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Regression Analysis for the Netherlands

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Published: Fri, 26 Jan 2018

TABLE OF FIGURES AND GRAPHS

Table 1: Coefficients of estimated OLS model

Table 2: Analysis of Variance and F-statistic

Table 3: Paired t-sample tests

Table 4: Analysis of Variance for pre structural break (b,c)

Table 5: Analysis of Variance for post structural break (b,c)

Table 6: Analysis of Variance and F-statistic

Table 7: Pearson’s Correlations

Graph 1: Scatterplot with best fit line

Graph 2: Simple scatterplot of imports

Introduction

The following document analyses the import aggregate demand for the Netherlands utilising data from the first quarter 1977 to the first quarter 2006. The aim is to determine the relationship between imports and five explanatory variables: relative prices (measured as the ratio of import to domestic prices), household consumption expenditures, government consumption expenditures, investment expenditures and exports. A regression utilising Ordinary Least Squares is run and then a series of analyses is done on the results of the estimated model.

Model Estimation

Data for the Netherlands was obtained from 1st quarter 1977 to 1st quarter 2006 from the International Monetary Fund’s International Financial Statistics, giving a sample population N = 117 and 116 degrees of freedom. It is worth noting that due to the use of the euro to report Netherland’s accounts starting in 1999, there was a break in the information presented as they were in two currencies pre 1999 (in Dutch gulden) and post 1999 (euros). In order to overcome this, all of the data was transformed into Dutch gulden, using the official euro/gulden exchange rate at the time of the entry of the euro.

To prepare the data for the regression, the natural log of the values for imports (M), relative prices (RP)—the index of import prices to consumer prices, household consumption expenditure (HC), government consumption expenditure (GC), investment expenditure (INV) and exports (EXP) were taken. By using SPSS to estimate the model via Ordinary Least Squares, the aggregate demand function (utilising the unstandardised coefficients) is estimated as:

M = 0.071 – 0.966 RP – 0.328 HC – 0.171 GC + 0.286 INV + 0.808 EXP

Std errors: (0.041) (0.022) (0.053) (0.035) (0.033) (0.026)

The model has an adjusted R2 = 0.992, indicating that 99.2% of the variance in imports is explained by the relative price and the four expenditure components. It has a standard error of regression of 0.02715.

With regards to the explanatory variables included in the regression, by analysing their t-values we are able to determine that each coefficient is statistically significant at all levels. Table 1 shows the results of the estimated coefficients along with their corresponding t-values and significance values.

Table 1: Coefficients of estimated OLS model

Model

 

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

   

1

(Constant)

.071

.041

 

1.706

.091

LN_RP

-.966

.022

-.522

-43.460

.000

LN_HC

-.328

.053

-.272

-6.195

.000

LN_GC

-.171

.035

-.141

-4.815

.000

LN_INV

.286

.033

.244

8.677

.000

LN_EXP

.808

.026

.745

30.777

.000

             

a Dependent Variable: LN_M

Plotting the values of imports (as ln(M)) with regards to the standardised predicted values from the model, we get the best-fit curve shown in graph 1.

Graph 1: Scatterplot with best fit line

Interpretation of slope coefficients

The estimated coefficients from the regression above can now be interpreted. The results are presented again for ease of reading:

M = 0.071 – 0.966 RP – 0.328 HC – 0.171 GC + 0.286 INV + 0.808 EXP

In general terms, each slope coefficient is the import elasticity with respect to each of the equation components: relative prices, household consumption, government consumption, investment expenditures and exports. Following is the explanation for each coefficient:

machinery and transport equipment, chemicals, fuels, foodstuffs, clothing from germ, belg and china

β2 = -0.966 represents the relative price import elasticity. This implies that a 1% increase in relative prices causes a reduction in imports of 0.966%. This is basically a unitary elasticity, the effect of a change in relative prices is almost identically reflected on imports. This occurs primarily in countries with an open economy that thrives on the balance of trade. Additionally, since the Netherlands’ most important trade partners are within the European Union, who use the same currency, the relative prices are similar for them. (Atlapedia Online, 2006)

β3 = -0.328 represents the elasticity of imports with respect to household consumption expenditure. It implies that a 1% increase in household consumption expenditure will translate into a 0.328% decrease in imports. The import elasticity of household consumption is inelastic. Household consumption has a small effect on imports, as although Netherlands does import foodstuffs and clothing, the bulk of imports is for machinery and transport equipment as well as chemicals, which have no relation with household consumption. (CIA World Factbook, 2006)

β4 = -0.171 represents the import elasticity with respect to government consumption expenditures. It follows that a 1% increase in government expenditure will result in a reduction in imports of 0.171%. The import elasticity of government consumption is highly inelastic. Due to the nature of imports mentioned in the paragraph above, it is logical to assume that the import composition is not widely affected by government consumption, except maybe in the import of fuels.

β5 = 0.286 is the import elasticity with respect to investment expenditure. It is a positive inelastic import elasticity as a 1% increase in investment expenditure will result in a 0.286% increase in imports. This makes sense with reality since investment expenditures are in part for importing machinery and transport goods.

