment, government spending, interest rates, andexports

Table.20.1.1.1 Index of real profit and labor income growth 1929–2010 (1960 = 1.00)

Table.20.1.1.2 Nominal income levels and shares for labor, profit, rent, and interest 1930–2010

Table.20.4.1.1 Stepwise estimate of individual variable's contributions to total explained variance

Table.20.4.1.2 Coefficient stability in Eq 20.4.1.2 2SLS labor share model

Table.20.4.1.3 Comparisons of GDP and labor productivity growth rates

Table.20.4.1.4 Effects of counterfactuals on labor's share

Table.20.4.3.1 Stepwise estimate of individual variable's contributions to total explained variance inprofit's share

Table.20.4.3.2 Determinants of profit's share of national income coefficient stability over time

Table.20.4.3.3 Simulation of effects on profit's share of counterfactuals

Table.20.4.4.1 Summary of factors affecting profit's % share and level of real national income

Table.20.4.5.1 Stepwise estimate of individual variable's contributions to total explained variance ininterest share model 20.4.5.1

Table.20.4.5.2 Determinants of rent's share of national income coefficient stability over time in Eq.20.4.5.1

Table.20.4.6.1 Summary of factors affecting profit's % share and level of real national income

Table.20.4.7.1 Stepwise estimate of individual variable's contributions to total explained variance ininterest share model 20.4.7.2

Table.20.4.7.2 Determinants of interest's share of national income coefficient stability over time in

University at Albany-SUNY, Albany, New York, USA

The econometric model of the U.S economy developed in this chapter follows the demand-drivenstructural modeling approach used by Lawrence Klein, and for which he received a Nobel Prize, aswell as by other major structural models developed by Eckstein, Goldberger, and De Leeuw in the1940–1980 period This modeling tradition is carried on today by Ray Fair, and by this model Thistype of model is a modern version of the “old” non-micro foundations Keynesian (i.e., demand

driven) model It incorporates additional equations and variables to address issues not dealt with inKeynes’ original work: for example, the crowd out problem resulting from government deficits, costpush inflation corrections to the Phillips curve, the Samuelson accelerator, and the Taylor rule

version of the LM function We show that these “Cowles Commission” models can easily be extended

to allow calculation of sector, industry, or even individual product demand curves That is, Cowlesmodels can be structured to allow analysis of microeconomic as well as macroeconomic issues

Hence, the description of “old” Keynesian models as not having micro foundations seems somewhatinaccurate

The production-side model contains 45 equations Thirty are behavior equations whose

determinants describe what drives the demand for consumer goods (8 equations), investment goods (9equations), exports (1 equation), and the demand for government goods, services, and transfers, andthe supply of government receipts (3 equations) Two other “IS curve” equations combine the

preceding equations to determine the Gross Domestic Product (GDP) Other behavioral equationsdescribe the factors which determine a key interest rate (two equations), the unemployment rate (twoequations), inflation (one equation), and the velocity of money (two equations) The other 15

equations are identities tying the various behavioral equations together

The eight consumer goods equations express the determinants of demand for

Domestically produced consumer goods and services Durable consumption goods

Nondurable consumption goods Imported consumer goods and services Consumer services

Consumer borrowing

The nine investment goods equations express the determinants of demand for

Total investment Corporate savings

Domestically produced investment goods Depreciation savings

Imported investment goods Plant and equipment investment

Business borrowing Residential housing investment

Business inventory investment

There are 75 variables (or different lags of variables) in the 45 equations A list is providedfurther below

The models are presented in traditional Investment, Savings − Money Demand, Money Supply(IS-LM) equation form in Chapters 4–16 But this format for presenting Keynesian models is beingreplaced in some texts by the AD–AS system However, none of these texts presents a system of

equations that show how the Keynesian system translates into the AS –AD model The exceptions arethose that show how, by shifting previously calculated IS or LM curves, you can shift the AD curve,producing Keynesian results But this makes AS–AD only a series of deductions derived from

previously calculated IS–LM curves, not the simpler, more intuitive, alternative to it, which was itsoriginal objective

