4. 4
1. Introduction
In this paper, structural model is used to make 8 quarters forecast of major macroeconomics
variables: Real GDP, Real Consumptions, Real Investment, Real Net Exports, Inflation
measured by GDP Deflator, Personal Income, Interest Rate, and Employment.
Section 2 is the description of variables and data. Section 3 is the model specification. Section 4
and 5 are the estimation of exogenous variables and endogenous variables. Forecast is made in
section 6. And section 7 is the conclusion.
2. Variables and Data
The data used in this paper is from national income and product accounts (NIPA), which is part
of the national accounts of the United States. They are produced by the Bureau of Economic
Analysis of the Department of Commerce.
It is quarterly data from the first quarter of 1980 to the first quarter of 2016. There 145
observations.
2.1 Difconsumption, Real_consumption, Consumption
Difconsumption is used as the measure of consumption. It is the first difference of real
consumption. According to the Augmented Dickey-Fuller test, the real consumption data is not
stationary. So first difference is taken to make it stationary. There could be spurious regression
for nonstationary variables. It’s in billion dollars.
2.2 Difinvestment, Real_investment, Investment
Difinvestment is used as the measure of investment. It is the first difference of investment.
Investment is the sum of real investment and real change in inventory. Investment is
nonstationary, and first difference is taken. It’s in billion dollars.
2.3 Difexports, Real_exports, Exports
Difexports is used as the measure of exports. It is the first difference of real exports. Real export
is nonstationary, and first difference is taken. It’s in billion dollars.
2.4 Difimports, Real_imports, Imports
Difimports is used as the measure of imports. It is the first difference of real imports. Real export
is nonstationary, and first difference is taken. It’s in billion dollars.
2.5 Dift, T_bond_10y
Dift is used as the measure of interest rate. It is the first difference of the interest rate of 10-year
treasury bond. The interest rate is nonstationary, and first difference is taken. It’s in percent.
2.6 Difemp, Employment
Difemp is used as the measure of employment. It is the first difference of employment.
Employment is nonstationary, and first difference is taken. It’s in millions.
2.7 Difave, Earn_income, Ave_earned
Difave is used as the measure of average income. It is the first difference of average income.
Average income is earned income divided by employment. And earned income is the sum of
wages, other labor income and property income, minus the social insurance tax. The earned
income is in billion dollars. The Difave is in billion dollars per million people.
5. 5
2.8 C_deflator, I_deflator, Exp_deflator, Imp_deflator
These deflators are use as the measure of price level of consumption, investment, exports and
imports. They are the ratio of nominal to real consumption, investment, exports and imports.
2.9 GDP_deflator
GDP_deflator is used as the measure of price level. It’s calculated as the ratio of nominal GDP to
real GDP.
2.10 Productivity
Productivity is the measure of productivity. It’s real GDP divided by employment. It’s in billion
dollars per million people.
2.11 Income, Personal Income
Income is used as the measure of real income. It’s personal income divided by GDP_deflator.
2.12 Ratio1, Ratio2, Ratio3, Ratio4
Ratio 1 to 4 is calculated as the ratio of C_deflator, I_deflator, Exp_deflator and Imp_deflator to
GDP_deflator.
2.13 Prop_income
Prop_income is used as the measure of property income. It’s personal income minus earned
income and transfer income. It’s in billion dollars.
2.14 Trend, Recessiondummy
Recessiondummy is a dummy that is used to capture the change during recessi on. During 2008
and the first 2 quarters of 2009, Recessiondummy equals to 1. Otherwise, Recessiondummy
equals to 0.
2.15 Corp_profit, Dis_2, GDPworld_index, Government, Hhequity, Pop_total,
Price_wd_index, Real_gov, Sp500, Transfer_income
Corp_profit is corporate profit. It’s in billion dollars.
Dis_2 is the difference between real GDP and the sum of its components. It’s caused by chain-
weighted calculation of GDP. It’s in billion dollars.
GDPworld_index is world GDP index. It’s used as a measure of world GDP.
Government and Real_gov is real and nominal government spending. It’s in billion dollars.
Hhequity is household wealth. It’s in billion dollars.
Price_wd_index is world price index. It’s used as a measure of world price.
Sp500 is Standard & Poor's 500 index. It’s used as a measure of volatility of capital market.
Transfer_income is transfer income. It’s in billion dollars.
