A	Addendum and additional information
A.1	Update of table 6.2 basic model results 
The basic R&D model results presented in table 6.2, page 106, were based on the following equation: 

where  is the foreign knowledge stock or potential spillover pool to Australia and is based on either foreign BERD or GERD,  is the ratio of intermediate and capital good imports to Australia over GDP, i represents a country, n is the number of countries included in the construction of the foreign knowledge stocks which is fourteen,  is each country’s share of Australian imports of capital and intermediate inputs, and  is the knowledge stock of country i constructed using the perpetual inventory method.  
Coe and Helpman’s preferred specification was: 

The log of the import share weighted stocks are scaled by Australia’s import intensity. Updated results based on this formulation are presented in table A.1 below. 
Evaluated at the mean import intensity from 1968-69 to 2002-03, the foreign elasticity is 0.067 in model CH3, which is a much smaller foreign effect than is commonly found for most countries. If the foreign effect was to be evaluated at the mean import intensity for later sub-samples of the data, then the elasticity would be larger as import intensities have increased over time.   
Under either formulation of the foreign knowledge stock, the estimates from the regressions are unreliable. The residuals display a high degree of serial correlation and each model fails the functional form and heteroskedasticity tests. 
Table A.1	Basic MFP and business R&D (BRD) model in levels
Stocks depreciated at 5 per cent. Foreign business R&D stock is log of sum of bilateral import share weighted stocks multiplied by Australian import intensity.a 
	Coe and Helpman’s original results for OECD b	Update of Coe and Helpman	Test: 
add cyclical variable	Test:
 add time trend	Test: alternative lag structure	
Lag structure	Aus.=(t-1)
For.=(t-1)	Aus.=(t-1)
For.=(t)	Aus.=(t-1)
For.=(t)	Aus.=(t-1)
For.=(t)	Aus.=(t-2)
For.=(t-3)	
Dep. Var. = ln(MFP)	CH1	CH2	CH3	CH4	CH5	
Domestic BRD stock	0.078***
(9.5)					
Aus. BRD stock 		0.055***
(2.8)	0.056***
(3.1)	0.024
(1.1)	0.132***
(8.3)	
Foreign BRD stock 	0.294***
(7.0)	0.377***
(7.6)	0.371***
(7.5)	0.195***
(2.9)	0.185***
(4.3)	
Cycle (growth of real GDP) 			0.133
(1.2)	0.196**
(2.3)	0.280***
(3.1)	
Time trend				0.005***
(3.0)		
Constant		3.976***
(87.1)	3.969***
(96.5)	4.095***
(79.3)	3.835***
(91.6)	
						
Foreign elasticity at mean m/y = 0.18		0.068	0.067	0.035	0.033	
						
Test statistics						
# of observations	440	34	34	34	32	
Time period 	1971-90	69/70-02/03	69/70-02/03	69/70-02/03	71/72-02/03	
R2 	0.630	0.954	0.956	0.965	0.951	
Durbin-Watson (d)		0.960	0.733	0.517	0.447	
White test 2(p) for heteroskedasticity		18.7
(0.002)	20.3
(0.016)	24.1
(0.044)	20.2
(0.017)	
RESET F(3,Z)		9.5
(0.000)	15.5
(0.000)	27.6
(0.000)	19.0
(0.000)	
a *** statistical significance at 1 per cent or greater. ** significance at 5 per cent or greater. * significance at 10 per cent or greater. Heteroskedasticity-consistent t-statistic in brackets.  b Equation (iii), table 3, pp. 869, Coe, D. and E. Helpman 1995, ‘International R&D spillovers’, European Economic Review, 39, pp. 859-887.  
Source: Commission estimates. 

The high degree of serial correlation is evident in the residual plots (figure A.1). 
Figure A.1	Plot of residuals from basic models, 1969-70 to 2002‑03
Actual MFP less predicted MFP 
Model CH2	Model CH3	
		
Model CH4	Model CH5	
		
Financial years beginning 1 July of year specified. 
Data source:  Commission estimates. 
Re-estimating the above models with a more rapid assumed decay rate of knowledge does not significantly improve the models. The results are similarly rejected as tests and residual plots point to substantial mis-specification. 