To deal with this deficiency, Chapter 17 develops an AD model for showing a full Keynesiansystem of fiscal and monetary policy effects It is derived from Fisher’s equation of exchange It iseasy to develop an AD curve to show monetary policy effects directly from Fisher’s equation

Econometric estimation of the determinants of velocity makes it just as easily using Fisher’s equation

to model the Keynesian stimulus effects of fiscal policy (with or without crowd out effect variablesincluded) This reconciles a major formulation of the neoclassical model with Keynesian mechanics

It shows that under the right assumptions, Keynesian results obtain from this neoclassical model.This chapter chooses to use Cowles Commission structural modeling techniques, yet today mostmacroeconomic models use either Vector autoregression (VAR) or Dynamic, Stochastic, GeneralEquilibrium(DSGE) techniques One can ask why the Cowles technique was chosen The answer isCowles-type models are both good economics (based on recognizable economic theory) and goodscience (use the best econometric methods available for presenting and testing the enormous detail insuch large models) By comparison, VAR is usually thought of as good science, but bad economics(atheoretical, so results can be hard to interpret), and DSGE is generally considered good economics,but bad science (key parameters calibrated, not estimated) These deficiencies have been widelycriticized during the past decade by major economists A summary of those criticisms is presentedbelow They suggest that a better alternative is needed Cowles modeling, by combining good

economics and good science, is not only better, it is really the only alternative available for scale modeling of the economy’s multitudinous determinants

Calibration approach unsatisfactory; econometrics needed

Solow ( 2010 ) “DSGE assumptions do not reflect reality … has nothing useful to say about antirecession policy … There are other

traditions with better ways to do macroeconomics.”

Solow ( 2016 ) “Whatever can be said for DSGE models … they are inferior in explaining the facts … the same for general VAR

models.”

Colander

( 2010 )

DSGE models don’t explain the data very well

Fair ( 2004 ) Tests lead to rejection of rational expectations hypothesis

Edge and

Gurnayak

Smets-Wouters DSGE model only explains 8–13% of the variance

Eckstein ( 1983 ) (Cowles) structural model forecasts better than VAR models tested

Gale and Orszag ( 2004 ) (∼ Cowles) structural model forecasts better than VAR models tested

Fair ( 2004 ) (Cowles) structural model forecasts better than VAR models tested

Earlier criticisms of Cowles models, particularly the Lucas critique, have simply been wrong.Our tests for this model, presented later in this chapter, as well as tests by earlier Cowles modelerslike Eckstein (1983) and Fair (2004) have shown the Lucas critique largely unfounded when applied

to Cowles models Another major criticism was that in Cowles models identification problems weredifficult to discover and address This seems fully resolved with the development of modern tools fordiscerning and resolving identification problems (see methodology section) The last major criticismwas that Cowles models lacked micro foundations, which we noted above does not seem completelytrue Cowles is certainly a better methodology than DSGE for determining, through scientific testing,what drives the demand for a specific product, like carrots, and how sensitive that demand is to theprices of other goods And this, we would argue, is the type of microeconomic issue most economistsneed to know how to resolve in order to practice their trade

The goal of this book is substantial: it is to develop a reliable engineering manual for the

macroeconomy, presenting in great detail the structure of the macroeconomy and how it operates.There are endless parameter estimates calculated Since we desire to elevate this work to the status

of an engineering manual, the reliability of each parameter estimate is actually more important thanthe initial estimate itself To determine reliability, each estimate in the model has its robustness istested three ways:

Testing the same model in four different sample periods (i.e., can the experimental results bereplicated?)

Using three different variants of each model to test the stability of each variable’s parameterestimates when variables are added to or subtracted from the model (Do our estimates avoidmulticollinearity problems?)