β6 = 0.808 is the import elasticity with respect to exports. It shows that a 1% increase in exports will result in a 0.808% increase in imports. This elasticity is also elastic, although it is more similar to the relative price import elasticity, approximating unit elasticity. This also reflects the Netherlands’ open economy and its active trading with neighbouring countries as a result of forming part of the European Union.

Overall significance of the regression

Now that we have seen the interpretations of each of the coefficients of our estimated model, and having seen that they are all statistically significant, we have to analyse whether the model as a whole is statistically significant. This is done by analysing the F-value of the regression. If the value of F is sufficiently large with a high confidence level, then it follows that the estimation we have done does indeed predict some of the values we have observed and the regression is statistically significant.

For this regression, SPSS calculates the F-value as 2784.8, which is statistically significant at all confidence levels. As mentioned above, this confirms the validity of the predicted equation in estimating the values of the components of imports.

Table 2 below presents SPSS’ results for the F-statistic and Analysis of Variance for our model.

Table 2: Analysis of Variance and F-statistic

Model

 

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

10.263

5

2.053

2784.805

.000(a)

Residual

.082

111

.001

   

Total

10.345

116

     

a Predictors: (Constant), LN_EXP, LN_RP, LN_INV, LN_GC, LN_HC

b Dependent Variable: LN_M

Test of equality of import elasticities

After having tested that the model as a whole is statistically significant, we will now test whether each of the import elasticities of final expenditures are equal amongst themselves. In order to do this, we will use a paired t-test, which will compare each elasticity against each other and determine whether the differences between them are statistically significant or not. If they are not statistically significant, then the elasticities are the same.

In the case of our estimated model, the t-statistics are significant at all levels for all of the relationships. This means that we cannot conclude that each of the import elasticities is the same, rather they are statistically significantly different from one another.

Table 3 shows the results provided by SPSS’ paired t-test for each of the import elasticity relationships tested:

Table 3: Paired t-sample tests

                 
 

Paired Differences

     
 

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

t

df

Sig. (2-tailed)

 
 

Lower

Upper

LN_HC – LN_GC

0.743944

0.074971

0.006931

0.730216

0.757672

107.3342

116

0.000

LN_HC – LN_INV

0.869318

0.079402

0.007341

0.854779

0.883857

118.4243

116

0.000

LN_HC – LN_EXP

-0.057368

0.099663

0.009214

-0.075617

-0.039119

-6.2263

116

0.000

LN_GC – LN_INV

0.125375

0.106033

0.009803

0.105959

0.144790

12.7897

116

0.000

LN_GC – LN_EXP

-0.801312

0.113483

0.010491

-0.822091

-0.780532

-76.3773

116

0.000

LN_INV – LN_EXP

-0.926686

0.123764

0.011442

-0.949348

-0.904024

-80.9900

116

0.000

                         

The Behaviour of Imports from 1977 to 2006

Having verified that our model is statistically significant and that each elasticity of imports is different, we now analyse the behaviour of imports during our sample period. The easiest way to do so is graphically. Using the scatterplot function from SPSS we plot the observed values of the Netherlands’ imports from 1st quarter 1977 to 1st quarter 2006. Graph 2 below shoes this relationship:

Graph 2: Simple scatterplot of imports

A structural break in imports

From the graph above, there seems to be a structural break around 2nd quarter 2002. This would make sense since it was around this time that the actual euro currency replaced the Dutch gulden (and all other European currencies for that matter). Such a significant change would be reflected in imports.

The actual occurrence of such a break, can be tested statistically using our observed data. This is done via a Chow Test, where we test whether the coefficients in our estimated equation are the same before and after the suspected structural break point, Q2 2002. However, since SPSS does not have a command for the Chow Test, we do this analysis by calculating an incremental F-value from a constrained (the model divided into the two periods pre Q2 2002 and post Q2 2002) and an unconstrained model (our original estimation).

The constrained model used divides our data into two, as mentioned above. The group labelled as “pre” represents observed values from Q1 1977 to Q2 2002, whilst the group labelled “pos” represents values from Q3 2002 to Q1 2006. Running a regression and using the Anova functionality on the constrained model yields the results presented in tables 4 and 5.

:

Table 4: Analysis of Variance for pre structural break (b,c)

Model

 

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

5.344

5

1.069

1574.636

.000(a)

Residual

.060

88

.001

   

Total

5.403

93

     

a Predictors: (Constant), LN_EXP, LN_RP, LN_INV, LN_GC, LN_HC

b Dependent Variable: LN_M

c struct_break = pre

Table 5: Analysis of Variance for post structural break (b,c)

Model

 

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

.219

5

.044

240.351

.000(a)

Residual

.003

17

.000

   

Total

.222

22

     

a Predictors: (Constant), LN_EXP, LN_HC, LN_INV, LN_RP, LN_GC

b Dependent Variable: LN_M

c struct_break = pos

Utilising the above with the results from the original unconstrained model:

Table 6: Analysis of Variance and F-statistic

Model

 

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

10.263

5

2.053

2784.805

.000(a)

Residual

.082

111

.001

   

Total

10.345

116

     

a Predictors: (Constant), LN_EXP, LN_RP, LN_INV, LN_GC, LN_HC

b Dependent Variable: LN_M

the incremental F-value is calculated using the residual sums of squares and degrees of freedom of the constrained and unconstrained models. In this case as:

F6,105 = [(0.063 -0.082)*(117 – 2*5-2)] / (0.082 * 6) = -4.05

The f-value of -4.05 when compared to the critical value of F6,105 = 2.19 at the 5% confidence level and 2.98 at the 1% confidence level, causes us to reject the null hypothesis which means that there is a difference in the coefficients between the “pre” and “pos” periods we chose. This confirms that there was a structural break in the 2nd quarter of 2002.