3. Model Specification
3.1 Theoretical framework
3.1.1 Consumption
Theoretically, consumption is affected by income, the cost of credit (interest rate), the stock of
personal wealth, expectation of unemployment, government policies, et al. Income, wealth, and
expansion policy should be positively correlated with consumption. Interest rate and expectation
of unemployment should be negatively correlated with consumption.
6. 6
3.1.2 Investment
Investment is affected by interest rate, uncertainty, income, government policies, et al. Income
and expansion policies should be positively correlated with investment, while interest rate and
uncertainty should be negatively correlated with investment.
3.1.3 Export and Import
Export and import is affected by exchange rate, interest rate, domestic and foreign income, et al.
Exchange rate (domestic currency/ foreign currency) and interest rate should be positively
correlated with net export. When domestic income is increasing faster than foreign income, net
export is supposed to decrease.
3.1.4 Interest Rate
Interest rate is affected by money demand and supply, government policy, uncertainty, et al. If
money demand is increasing faster than money supply, interest rate should increase. Expansion
policy should decrease interest rate. Interest rate will also increase as uncertainty increases.
3.1.5 Unemployment
Unemployment is affected by output growth and labor demand and supply, et al. When there is a
high output growth rate, the unemployment should be low. When the growth of labor demand is
higher than the growth of labor supply, unemployment should decrease.
3.1.6 Income
Income is affected by output growth, inflation, et al. Both output growth rate and inflation should
be positively correlated with income.
3.2 Endogenous Variables
There are stochastic equations and identity equations in the structural model.
3.2.1 Difconsumption
𝑑𝑖𝑓𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛
= 𝑎. 𝑙𝑎𝑔 𝑑𝑖𝑓
𝑝𝑒𝑟𝑠𝑜𝑛𝑎𝑙_𝑖𝑛𝑐𝑜𝑚𝑒
𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
+ 𝑎8 𝑙𝑎𝑔 𝑑𝑖𝑓𝑡 + 𝑎9 𝑑𝑖𝑓
ℎℎ𝑒𝑞𝑢𝑖𝑡𝑦
𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
+ 𝑎= 𝑙𝑎𝑔 𝑑𝑖𝑓𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 + 𝑎> 𝑑𝑖𝑓𝑒𝑚𝑝 + 𝑎? 𝑑𝑖𝑓(𝑝𝑜𝑝_𝑡𝑜𝑡𝑎𝑙)
As has been mentioned in the theoretical framework, variable personal_income and hhequity are
measures of income and wealth. They are both divided by GDP_deflator, because they are
originally nominal value. Dift is interest rate, and Difemp is employment. Since Difemp is in
million people instead of percentage, pop_total is added to the equation to control population
growth. All independent variables are taken first difference. The lag of Difconsumption is also
added to the equation.
There is no intercept in this equation, because it’s not statistically significant and removed.
The variable for parameter a3 and a5 are considered possible correlation with the OLS regression
residual. Therefore, instrument variables are used to solve the endogenous problem. The
instrument variables will be specified in the following Exogenous Variables part.
3.2.2 Difinvestment
7. 7
𝑑𝑖𝑓𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
= 𝑏D + 𝑏. 𝑑𝑖𝑓 log 𝑟𝑒𝑎𝑙_𝐺𝐷𝑃 + 𝑏8 𝑙𝑎𝑔 𝑑𝑖𝑓𝑡 + 𝑏9 𝑙𝑎𝑔 𝑑𝑖𝑓𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
+ 𝑏= 𝑑𝑖𝑓(𝑠𝑝500)
Log(real_GDP) is used as a measure of real GDP growth. Dift is interest rate, and SP500 is used
as the measure of uncertainty. All independent variables are taken first difference. The lag of
Difinvestment is also added to the equation.
Employment and population variable were originally added to the equation, but then removed
because the estimates are not significant.
The variable for parameter b1 is considered endogenous.