Using two different regression tools (Ordinary Least Squares [OLS] and 2 Stage Least Squares[2SLS]), and sometimes a third (stepwise regression) to determine consistency over time andimportance of results with older studies

Results of all these reliability tests are presented in the sections dealing with each of the 30

behavioral equations This information provides readers with an unprecedented level of knowledgeregarding the robustness of parameter estimates presented in the model

Our objective is to develop a model whose parameter estimates can be used by economists andpolicy makers with confidence in their reliability In most cases, we feel this objective is adequatelyachieved

1.1 Modern Macroeconomics: Moving from the Methods of Economic

Philosophy to Those of Economic Science

Over eighty years ago, Keynes (1936) put forth a theory of how the macroeconomy operates Its

fundamental assumption was that the economy is demand driven, and that absent supply constraints,modeling the determinants of demand is to model the determinants of supply Because it was so

testable, Keynes’ theory served as a good basis for developing macroeconomics into a science whosepurpose was to discover the actual, measurable causes of fluctuations in observable economic

behavior, rather than just offer philosophical statements of the fundamental factors that underlie

humans’ economic behavior His theory provides a basis for good science because all its basic

assertions are directly testable (e.g., is current income the principal determinant of current

consumption? Is it more important than interest rates? Are interest rates or is the accelerator the keydeterminant of investment?) There simply is no equation in Keynesian theory that cannot be directlytested (and each is tested in this study) This is an absolute requirement for good science As NobelLaureate Adam Riess has emphasized, “Historically, this method (the scientific method) has requiredthat hypotheses should be directly testable by new experiments or observations.” Riess, awarded a

Nobel Prize for his part in discovering that the universe was expanding, also noted that accepting

hard to test hypotheses would signify the end of the scientific method as we know it (Riess and

from assumptions about human behavior (e.g., rational expectations, intertemporal utility, and profit

maximization), rather than from empirical findings For scientists, an asserted theory (philosophy) can

only be considered valid if holds in all instances (ceteris paribus), and testing is done to assure it is.

In our example, science requires commonly held theoretical hypotheses about interest rates and

deficits to hold for all instances in which deficits occur, controlling for other factors which can alsoaffect them (they don’t as our Taylor rule interest rate model below shows) Tests of “old” Keynesian(non-micro foundations) structural models are scientific in this way

Philosophy becomes science only when all basic assumptions of theory (its priors) can be testeddirectly, so that we know that the assumptions from which policy conclusions are derived are

themselves empirically true (and not, perhaps, one of several sets of priors which might be consistentwith observed results) Keynesian structural models allow for this DSGE models don’t (e.g., how do

we empirically test the hypothesis that consumers successfully maximize utility intertemporally? And

if we find the data do not support the hypothesis, do we scrap DSGE theory?) DSGE typically statesthat if such and such a condition holds (e.g., successful intertemporal utility maximization), then suchand such a result should obtain (consumption spending, except for unforeseeable shocks, will be

constant from period to period)

The econometric revolution, starting at about the same time Keynes’ theory was introduced,

handed macroeconomists tools with which they could scientifically test that theory’s precepts for

consistency with the real world.

Thanks to the statistical stability of the average performance of large numbers of people,

parameters governing the relationship between people and their economic behavior could be stableover long periods of time, eliminating much of the distinction between the stability of parameter

estimates in fields of “social science” and “science,” at least for economics Kuznets ’ (1952) finding

of a (0.88) coefficient for the relationship of consumption to national income for the 1867–1929

period, and (0.86) separately for the 1867–1948 period, and Heim’s (2008) finding of (0.82) for thesame relationship for the 1960–1990 period is a case in point Hence, as science, macroeconomicsseems more like geology than sociology: parameters may shift, but at a glacial pace In the meantime,

they are perfectly adequate for assessing the impact of one economic variable on another (ceteris

paribus).

With the advent of econometrically based macroeconomic modeling, it seemed only a matter oftime before the “alphas” and “betas” used in classroom exposition of key economic relationships likethe consumption function could be replaced by hard, empirically verified numbers, turning economicsfrom a branch of natural or moral philosophy into a legitimate branch of science and engineering.Cowles-type models were intended to provide engineering models describing in great detail the

structure of the economy and how it operates

This led to efforts in the 1950s and 1960s, building on Jan Tinbergen ’s work (1939), to developlarge-scale econometric models providing inductively (not deductively) determined parameter

estimates for all the key parameters in this new demand-driven macroeconomics

On the supply side, Leontief’s (1952) models were performing a similar function, allowing us toprovide scientifically inductive, not deductive, answers to supply questions such as “If we expectdemand in the aggregate to be this much, what demands will this place on individual industries? Arethey reasonable or will there be supply constraints?”