A.2	Residual plots and test statistics for chapter 10 2‑equation models  
The information below supplements information provided in chapter 10 and appendix E on the 2‑equation  models of chapter 10.  
2‑equation ‘Extended’ Models 
The residual plots for the ‘extended’ two-equation or system models in chapter 10 do not point to model mis-specification (figure A.2).  
Figure A.2	Scatterplot of residuals for table 10.2 models, page 191-92
Actual MFP less predicted MFP. 
Model S1: MFP equation	Model S1: R&D equation	
		
Model S2: MFP equation	Model S2: R&D equation	

Model S3: MFP equation	Model S3: R&D equation	
		
Model S3LP: LP equation	Model S3LP: R&D equation	
		
Model S4: MFP equation	Model S4: R&D equation	

Model S4LP: LP equation	Model S4LP: R&D equation	
		
Financial years beginning 1 July of year specified. 
Data source:  Commission estimates. 
Table A.2	Test statistics for table 10.2 models, page 191-92
Multi-factor productivity (MFP) and Labour Productivity (LP) models 
Model - 	S1	S2	S3	S3LP	S4	S4LP	
Dep. Var. - 	Ln(mfp)	Ln(mfp)	ΔLn(mfp)	ΔLn(LP)	ΔLn(mfp)	ΔLn(LP)	
Know. Stock spec. - 	Ln(K)	Ln(K)	Ln(K/Y)	Ln(K/(Y*hrs))	Ln(ΔK/Y)	Ln(ΔK/(Y*hrs))	
No. of observations	29	26	27	27	26	25	
Degrees of freedom	22	35	28	27	39	32	
RMSE a - 							
   R&D eq’n	0.008	0.008	0.014	0.022	0.054	0.044	
   Productivity eq’n	0.005	0.000	0.002	0.004	0.002	0.004	
Log Likelihood	213	260	205	176	159	152	
AIC b	-382	-449	-353	-299	-240	-240	
BIC b	-351	-405	-317	-264	-191	-201	
							
a  Root MSE is the standard deviation of the error term, and is the square root of the Mean Square Residual (or Error).  b For the Akaike and Bayesian Information Criteria, a smaller statistic suggests better model fit (for example, model S2 fits the data better than model S1). 
Source: Commission estimates. 

2‑equation Basic Models 
Residual plots and test statistics for the 2-equation basic models of chapter 10, table 10.4, page 197, are provided in figure A.3 and table A.3. 
Figure A.3	Productivity equation residuals from basic 2-equation models
Actual MFP less predicted MFP. 
S1 Basic	S2 Basic	
		
S3 Basic	S3LP Basic	
		
S4 Basic	S4LP Basic	
		
Financial years beginning 1 July of year specified. 
Data source:  Commission estimates. 
Table A.3	Test statistics for table 10.4 basic models, page 197 
Multi-factor productivity (MFP) and Labour Productivity (LP) models
	S1 Basic	S2 
Basic	S3 
Basic	S3LP 
Basic	S4 
Basic	S4LP
 Basic	
Dep. Var. - 	Ln(mfp)	Ln(mfp)	ΔLn(mfp)	ΔLn(LP)	ΔLn(mfp)	ΔLn(LP)	
Know. Stock spec. - 	Ln(K)	Ln(K)	Ln(K/Y)	Ln(K/(Y*hrs))	Ln(ΔK/Y)	Ln(ΔK/(Y*hrs))	
No. of observations	29	28	27	27	26	26	
Degrees of freedom	20	22	15	13	24	24	
RMSE  - 							
   R&D eq’n	0.008	0.008	0.014	0.024	0.054	0.045	
   Productivity eq’n	0.005	0.006	0.008	0.009	0.009	0.009	
Log Likelihood	210	202	174	160	125	136	
AIC 	-380	-359	-318	-294	-202	-223	
BIC 	-353	-330	-298	-277	-172	-194	
							
Source: Commission estimates. 
A.3	Model S2, table 10.2, chapter 10  
The MFP equation of model S2 investigated the relationship between the natural log of MFP, the natural log of the knowledge stocks, and other control variables. The equation also included a number of dummies and intercept shift parameters. The text on page 193 discusses the results from this model when the shift parameters are dropped. Own-financed business R&D becomes insignificant and also tests out of the model. The resulting elasticities and standard errors are: 
Variable	Coefficient	Std. Error	
Trend	0.017	0.006	
Cycle	0.425	0.018	
Rfrg_te	0.492	0.044	
Ci5iousage	-0.086	0.022	
Nonggit	-0.146	0.018	
Education	0.326	0.042	
era	-0.068	0.010	
Centbrg	-0.033	0.004	
intercept	1.699	0.315	
The elasticity and standard error for education was inadvertently left out of the text. 
If communication infrastructure (ci5iousage) and private IT capital (nonggit) are further dropped from the model (on the basis of a rejection of the plausibility of the negative coefficients), then the results are as below (as discussed in the text on page 193). 
Variable	Coefficient	Std. Error	
Trend	-0.015	0.004	
Cycle	0.497	0.028	
Rfrg_te	0.335	0.067	
Education	0.088	0.033	
era	-0.101	0.016	
Centbrg	-0.008	0.003	
intercept	3.785	0.186	
The residuals for this model are plotted in figure A.4. The log likelihood, AIC and BIC are 219, -389 and -355, respectively. 
Figure A.4	Residuals for model S2 without shifts, own-financed R&D, communication infrastructure or IT capital
MFP equation 	R&D equation