3.2.3 Difexports and Difimports
𝑑𝑖𝑓𝑒𝑥𝑝𝑜𝑟𝑡𝑠 = 𝑐D + 𝑐. 𝑑𝑖𝑓𝑡 + 𝑐8 𝑙𝑎𝑔(𝑑𝑖𝑓(𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟)) + 𝑐9 𝑑𝑖𝑓(
𝑝𝑒𝑟𝑠𝑜𝑛𝑎𝑙_𝑖𝑛𝑐𝑜𝑚𝑒
𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
)
+ 𝑐= 𝑙𝑎𝑔(𝑑𝑖𝑓𝑒𝑥𝑝𝑜𝑟𝑡𝑠)
𝑑𝑖𝑓𝑖𝑚𝑝𝑜𝑟𝑡𝑠 = 𝑑D + 𝑑. 𝑑𝑖𝑓𝑡 + 𝑑8 𝑙𝑎𝑔(𝑑𝑖𝑓(𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟)) + 𝑑9 𝑑𝑖𝑓(
𝑝𝑒𝑟𝑠𝑜𝑛𝑎𝑙_𝑖𝑛𝑐𝑜𝑚𝑒
𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
)
+ 𝑑= 𝑙𝑎𝑔(𝑑𝑖𝑓𝑖𝑚𝑝𝑜𝑟𝑡𝑠)
GDP_deflator and personal_income are added to the equation as the measures of domestic
income and inflation. All independent variables are taken first difference. The lag of difexports
and difimports are also added to the equation.
Price_wd_index was originally added to the equation as a measure of world price, but then
removed because the estimate is not significant.
The variable for parameter c1, c3 and d1, d3 are considered endogenous.
3.2.4 Dift
𝑑𝑖𝑓𝑡 = 𝑔D + 𝑔. 𝑑𝑖𝑓
𝑖𝑛𝑐𝑜𝑚𝑒 − 𝑙𝑎𝑔 𝑖𝑛𝑐𝑜𝑚𝑒
𝑙𝑎𝑔 𝑖𝑛𝑐𝑜𝑚𝑒
+ 𝑔8 𝑑𝑖𝑓 𝑃𝑟𝑖𝑐𝑒_𝑤𝑑_𝑖𝑛𝑐𝑜𝑚𝑒 + 𝑔9 𝑑𝑖𝑓 𝑠𝑝500
+ 𝑔= 𝑙𝑎𝑔(𝑑𝑖𝑓𝑡)
Income is used to calculate the growth of domestic income. Price_wd_income is used as a
measure of world price. SP500 is used as measure of uncertainty. All independent variables are
taken first difference. The lag of dift is also added to the equation.
The variable for parameter g1 is considered endogenous.
3.2.5 Difemp
𝑑𝑖𝑓𝑒𝑚𝑝 = 𝑒. 𝑙𝑎𝑔 𝑑𝑖𝑓𝑒𝑚𝑝 + 𝑒8(log (𝑟𝑒𝑎𝑙_𝐺𝐷𝑃) − 𝑙𝑎𝑔(log (𝑟𝑒𝑎𝑙_𝐺𝐷𝑃)))
+ 𝑒9 𝑑𝑖𝑓(𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦) + 𝑒= 𝑑𝑖𝑓(𝑐𝑜𝑟𝑝_𝑝𝑟𝑜𝑓𝑖𝑡)
8. 8
Real_GDP is used as the measure of output growth. Productivity and corp_profit are used to
measure the labor demand. All independent variables are taken first difference. The lag of dif is
also added to the equation.
Population and interest rate variables are originally added to the equation, but then removed
because the estimates are not significant. The intercept is also removed because of
insignificance.
The variable for parameter e2, e3 and e4 are considered endogenous.
3.2.6 Difave
𝑑𝑖𝑓𝑎𝑣𝑒 = 𝑓. 𝑙𝑎𝑔(𝑑𝑖𝑓(𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟)) + 𝑓8 𝑙𝑎𝑔(𝑑𝑖𝑓𝑒𝑚𝑝) + 𝑓9 𝑙𝑎𝑔(𝑑𝑖𝑓(𝑐𝑜𝑟𝑝_𝑝𝑟𝑜𝑓𝑖𝑡))
+ 𝑓= 𝑙𝑎𝑔(𝑑𝑖𝑓(𝑟𝑒𝑎𝑙_𝐺𝐷𝑃))
GDP_deflator and real_GDP are used as measures of output growth and inflation. Difemp is
used as measure of employment. Corp_profit is used as measure of corporate profit. All
independent variables are taken first difference.
The lag of difave was originally added to the equation, but then removed because the estimate is
not significant. The intercept is also removed because of insignificance.