Earlier large-scale econometric models of the macroeconomy, such as Klein and Evans (1968)and Eckstein’s (1983), achieved remarkable results in moving toward this goal, but not without

problems These problems kept their models from explaining the economy as well as they would haveliked Some problems only became obvious retrospectively, after further developments in the field ofeconometrics Problems such as multicollinearity, stationarity, and identification were not tractable(or even fully recognized) in some of those early models

Today, we have methods which can eliminate the identification and nonstationarity problems Wecan substantially reduce the multicollinearity problem by using data in first differences rather thanlevels

In addition, computerization has made it easy to test alternative models and evaluate the stability

of parameter estimates by “tinkering” with model specification changes, varying sample periods

tested, and by varying the type of regression technique used

The econometric models developed here test for parameter estimate stability by reporting resultsfor at least two other specifications of the same model with some additional variables added or

subtracted to validate reliability of the initial parameter estimate results Adding and subtractingvariables generally did not significantly affect estimates of parameters of the most important

explanatory variables remaining in the model, provided the variables deleted were not themselvesmajor explanatory variables whose elimination would cause a “left out variables” problem, i.e., justanother form of multicollinearity

In addition, consistency and reliability of test results when sample periods were changed was anissue with older models Little if any effort was made to ensure the robustness of regression results to

different sampling periods (i.e., to ensuring the results were replicable) The econometric modeldeveloped here eliminates this problem by reporting results for several sample periods to validatereliability of the results Parameters initially estimated here using a 50-year sample period wereretested using three other separate samples each covering only part of the larger 50-year test periodinitially used Generally, the job of obtaining reliable parameter estimates in the initial sample wasdone well enough so that retesting on other sample periods confirmed the initial results, i.e., the

models explain as well in one period as another

Computerization has also simplified the process of reevaluating landmark models estimated inearlier times using methods now considered inadequate At virtually no marginal cost, computer

programs can provide OLS and 2SLS estimates for the same problem to allow reevaluation of resultsusing older techniques with new methods better able to deal with identification (and other) problems.For all models in this study, robustness testing extends to comparing results derived from OLS ascompared to 2SLS results for the same model This has indicated results are much the same for mostvariables, provided the models tested are well constructed to start with, i.e., contain enough

explanatory variables to explain 85% or more of the variance, and provided the instruments used in2SLS models are strong, i.e., very good proxies for the variable they are replacing, explaining most

of their variance And of course, the instruments themselves must not be endogenous We typicallyprovide both sets of results (OLS and 2SLS) to allow evaluation of sensitivity of this chapter’s

results to method used

Structural modeling has been replaced in recent decades by VAR and DSGE modeling Neither ofthese alternatives tells us much about structure, particularly any detailed assessment of demand’smultitude of different determinants If the questions an economist/researcher is interested in are

structural in this sense, there does not seem to be an alternative to using Cowles-type structural

models And many, if not most, questions of interest to most economists are structural

Economists need structural models of the economy for the same reason astronomers need

structural models of the solar system: to explain how the solar system will operate over long periods

of time They can’t fit a linear curve to last month’s path a planet followed and project a linear trendforward for the rest of the year (the VAR method) Nor can astronomers be content relying on

philosophical “self-evident” truths about how the universe operates That was the methodology thenatural philosophers of the Enlightenment (and medieval theologians) had to rely on before the

scientific revolution It is an outdated method of discerning empirical reality today in astronomy.Similar methods for evaluating economic questions would seem as outdated

1.2 Summary of Ways in Which This Large-Scale Econometric Model Improves on Past Work

Currently, there is only one large-scale Cowles Commission-type structural model available foreconomists to use for guidance on what makes the economy work It is Yale economist Ray

Fair’s (2004) large-scale econometric model (29 behavioral equations, 71 identities), thoughsome parts of Eckstein’s 1983 Data Resources, Inc (DRI) model, which is proprietary, may still

be in use by DRI This book advances the field by adding a second model of the same type, a equation model containing 38 behavioral equations and 18 identities It is the first new CowlesCommission-type model since Fair’s last major revision in 2004, which itself was the first newmodel since Eckstein (1983)

