RDP 9612: External Influences on Output: An Industry Analysis Appendix C: Panel Data Estimation Method
December 1996
- Download the Paper 182KB
Following Stockman (1988), an error-components model is used to estimate the fraction of the variation in output growth that can be attributed to industry-specific shocks and the fraction that can be attributed to nation specific shocks:
where Δytni is the growth rate of output in industry i within nation n at time t. The term mni is a constant specific to industry i within nation n. The term fti is a vector of dummy variables, multiplied by their coefficients, for each industry at each time but common to all nations. This term captures any variation in output that is confined solely to a particular industry regardless of its location. The term gtn is a vector of dummy variables, multiplied by their coefficients, for each nation at each point in time, and captures the variation in output stemming from differences across nations. A random disturbance term utni is added.
Several normalisations are needed to identify the model. The nation effect is set to zero for one country, initially the United States. The results are not very sensitive to the choice of country for this normalisation. The estimated nation effects then measure the difference between the nation-specific component of output growth in nation n and the United States. The industry and nation effects were set to zero for the last period for all industries and all nations. These effects therefore must be interpreted relative to the last period in the sample (1994). The OECD's STAN database was used for these calculations.
The results for the set of countries including and excluding Australia are provided in Tables C.1 and C.2, respectively. The table's sub-titles includes the number of observations, the explanatory power of the equation and the sum of squares attributable to Equation (C.1). In both cases, the model explains about one-half of the variation in industrial output growth rates. The rows list the industry and country specific effects. Column 1 tells the sum of squares explained by the factor; column 2 states the per cent of total effect the factor represents; column 3 gives the F-statistic; and column 4 gives the marginal significance. The industry and country specific effects are strongly significant.
| SS 1 |
Per cent of total 2 |
F-statistic 3 |
Marginal significance 4 |
|
|---|---|---|---|---|
| Orthogonal industry*time, fti | 4.39 | 30% | 1.54 | 0.0000 |
| Orthogonal nation*time, gtn | 6.21 | 43% | 10.20 | 0.0000 |
| SS | Per cent of total | F-statistic | Marginal significance | |
|---|---|---|---|---|
| Orthogonal industry*time, fti | 4.13 | 32% | 1.52 | 0.0000 |
| Orthogonal nation*time, gtn | 5.29 | 41% | 10.13 | 0.0000 |
Dependent variable:  ,
Sample period: 1980:Q3 to 1994:Q4
|
||
|---|---|---|
| Constant | −283.85***, | (35.49) |
 |
−0.47***, | (0.06) |
 |
0.57***, | (0.07) |
 |
−0.066***, |
{0.00} |
| Δfarmt− 2 | 0.019**, | (0.08) |
| Δfarmt− 4 | −0.023***, | (0.08) |
 |
0.38***, | (0.10) |
 |
−0.33***, | (0.09) |
 |
−0.27***, | (0.10) |
 |
−0.27***, | (0.09) |
| shockt−1 | 0.24***, | (0.07) |
 |
0.71 | |
| LM(1) | 0.78 | |
| LM(4) | 3.42 | |
Notes: *, **, and *** denote significance at the 10%, 5% and 1% levels, respectively. Numbers in parentheses ( ) are standard errors; the number in braces { } is the p-value for the joint significance of real cash rates. LM(1) and LM(4) are test statistics for Lagrange multiplier tests for first and first to fourth order residual autocorrelation. |
||
To test whether Australia exhibited a significantly different pattern of shocks to the other countries, a set of dummy variables was inserted to pick out each of the Australian observations. The p-value for exclusion of all these variables is 0.74. The hypothesis that Australia exhibits the same pattern of shocks is not rejected.