Autocorrelation

We can now check if our estimated model suffers from autocorrelation by examining the Durbin-Watson statistic. According to a statistical table for Durbin-Watson statistics, the critical values for the Durbin-Watson statistic with N = 117 and k = 6, at the 5% confidence level are dL = 1.61045 and dU = 1.78828. In this model, the D-W statistic was calculated by SPSS as 0.661. This implies that the model does suffer from autocorrelation, as the statistic falls below the lower critical value. It has positive autocorrelation. To correct this, we have to determine whether or not the aggregate demand relation is in fact linear, otherwise we need to choose a different functional form and re-run our regression. If we do have the correct functional form, we need to determine whether there are any other variables which can be included in the model to help explain the effect on imports and which may eliminate this autocorrelation. Any changes that are made to the model or the data itself will imply that a new regression must be run and new tests for autocorrelation carried out until this problem is eliminated.

Correlation of final expenditure components

Only because the model as a whole suffers from autocorrelation, it does not mean that each of the explanatory variables is significantly correlated. In order to test this, we must calculate Pearson’s correlation coefficient. SPSS can calculate these coefficients by analysing the relationship between each one of the variables with the others in the equation. Table 7 below shows the results from SPSS, as well as the statistical significance of each of the calculated correlation coefficients.

Table 7: Pearson’s Correlations

   

LN_HC

LN_GC

LN_INV

LN_EXP

LN_HC

Pearson Correlation

 

.954(**)

.950(**)

.933(**)

Sig. (2-tailed)

 

.000

.000

.000

N

117

117

117

117

LN_GC

Pearson Correlation

.954(**)

 

.911(**)

.911(**)

Sig. (2-tailed)

.000

 

.000

.000

N

117

117

117

117

LN_INV

Pearson Correlation

.950(**)

.911(**)

 

.894(**)

Sig. (2-tailed)

.000

.000

 

.000

N

117

117

117

117

LN_EXP

Pearson Correlation

.933(**)

.911(**)

.894(**)

 

Sig. (2-tailed)

.000

.000

.000

 

N

117

117

117

117

** Correlation is significant at the 0.01 level (2-tailed).

As can be seen, all of the correlation coefficients are statistically significant at all levels, thus they are positively correlated. The highest correlations are between household consumption expenditures and the other three expenditure components: government consumption, investments and exports with correlation coefficients of 0.954, 0.950 and 0.933 respectively. This means that these variables vary together in a linear manner. Due to this high level of statistically significant correlation, the premise of regressing the model via OLS and the corresponding interpretations are put into question, as one of the basic premises is that the value of each coefficient represents the change it causes on the independent variable, leaving the rest of the explanatory variables unchanged. Yet, if they are so highly correlated, you cannot assume that they can ever be unchanged.

Conclusions

Through the analysis of the Netherlands’ quarterly statistics on imports, relative import/domestic prices, household consumption, government consumption, investments and exports, we estimated via OLS a model to explain elasticity of imports. We underwent a series of analysis of the results of the model, finding that our estimate is statistically significant, as are each of the individual import elasticities. Additionally, we were able to demonstrate that the switch of currency to the euro caused a structural break in the import relationship. Notwithstanding this, the estimated model suffers from autocorrelation, which brings into question whether the OLS approach and its findings are in fact correct. Additionally, the high correlations that exist between the various expenditure components also puts into question our interpretations of the estimated coefficients, as none of them can be fully isolated to measure the effect on imports.

References

Atlapedia Online, 2006, Netherlands [online], available at: http://www.atlapedia.com/online/countries/netherla.htm [accessed 12 December 2006]

Biokin, Ltd., 2006, Critical values of F-statistics [online], (updated 16 November 2006), Available at http://www.biokin.com/tools/fcrit.html [accessed on 10 December 2006]

Central Intelligence Agency, 2006, The World Factbook: Netherlands [online], updated on 30 November 2006, available at: https://www.cia.gov/cia/publications/factbook/geos/nl.html [accessed on 11 December 2006]

Critical Values for the Durbin-Watson Test: 5% Significance Level [online]. Available at: http://www.stanford.edu/~clint/bench/dw05b.htm [accessed 10 December 2006]

Hamilton, J.D., 1994, Time Series Analysis, New Jersey: Princeton University Press.

International Monetary Fund (IMF), International Financial Statistics (IFS) November 2006, ESDS International, (MIMAS) University of Manchester.


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