56-This model builds on Fair’s model by identifying additional determinants of consumption andinvestment required to fully explain variation in these variables in economic terms These newvariables include

Additional consumption determinants Additional investment determinants

Government deficit (crowd out) Government deficit (crowd out)

Prime interest rate Prime interest rate

Consumer confidence index Capacity utilization rate

Past savings levels Depreciation

Consumer borrowing Tobin’s q (proxy)

Substitution effects of a change in demand for one type of consumption Profit levels

Population levels (some models) (D, ND, S) on another Business borrowing

The wide range of variables used also builds on the more limited number typically used inVAR and DSGE analysis

It also builds on Fair’s work by providing separate behavioral models of demand for

domestically produced and imported consumer and investment goods It also adds models forexports, personal and corporate savings, and the Keynesian LM function All models are tested

in first differences rather than levels to help address stationarity and multicollinearity issues.This model is different from most past structural models in that it does not use lagged values of

an equation’s dependent variable on the right-hand side of the equation Many past Cowles

models use lagged values of the dependent variable to explain variation in the current value ofthe dependent variable in some models They can be useful in forecasting models, where

definitionally the present cannot be predicted except from the past

The reason they are not used in this 56-equation model is because this model is intended to be an

explanatory, not a forecasting model extrapolating foreword from past trends This model’s

goal is to develop equations that accurately identify the fundamental determinants of each

endogenous variable in the model Given this goal, to use lagged values of the dependent

variable on the right-hand side would seem self-defeating We would then need to model thevariables that determine the lagged value of the dependent variable and substitute them in for thelagged in order to find out what drives the dependent variable’s current value In models whoseprincipal objective is to accurately describe the determinants of endogenous variables,

backward substitution is always required to eliminate any lagged dependent variables from themodel’s right-hand side, otherwise we just obfuscate the true causes of variation in endogenousvariables It is like the difference between forecasting and explaining in astronomy; you canvector forward linearly from your present position by adding a few percent to its current

location and speed and reasonably accurately predict where you will be, but if you want to

explain why the orbit will eventually vary in elliptical fashion as a body circles the sun, you

better scrap the linear forecasting approach in favor of a fundamentals description of what

causes heavenly bodies to move, like Newton’s and Kepler’s gravitational formulae

By extension of this argument we can say that if a lagged value of the dependent variable does

seem to explain variance in a dependent variable for causal, rather than inertial, reasons, it is

because the dependent variable’s lagged value is causally determined by lagged values of othervariables Our approach in this model is to include the lagged values of those other variablesdirectly to clarify what exactly drives the dependent variable, and with what lags.

By comparison, lags of the explanatory variables are used in this chapter’s models Some

variables only affect a dependent variable after a lag The effect of consumer confidence onconsumer spending and the effect of interest rates on construction spending are examples Bothwere found systematically related to their dependent variable, but only after an adjustment

period, and there are theoretical foundations for the findings

This model tests far more exhaustively for robustness of results than prior large-scale

econometric models, and this may be its most important contribution to strengthening economics’reputation as a science Three different kinds are robustness testing are employed: (1) modifyingmodel variables to test the stability of parameter estimates for variables in both the original andmodified models, (2) requiring models to be replicable in different sample periods, and (3)using different statistical methods and comparing results for consistency Findings for all

variables are subjected to robustness tests using four sample periods, three different model

specifications, and two different estimation methods (2SLS and OLS) Testing in both OLS and2SLS simplifies comparisons of current results with historical studies examining the same thing,but which only used OLS methods prevalent at the time Similarly, testing different time periodsallows a way of determining if different results obtained in earlier studies differ because ofperiod sampled Robustness testing is hugely important for any study, like this one, desiring itsresults to have engineering manual levels of reliability How else can one ensure that the nextstudy done on the same topic won’t come up with different results? Robustness testing is theeconomist’s equivalent of replicating experimental findings in the natural sciences and is just asnecessary to establish the credibility of findings