No variable in this equation is considered endogenous, because they are all lags. The reason why
income is decided by lags of variable is probably because of wage rigidity. That is, income that
decided in the former period is not able to be changed in short period.
3.2.7 Identity Equations
𝑟𝑒𝑎𝑙_𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 = 𝑑𝑖𝑓𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 + 𝑙𝑎𝑔(𝑟𝑒𝑎𝑙_𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛)
𝑟𝑒𝑎𝑙_𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 = 𝑑𝑖𝑓𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑙𝑎𝑔(𝑟𝑒𝑎𝑙_𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡)
𝑟𝑒𝑎𝑙_𝑒𝑥𝑝𝑜𝑟𝑡𝑠 = 𝑑𝑖𝑓𝑒𝑥𝑝𝑜𝑟𝑡𝑠 + 𝑙𝑎𝑔(𝑟𝑒𝑎𝑙_𝑒𝑥𝑝𝑜𝑟𝑡𝑠)
𝑟𝑒𝑎𝑙_𝑖𝑚𝑝𝑜𝑟𝑡𝑠 = 𝑑𝑖𝑓𝑖𝑚𝑝𝑜𝑟𝑡𝑠 + 𝑙𝑎𝑔(𝑟𝑒𝑎𝑙_𝑖𝑚𝑝𝑜𝑟𝑡𝑠)
𝑡_𝑏𝑜𝑛𝑑_10𝑦 = 𝑑𝑖𝑓𝑡 + 𝑙𝑎𝑔(𝑡_𝑏𝑜𝑛𝑑_10𝑦)
𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 = 𝑑𝑖𝑓𝑒𝑚𝑝 + 𝑙𝑎𝑔(𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡)
𝑎𝑣𝑒_𝑒𝑎𝑟𝑛𝑒𝑑 = 𝑑𝑖𝑓𝑎𝑣𝑒 + 𝑙𝑎𝑔(𝑎𝑣𝑒_𝑒𝑎𝑟𝑛𝑒𝑑)
In equations above, first-difference data are transferred to level data.
𝑒𝑎𝑟𝑛_𝑖𝑛𝑐𝑜𝑚𝑒 = 𝑎𝑣𝑒_𝑒𝑎𝑟𝑛𝑑𝑑×𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡
In this equation, earned income is calculated using ave_earned and employment.
𝑐_𝑖𝑛𝑓𝑙𝑎𝑡𝑜𝑟 = 𝑟𝑎𝑡𝑖𝑜1×𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
𝑖_𝑖𝑛𝑓𝑙𝑎𝑡𝑜𝑟 = 𝑟𝑎𝑡𝑖𝑜2×𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
𝑒𝑥𝑝_𝑖𝑛𝑓𝑙𝑎𝑡𝑜𝑟 = 𝑟𝑎𝑡𝑖𝑜3×𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
𝑖𝑚𝑝_𝑖𝑛𝑓𝑙𝑎𝑡𝑜𝑟 = 𝑟𝑎𝑡𝑖𝑜4×𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
In equations above, C_deflator, I_deflator, Exp_deflator, Imp_deflator are calculated using
ratio1, ratio2, ratio3, ratio4 and GDP_deflator.
9. 9
𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 = 𝑟𝑒𝑎𝑙_𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛×𝑐_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 = 𝑟𝑒𝑎𝑙_𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡×𝑖_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
𝑒𝑥𝑝𝑜𝑟𝑡𝑠 = 𝑟𝑒𝑎𝑙_𝑒𝑥𝑝𝑜𝑟𝑡𝑠×𝑒𝑥𝑝_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
𝑖𝑚𝑝𝑜𝑟𝑡𝑠 = 𝑟𝑒𝑎𝑙_𝑖𝑚𝑝𝑜𝑟𝑡𝑠×𝑖𝑚𝑝_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
In equations above, nominal consumption, investment, exports and imports are calculated using
real consumption, investment, exports, imports, C_deflator, I_deflator, Exp_deflator and
Imp_deflator.
𝑟𝑒𝑎𝑙 𝐺𝐷𝑃 = 𝑟𝑒𝑎𝑙_𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 + 𝑟𝑒𝑎𝑙_𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑟𝑒𝑎𝑙_𝑒𝑥𝑝𝑜𝑟𝑡𝑠 − 𝑟𝑒𝑎𝑙_𝑖𝑚𝑝𝑜𝑟𝑡𝑠
+ 𝑟𝑒𝑎𝑙_𝑔𝑜𝑣 + 𝑑𝑖𝑠_2
𝐺𝐷𝑃 = 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 + 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑒𝑥𝑝𝑜𝑟𝑡𝑠 − 𝑖𝑚𝑝𝑜𝑟𝑡𝑠 + 𝑔𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡
In equations above, real and nominal GDP are calculated using real and nominal components of
GDP.
𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟 = 𝐺𝐷𝑃/𝑟𝑒𝑎𝑙_𝐺𝐷𝑃
In the equation above, GDP_deflator is calculated using real and nominal GDP.
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 =
𝑟𝑒𝑎𝑙_𝐺𝐷𝑃
𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡
𝑝𝑒𝑟𝑠𝑜𝑛𝑎𝑙_𝑖𝑛𝑐𝑜𝑚𝑒 = 𝑒𝑎𝑟𝑛_𝑖𝑛𝑐𝑜𝑚𝑒 + 𝑝𝑟𝑜𝑝_𝑖𝑛𝑐𝑜𝑚𝑒 + 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟_𝑖𝑛𝑐𝑜𝑚𝑒
𝑖𝑛𝑐𝑜𝑚𝑒 = 𝑝𝑒𝑟𝑠𝑜𝑛𝑎𝑙_𝑖𝑛𝑐𝑜𝑚𝑒/𝐺𝐷𝑃_𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟
In equations above, productivity and income are calculated according to their definition.
3.3 Exogenous Variables
Ratio1, Ratio2, Ratio3, Ratio4, Corp_profit, Dis_2, GDPworld_index, Government, Hhequity,
Pop_total, Price_wd_index, Real_gov, Sp500, Transfer_income and Recessiondummy are used
as exogenous variables in the structural model.
Ratio1, Ratio2, Ratio3, Ratio4, Dis_2, GDPworld_index, Government, Hhequity,
Price_wd_index, Real_gov, Transfer_income and Recessiondummy are used as instrument
variables to the model.
These variables are believed to be decided outside the model, and their forecasts are using
ARIMA model and exponential model.
4. Exogenous Variables Estimation
Since exogenous variables are decided without the model, it should be forecast in advance, so
that their forecast values can be used to forecast the endogenous variables.
There are 15 exogenous variables, and both ARIMA and exponential model are used in the
forecasting process.
10. 10
ARIMA model are used to forecast variables except for Ratio1, Ratio2, Ratio3 and Ratio4. All
lags have significant estimates, and the residuals pass White Noise test.
ARIMA Regression Result
Variable p d q
transfer_income 1, 2, 3 1, 1 1 Figure 7
government 2, 8, 22 1, 1 1 Figure 8
real_gov 4 1, 1 1 Figure 9
hhequity 20 1 - Figure 10
dis_2 1, 4 1 1 Figure 11
GDPworld_index 1 1 1 Figure 12
price_wd_index 1, 2 1 - Figure 13
prop_income 2, 9 1 - Figure 14
pop_total 2, 4 1, 1 1 Figure 15
sp500 1 1 - Figure 16
corp_profit - 1 - Figure 17
And for Ratio1, Ratio2, Ratio3 and Ratio4, it’s believed that more recent data should have larger
weight when forecasting. So exponential model is used to forecast these variables.
5. Endogenous Variables Estimation
For the final model, all estimates are significant at 0.1 level except for the parameter of interest
rate (b2) in Difinvestment. The p-value for b2 is 0.1888. The reason why I keep interest rate,
although its parameter is not significant, is because theoretically interest rate is one of the most
important factors that affect investment.
Figure 2 and Figure 3 show the regression result.
5.1 Difconsumption
The RMSE is 27.6633. The Adj R-Sq is 0.4161. The DW statistic is 2.2039. It’s not very close to
2, but I consider it’s acceptable.
The estimates of a1, a3, a4, a5 and a6 are positive, and the estimate of a2 is negative, which are
all consistent with the theoretical framework that consumption increases with income, wealth,
employment and population, and decrease with interest rate.
5.2 Difinvestment
The RMSE is 27.1987. The Adj R-Sq is 0.7829, which is good. The DW statistic is 1.7978,
which is acceptable.
The estimates of b1, b3, b4 are positive, and the estimate of b2 is negative, which are all
consistent with the theoretical framework that investment is positively correlated with output,
and negatively correlated with interest rate and volatility of market.
