On June 23 2016, the United Kingdom narrowly voted in a country-wide referendum to leave the European Union (EU). Economists at the time warned of economic losses; the Bank of England produced estimates that that GDP could be as much as 10.5% lower than the previous trend.

2016年6月23日，英國在全國范圍的公民投票中以微弱的票數離開了歐盟(EU)。 當時的經濟學家警告經濟損失。 英格蘭銀行(BoE) 估計 ，GDP可能比以前的趨勢低10.5％。

The latest update from the Bank of England has lowered estimates: a 5.5% loss of GDP is now expected if a no-deal Brexit were to occur.

英格蘭銀行的最新消息降低了預期：如果無協議脫歐，現在預計GDP將下降5.5％。

The divorce has yet to happen of course, dragging on for three and a half years with no clear end in sight. However, the uncertainty and expectation that the UK will eventually succeed in leaving the EU is able to cause substantial harm to the economy even before the official withdrawal occurs. Here, I will be using Synthetic Control Method to produce a model that can estimate the economic impacts of Brexit so far. If you are simply interested in seeing the results and don’t care for the methodology, skip to the Conclusion section at the bottom.

離婚當然還沒有發生，拖延了三年半，沒有明確的結局。 但是，即使英國正式退出歐盟，英國最終能否成功退出歐盟的不確定性和期望仍可能對經濟造成重大損害。 在這里，我將使用綜合控制方法生成一個模型，該模型可以估計到目前為止英國脫歐的經濟影響。 如果您只是對查看結果感興趣，而不關心方法論，請跳至底部的結論部分。

方法 (Methodology)

For a sample of potential donor countries to form the synthetic control, I used all current OECD countries. The OECD consists of 36 mostly developed countries. Using OECD countries allows me to pull from OECD Data.

為了對潛在的捐助國進行綜合控制，我使用了所有經合組織國家作為樣本。 經合組織由36個最發達國家組成。 使用OECD國家可以使我從OECD數據中受益。

In constructing the synthetic control, I will be using the Synth package for R.

在構建綜合控件時，我將使用Synth包用于R。

Selection of Predictors

預測變量的選擇

To form the synthetic control, we need to include several variables that are predictive of our outcome variable (Real Gross Domestic Product per capita). I collected data on the following variables:

為了形成綜合控制，我們需要包括幾個可以預測結果變量(人均實際國內生產總值)的變量。 我收集了以下變量的數據：

• Exports as a percentage of GDP
  出口占GDP的百分比
• Employment rate
  就業率
• Working age population as a percentage of the total population. The working age population is defined as aged 15–64.
  勞動年齡人口占總人口的百分比。 勞動年齡人口定義為15-64歲。
• Human capital. Specifically, the percentage of 25–34 year old’s with tertiary education.
  人力資本。 具體來說，是25-34歲的大專以上學歷的百分比。

Selection of Donor States

選擇捐助國

In this process, any other countries that underwent a similar intervention should be removed. Luckily, no other countries have left the EU. As the OECD is mostly formed of relatively similar developed countries, I will not remove any from the sample.

在此過程中，任何接受過類似干預的國家都應刪除。 幸運的是，沒有其他國家離開歐盟。 由于經合組織主要由相對類似的發達國家組成，因此我不會從樣本中刪除任何內容。

Optimization Algorithm

優化算法

I will leave this as the default setting, which takes the best result from Nelder-Mead and BFGS. Nelder-Mead produces a better result in this case.

我將其保留為默認設置，它將獲得Nelder-Mead和BFGS的最佳效果。 在這種情況下，Nelder-Mead會產生更好的結果。

I will optimize the model from 2000 to 2015.

我將從2000年到2015年對模型進行優化。

綜合控制 (The Synthetic Control)

After running the function, we can review the synthetic control it has produced. The function has selected the following weights for our predictors:

運行該函數后，我們可以查看它產生的綜合控件。 該函數為我們的預測變量選擇了以下權重：

Note the synthetic is virtually identical to the UK in our predictor variables:

請注意，在我們的預測變量中，合成實際上與英國相同：

The synthetic is primarily composed of Japan (35%), Iceland (21.5%), and the US (14.4%) with smaller weights coming from several other countries. We can now see that our synthetic does a fairly good job of following the trends of the UK.

合成纖維主要由日本(35％)，冰島(21.5％)和美國(14.4％)組成，其重量較小來自其他幾個國家。 現在我們可以看到，我們的合成材料在追隨英國趨勢方面做得相當不錯。

The period from 2002 to 2005 shows some deviation, but overall the result looks okay. The model has a Mean Squared Prediction Error (MSPE) of 214,588.

從2002年到2005年這段時期顯示出一些偏差，但總體而言結果還不錯。 該模型的均方預測誤差(MSPE)為214,588。

結果 (Results)

We can now see a plot of the UK against the synthetic control extended to 2018.

現在我們可以看到英國針對合成控制的情節延至2018年。

The vertical red line represents the last year before the intervention (when the referendum took place).

垂直的紅線表示干預前的最后一年(舉行公民投票時)。

The size of the graph makes it it difficult to assess, so we are also able to view a plot of the gaps between the synthetic and the UK to view more easily view the differences:

該圖的大小使其難以評估，因此我們還可以查看合成圖和英國之間的差距圖，從而更輕松地查看差異：

The model uses annual GDP, where the last year is 2018. As of this date, the UK has lost approximately $1500 per capita according to this estimate. While this model does suggest UK GDP is lower due to Brexit, the fact that the UK and the synthetic control don’t perfectly track each other means we can’t be certain of the magnitude. However, given weak GDP growth so far in 2019, we are likely to see the damage continue to grow.

該模型使用的年度GDP(去年是2018年)。根據該估計，截至該日期，英國人均損失了大約1500美元。 盡管該模型確實表明英國脫歐導致英國GDP下降，但英國和綜合控制機構之間無法很好地相互追蹤這一事實意味著我們無法確定其幅度。 但是，鑒于2019年迄今為止GDP增長疲軟 ，我們很可能看到損失繼續增加。

These results are broadly in line with results from most experts; two economists from the London School of Economics noted the UK has experienced slow-downs in GDP, investment, productivity growth, and a weakened currency since the referendum.

這些結果與大多數專家的結果基本一致； 倫敦經濟學院的兩位經濟學家指出 ，自公投以來， 英國的 GDP，投資，生產率增長和貨幣走弱都經歷了放緩。

結論 (Conclusion)

• This analysis suggests the UK has already experienced a significant economic hit due to the Brexit referendum
  該分析表明，由于英國退歐公投，英國已經遭受了重大的經濟打擊
• The UK has likely lost about $1500 per person of GDP from the impacts of Brexit so far
  迄今為止，英國可能因英國脫歐的影響而使每人GDP損失約1500美元
• If the UK had not voted to leave the EU, UK GDP per capita would likely be about 3.25% higher than it is right now
  如果英國沒有投票決定退出歐盟，那么英國人均GDP可能會比目前高出約3.25％。
• The economic damages are likely to get worse as the saga continues, and 2019 was very possibly the worst year for the UK economy yet
  隨著傳奇的繼續，經濟損失可能會變得更糟，2019年很可能是英國經濟最糟糕的一年