| first_period | last_period | observations | mean_ee_growth | mean_external_growth | mean_weight_coverage |
|---|---|---|---|---|---|
| 2005-04-01 | 2026-01-01 | 84 | 2.147 | 1.662 | 0.997 |
Eesti SKP reaalkasvu mudel välisnõudluse abil
1 Purpose
The purpose of this exercise is to estimate how Estonia’s real GDP growth is related to the GDP growth of Estonia’s main trading partners. Instead of entering each trading partner separately in the main specification, the model constructs a weighted external-demand index using Estonia’s goods export weights.
The dependent variable is Estonia’s real GDP growth. The main explanatory variable is the export-weighted real GDP growth of selected partner economies: Finland, Sweden, Germany, Latvia, Lithuania, Poland, the Netherlands, and Denmark.
2 Data and variables
The model uses quarterly real GDP data for Estonia and partner countries. GDP growth is calculated as year-on-year quarterly growth by default. Estonia’s goods export weights are calculated from monthly export values by partner country, aggregated to annual weights. The baseline specification uses lagged export weights, meaning that the external-demand index in year t uses export weights from year t - 1. This reduces look-ahead bias.
The external-demand index is defined as:
\[ g^{EXT}_t = \sum_i w_{i,t-1} g^i_t \]
where:
- \(g^{EXT}_t\) is the external-demand index;
- \(w_{i,t-1}\) is partner \(i\)’s lagged export weight;
- \(g^i_t\) is partner \(i\)’s real GDP growth.
3 Model specifications
Three specifications are estimated.
The first model is a simple contemporaneous relationship:
\[ g^{EE}_t = \alpha + \beta g^{EXT}_t + u_t \]
The second model is the preferred dynamic specification:
\[ g^{EE}_t = \alpha + \rho g^{EE}_{t-1} + \beta_0 g^{EXT}_t + \beta_1 g^{EXT}_{t-1} + u_t \]
The third model extends the dynamic specification with shock dummy variables for the Covid period and the 2022–2023 war/energy shock period:
\[ g^{EE}_t = \alpha + \rho g^{EE}_{t-1} + \beta_0 g^{EXT}_t + \beta_1 g^{EXT}_{t-1} + \delta_1 D^{Covid}_t + \delta_2 D^{Energy}_t + u_t \]
Newey-West/HAC standard errors are used to account for possible autocorrelation and heteroskedasticity in quarterly macroeconomic data.
4 Model fit
| model | r_squared | adj_r_squared | rmse | mae | n_obs |
|---|---|---|---|---|---|
| M1: simple | 0.790 | 0.787 | 2.629 | 2.005 | 84 |
| M2: dynamic | 0.862 | 0.857 | 2.132 | 1.506 | 84 |
| M3: dynamic + shocks | 0.869 | 0.860 | 2.078 | 1.480 | 84 |
R-squared measures the share of variation in Estonia’s GDP growth explained by the model. Adjusted R-squared is more appropriate when comparing models with different numbers of explanatory variables. RMSE and MAE measure the average in-sample fitting error in GDP-growth percentage points; lower values indicate a better in-sample fit.
5 Coefficient estimates
5.1 HAC coefficient table: M1
| term | estimate | std_error | statistic | p_value |
|---|---|---|---|---|
| (Intercept) | -0.450 | 0.527 | -0.855 | 0.395 |
| external_growth | 1.563 | 0.138 | 11.320 | 0.000 |
5.2 HAC coefficient table: M2
| term | estimate | std_error | statistic | p_value |
|---|---|---|---|---|
| (Intercept) | -0.060 | 0.332 | -0.182 | 0.856 |
| ee_growth_lag1 | 0.664 | 0.145 | 4.578 | 0.000 |
| external_growth | 1.032 | 0.191 | 5.397 | 0.000 |
| external_growth_lag1 | -0.572 | 0.164 | -3.479 | 0.001 |
5.3 HAC coefficient table: M3
| term | estimate | std_error | statistic | p_value |
|---|---|---|---|---|
| (Intercept) | -0.045 | 0.401 | -0.112 | 0.911 |
| ee_growth_lag1 | 0.570 | 0.164 | 3.482 | 0.001 |
| external_growth | 1.084 | 0.198 | 5.465 | 0.000 |
| external_growth_lag1 | -0.449 | 0.197 | -2.273 | 0.026 |
| covid_dummy | 1.274 | 1.093 | 1.165 | 0.248 |
| war_energy_dummy | -1.557 | 1.004 | -1.551 | 0.125 |
6 Long-run effect of external demand
In the dynamic models, the approximate long-run effect of external demand is calculated as:
\[ \frac{\beta_0 + \beta_1}{1 - \rho} \]
| model | long_run_external_demand_effect |
|---|---|
| M2: dynamic | 1.370 |
| M3: dynamic + shocks | 1.476 |
The long-run effect should be interpreted as the cumulative association between a one percentage point increase in partner-country weighted GDP growth and Estonia’s real GDP growth, after accounting for persistence in Estonia’s own GDP growth.
7 Charts
8 Interpretation
The preferred model is usually M2, because it captures both contemporaneous external demand and short-run persistence in Estonia’s own GDP growth. M3 is useful as a robustness check because it controls for exceptional shock periods, but dummy variables can also absorb part of the variation that might otherwise be attributed to external demand.
A positive and statistically meaningful coefficient on the external-demand index supports the interpretation that stronger growth among Estonia’s main trading partners is associated with stronger real GDP growth in Estonia. The lagged external-demand coefficient captures delayed transmission through exports, investment, production chains, and confidence effects.
9 Caveats
The model should be interpreted as a compact macroeconomic association, not as a fully structural causal model. The export weights currently use goods exports only, so the model may understate the role of services trade. Results may also be sensitive to extraordinary periods such as Covid, the energy-price shock, and Russia’s war against Ukraine. For forecasting, the model should be evaluated with an out-of-sample or rolling-window exercise.