5.3 Difexports and Difimports
For exports, the RMSE is 23.7460. The Adj R-Sq is 0.2036. The DW statistic is 1.9836, which is
close to 2. For imports, the RMSE is 25.8674. The Adj R-Sq is 0.4300. The DW statistic is
2.0467, which is close to 2.
The estimates of c1, c3, c4 and d1, d3, d4 are positive, and the estimates of c2 and d2 are
negative, which is consistent with the theoretical framework that export and import should be
positively correlated with interest rate, income. Although export should be negatively correlated
11. 11
with domestic price level, import is not supposed to be positively correlated with domestic price
level. The reason why the estimate is negative is probably because the foreign price level is not
controlled. World price variable was originally in the model, but then removed because of
insignificance. A better measure for foreign price level is needed.
5.4 Dift
The RMSE is 0.4663. The Adj R-Sq is 0.1684, which is not very good. The DW statistic is
1.8215.
The estimates of g1, g2, g3 and g4 are all positive, which is consistent with the theoretical
framework that interest rate increase with domestic and foreign inflation, and the volatility of
market.
5.5 Difemp
The RMSE is 0.1826. The Adj R-Sq is 0.8952, which is very good. The DW statistic is 2.0601,
which is close to 2.
The estimates of e1, e2 and e4 is positive, and the estimate of e3 is negative. This result is
consistent with the theoretical framework that employment should be positively correlated with
GDP growth and corporate profit, and negatively correlated with productivity.
5.6 Difave
The RMSE is 0.3552. The Adj R-Sq is 0.1019, which is not very good. The DW statistic is
2.3748.
The estimates of f1, f3 and f4 is positive, and the estimate of f2 is negative. This result is
consistent with the theoretical framework that average income is positively correlated with
inflation, GDP growth and corporate profit, and negatively correlated with employment.
5.7 Hausman Test
The p-value of Hausman Test is 0.0302, which means that we should reject the null hypothesis
and use 2SLS model.
Figure 4 shows the Hausman test result.
6. Forecast
From the forecast data, we can see that, real GDP is increasing, and so is real consumption.
However, real investment is going down. Both real exports and imports will decrease for 2
periods, and then increase. The net export calculated from real exports and imports will still be
negative and stay at about the same level. The interest rate is going down, following the currency
trend. GDP_deflator will go up, but not as fast as it is in 2015. Personal_income will also go up,
following the current trend. Employment will stay at about the same level as the beginning of
2016.
Generally, the forecast for most variables are good, and it’s consistent with current economy
trend. And the confidence interval is relatively some for most variables.
However, for real investment and interest rate, the confidence interval is big, which means the
forecast is not very accurate and not convincing. That is, the change of investment and interest
rate in the future is not very clear. This is result from the very some Adj R-Sq of this variables.
Therefore, without considering real investment and interest rate, the forecast of the next 8
quarters shows that the economy is still going to grow at a normal speed.
The forecast value is in Table 1.
12. 12
Figure 5 and Figure 6 are the plot of growth rate of variables. Figure 5 shows growth rate for
variables except for interest rate. It shows that there will be some big variance in 2016, but the
variance dies out in 2017. Figure 6shows the growth rate of interest rate.
Figure 18 plot the result of Monte Carlo Simulation. The difference between High and Low is 4
standard deviations.
7. Conclusion
The structural model in this paper is mostly based on economic theory, and made some
adjustment for the empirical data.
The forecast for real GDP, consumption, exports, imports, GDP deflator, personal income and
employment is good. It shows that the economy from 2016Q2 to 2018Q1 will stay at the same
growth trend as 2015.
The forecast for real investment and interest rate is not very accurate, and the trend is not
convincing. That is because the model doesn’t have much explanatory power for these two
variable.
There is still some improvement need to be done. Firstly, the instrument variables in this model
may not be very good. They may not be totally exogenous. Secondly, the choice of variables to
run 2SLS is partly based on the empirical data. More economic evidence is need to back up my
theory. Thirdly, some variables may not be good enough. There is not a good variable to measure
foreign price level. Exchange rate is not included in the model. SP500 may have some
explanation for volatility, but it’s probably not good enough.
8. Appreciation
Many thanks to Professor Qiang Xu, who generously help me with my model and code, and to
Xinyue and Chun from the class.