Another contribution this chapter makes is that it tests the Lucas critique to determine its

validity The chapter’s robustness tests over different sample periods generally show the Lucascritique not valid Roughly the same coefficients on tax and government spending stimulus

effects are found over time, removing one of the major criticisms of Cowles structural modeling

in the 1980s which led to its replacement by DSGE

Some of this study’s most important findings show key assumptions underlying rational

expectations theory are simply not valid This is particularly true for the notion that consumersrely on accurate expectations of long-term future income as the key determinant of current

consumption This finding implies any DSGE micro foundations model that relies on the

correctness of this assumption for its own correctness, is not valid Tests in this chapter indicateconsumption is driven by current, not by accurately estimated averages of current and futureincome Our tests also find that consumption is not constant from year to year except for

unexpected technology shocks, as DSGE models suggest would result from the intertemporalutility maximization implied by the rational expectations assumption, a result typically deducedfrom Euler equations A major criticism of “old” Keynesian structural modeling in the 1980s and1990s was that it had no micro foundations of the sort found in DSGE models But key

assumptions underlying the “old” Keynesian model, such as consumption’s determinants, seembetter supported by the data than micro foundations model assumptions This would suggest the

“no micro foundations” criticism of “old” macroeconomics is no longer reasonable

The “old” Keynesian structural Model developed in this chapter explains the behavior of keyeconomic variables very well for a full decade after the period used to estimate the test model(1960–2000) The average yearly error explaining out-of-sample yearly changes in the 2001–

2010 decade following the estimation period (as a % of GDP) was

Critically important, the model is good enough at identifying the fundamental underlying structure

of the economy that it can explain changes in GDP, consumption, and investment, in any of thepast five decades about equally well Graphs showing this tightness of fit are presented in thetext

All parameters are econometrically estimated; nothing “calibrated,” as in DSGE models, hencemore reliably reflective of economic behavior as it actually occurs It is better science

Models are theoretically based, and only lags consistent with theory, and found statisticallysignificant are included, unlike VAR models

Better scientific methods than many earlier models: more up-to-date econometric techniquesused to ensure

Stationarity issues fully resolved

Identification (endogeneity) issues fully resolved only Wald-strong Instruments used toresolve endogeneity

Minimize multicollinearity and serial correlation issues

This chapter is also unique in that it provides a way of unifying micro and macro different fromthe micro foundations approach used in DSGE models In fact, the approach used is just the

opposite of the micro foundations approach It is based on the assumption that macroeconomicvariables are the principal determinants of microeconomic demand (and therefore production) in

a given period, mitigated to some extent by relative price effects The approach starts with alarge-scale macro model, whose consumption and investment functions, when divided into

successively smaller parts, can be reduced to a series of evermore micro-sized models, exceptwith macro determinants found irrelevant for a specific micro portion of the macro model

deleted (e.g., mortgage interest rates may affect residential construction, but not inventory

investment) When doing so, the basic macro model stays intact, with a relative prices variableadded to allow estimation of substitution effects between goods in the micro model and goodsthat are not The idea is not new; it was used in the 1980s by Eckstein in his huge 800-equationmodel of the U.S economy Eckstein’s model used a “macro foundations of micro” approach tounifying the two fields It was similar to that used in this book to evaluate the demand for

domestically produced versus imported goods: same basic determinants used in both models, butwith the exchange rate used to measure the effects on demand of relative prices of imports

compared to domestic goods

A final way this study improves on other models is by distinguishing what the model’s

parameters say a variable can potentially do, from what it actually did during a sample period.

Stepwise regression is used to estimate each variable’s actual importance in explaining varianceduring a sample period This is a way of distinguishing between the potential contribution avariable can have (using β, ), and the actual importance it did have during the sample period

by measuring its contribution to explaining variance compared to other variables in the same

model Explanatory variables that do not move cannot explain variance, even though if they did

move, they would explain variance

1.3 The 56-Equation Model: 30 Behavioral Equations, 15 Identities

(Product Side of National Income and Product Accounts (NIPA)), and 8 Behavioral Equations, 3 Identities (Income Side of NIPA)

1.3.1 Eight Consumption Equations, Econometrically Estimated

1 domestically produced and imported consumer G&S

2 domestically produced consumer G&S

3 imported consumer G&S

4 durable consumer goods

5 nondurable consumer goods

domestically produced and imported investment G&S

10 domestically produced investment G&S

11 imported investment G&S

12 IP&E = investment in plant and equipment

13 investment in residential housing

14 investment in inventories

15 business borrowing

16 corporate savings (retained earnings)

17 depreciation allowance savings

1.3.3 Five Others Related to the GDP Identity, Econometrically

Estimated

18 GG&S = government spending on G&S only = f(economic conditions)

19 GT&I = all government spending (G, S & Trans.) = f(econ conditions)

20 foreign demand for U.S exports

21 (determinants of C, I), plus G, X-M

22 (determinants of , ), plus G, X

1.3.4 Eight Others Econometrically Estimated: Two Interest Rate, Two Unemployment, One Inflation, On Taxes, M1 and M2 Velocity

23 Taylor rule interest rate model

24 Keynesian LM theory interest rate model

25 Okun unemployment determination model

26 tech progress unemployment determination model

27 INFL = Phillips curve model of determinants of inflation

28 government receipts = f(economic conditions)

29 V1 = determinants of M1 velocity

30 V2 = determinants of M2 velocity

1.3.5 Eight Equations Describing Factor Shares and Total Factor Income, Econometrically Estimated

31 Labor’s percentage share of national income

32 Labor’s total income

33 Profit’s percentage share of national income

34 Profit’s total income

35 Rent’s percentage share of national income

36 Rent’s total income

37 Interest’s percentage share of national income

38 Interest’s total income

1.3.6 The 18 Identity Equations

6 IT = IP&E + IH + IINV = total plant and equipment, housing and inventory investment

7 = total imports of consumer and investment goods

13 = government spending on goods and services

15 MV = PY Fisher’s equation of exchange (using income)

16 GDP = product side = income side

17 GDP = depreciation + indirect taxes + labor income + profit income + rental income + interestincome + proprietor’s income + GDP/GNP definition adjustments

18 National income = labor income + profit income + rental income + interest income +

proprietor’s income

1.4 The 38 Behavioral Equations: Coefficients, Significance, R2, and Durbin Watson Tests: (Summary of Results: Detailed Explanations of Findings Presented in Chapters 4–20)

Tables 1.4.1–1.4.14 present statistical findings for each of the 38 behavioral equations Included witheach is a list of variable names and the acronym used for each in the equations Two models are

shown for each dependent variable The left column of data for each dependent variable shows theinitial model run, and the regression coefficients and significance levels for each included variable,and the R2 and Durban Watson serial correlation results for the model The second column of datapresents the final, time period and model specification robust model Typically, some variables in theinitial model will be missing, initial estimates of their effect having not proved reliable (robust) when

we attempted to replicate our initial results in other time periods and models These robust equationsare this chapter’s final model We hope they will be received as not “just another model,” but one forwhich many parameter estimates approach engineering manual levels of reliability, a first-in large-scale macroeconomic modeling

The process of moving from initial findings to finalized, robust models was as follows:

1 An extensive literature review identified variables thought to be determinants of each dependentvariable Preliminary testing, using the full 50-year sample, was undertaken using OLS or 2SLS

as appropriate Variables found significant in preliminary testing became the “initial” model Forexample, total consumption’s initial model ( ) in Table 1.4.1 is in the leftmost column underlabeled equation “4.1T.”

2 The initial model was then retested in three additional, though overlapping time periods for

robustness Variables not significant in 3 of 4 total time periods tested were discarded as

spurious This became our semi-final model

3 The final model was tested by adding and then subtracting two variables from the

semi-final model to determine robustness of parameter estimates to changes in model specification

4 The model passing these robustness tests is listed next to its own initial model with notation

“TR” added, e.g., for , the robust model is designated “4.1T.TR” in Table 1.4.1

Steps 2–4 were uniformly applied in the development of all 38 stochastic equations The

consumption, investment, and labor share equations received the most extensive literature reviewswhen developing the initial models in step 1 In large part, this was because there is so much morewritten in these areas than in the others The goal was to have the initial models tested reflect theeconomic equivalent of the physicist’s “standard model,” reflecting consensus opinion on what drives