Category Archives: Original Articles

The Aftermath of COP22 – A Reality Check for Fighting Climate Change

Amid the Trump elections and fake news outrage, a summit was held in Marrakech Morocco dedicated to Climate Change. The summit named COP22 was held in November 2016 and presented a significant reality check for the ambitious goals  that were set by the Paris Agreement. With 2018 as the next major checkpoint, the United Nations Framework Convention on Climate Change (UNFCCC) began to: reevaluate those ambitious goals set by the Paris Agreement, and ratify it to add  more countries. With the commencement of the summit, the ratifications made during the Paris Agreement have been passed into law, as the number of national commitments surpassed 55% of global emissions. [1] The newest members who have ratified the Paris climate change agreement include Australia, Botswana, Burkina Faso, Djibouti, Finland, Gambia, Italy, Japan, Malaysia, Pakistan, and the UK.

One major cause for concern during the summit is skepticism regarding whether or not goals set by the Paris Agreement will be met as well as the transparency of the cooperations between nations. Voluntary national emission targets have not had the desired effect as countries like the USA that  contribute over 16% of global emissions for CO2 have yet to commit to cut back their emissions. [3] With only a year left until the next checkpoint, the COP22 summit focused on improving current agreements to make countries more accountable instead of laying down more policies. On the bright side, improvements were made to the agreements of the Climate Vulnerable Forum, which is a coalition of developing countries committing to ultimately reach 100% renewable energy. The proposed strategy was to have rich nations contribute USD 100 billion to developing countries so that they can transition to renewable energies. This will reduce the need for developing countries to consume and invest in cheaper fuel options. One clear problem with this commitment is Climate Finance. The US, Germany and, and UK contributed: USD 50 million to improve carbon accounting in developing countries, USD 23 million for a centre to share clean technology expertise, and Germany single handedly replenished the adaptation fund with USD 80 million. [5] Although these numbers show progress, it is only a drop in the bucket for the goal of USD 100 billion by 2020, set by the Paris Agreement. The COP22 summit did not produce any significant new financial pledges for ratified nations but instead worked on clarifying financial contributions nations need to make, highlighting the need for adaptation funds to the poorest nations who are being affected by climate change the most.

The summit marked the emergence of clear demands from African countries. These demands include more funding to enforce the goals set by the Paris Agreement and mechanisms to move away from dependence on foreign aid. The ambitious African Renewable Energy Initiative (AREI) will be a self-sustaining initiative that plans to achieve 10 gigawatt of additional generation capacity by 2020 and 300 gigawatt by 2030. [1] This initiative will attract investors in public and private realms due to its highly ambitious results and profit margins.

Now that the summit has ended and U.S. presidential elections are finished many questions are being asked as 2018 approaches. Trump has famously proclaimed that upon his ascension to the presidency he would disengage the United States from the Paris Agreement established by Obama administration. Moving forward, if the Trump administration sticks to their claims it would mean the loss of support from the USA who carry the second highest emissions in total kiloton, up to 5,335,000kt in 2014, the USA accounts for approximately 16% of global CO2 emissions and without their support on this agreement it would be almost impossible to achieve the goals set by the Paris Agreement. [4]
Just north of the USA, Canada is holding firm to commitments made in the Paris Agreement as well as spearheading other initiatives. Canadian Minister of the Environment and Climate Change, the Honourable Catherine McKenna, stated during the summit that since COP21 Canada has negotiated an amendment to the Montreal Protocol to phase down hydrofluorocarbons in air-conditioners and refrigerants. [5] Canada has also co-chaired the Climate and Clean Air Coalition, and are implementing new measures to reduce emissions from aviation under the Civil Aviation Organization. Like many developing nations including China who are investing billions into renewable energy, Canadians are also committing more resources to increase innovations in climate resilience and adaptation technologies. The future although still uncertain, is without a doubt moving towards a low carbon way of life. [2]

References

[1] http://www.climatechangenews.com/2016/11/10/7-things-you-missed-while-trump-hogged-the-headlines/
[2] http://www.davidsuzuki.org/issues/climate-change/science/climate-change-basics/climate-change-101-1/?gclid=Cj0KEQiA56_FBRDYpqGa2p_e1MgBEiQAVEZ6-87_35Dye_ytxNfP-dKANh_5pTRa88YNDFzLchAUvvkaAveA8P8HAQ
[3] http://www.ipcc.ch/index.htm
[4] https://www.epa.gov/ghgemissions/global-greenhouse-gas-emissions-data
[5] http://news.gc.ca/web/article-en.do?nid=1155259

OLS, BLUE and the Gauss Markov Theorem

From left to right, Carl Friedrich Gauss and Andrey Markov, known for their contributions in statistical methods.

In today’s article, we will extend our knowledge of the Simple Linear Regression Model to the case where there are more than one explanatory variables. Under certain conditions, the Gauss Markov Theorem assures us that through the Ordinary Least Squares (OLS) method of estimating parameters, our regression coefficients are the Best Linear Unbiased Estimates, or BLUE (Wooldridge 101). However, if these underlying assumptions are violated, there are undesirable implications to the usage of OLS.

In practice, it is almost impossible to find two economic variables that share a perfect relationship captured by the Simple Linear Regression Model. For example, suppose we are interested in measuring wage for different people in Canada. While it is plausible to assume that education is a valid explanatory variable, most people would agree it is certainly not the only one. Indeed, one may include work experience (in years), age, gender or perhaps even location as regressors.

As such, suppose we have collected the data for multiple variables, x1,… xn, and y. Through a Multiple Linear Regression Model, we can estimate the relationship between y and the various regressors, x1,… xn (Wooldridge 71).

  • yi is the ith observation for the independent variable
  • xki is the ith observation for the kth regressor
  • βk is the coefficient for the kth regressor
  • εi is the error term

As in the simple case, we can use the Ordinary Least Squares method (OLS) to derive the estimates for our coefficients in the Multiple Linear Regression Model. Recall, our goal is to summarize the sum of squared residuals, that is (Wooldridge 73) :

If we take the partial derivatives of the above equation with respect to β0, β1, …, βn and set them to zero, the result is a system of n+1 equations. The solution to this system will produce the estimates for each βi.

In general, the OLS method for estimation is preferred because it is easy to use and understand. However, simplicity comes with its limitations. Ordinary Least Squares provides us with a linear estimator of parameters in Multiple Linear Regression. In other words, we obtain a column vector of estimates for βi that can be expressed as a linear function of the dependent variable y. Like all other linear estimators, the ultimate goal of OLS is to obtain the BLUE Let us first agree on a formal definition of BLUE. On one hand, the term “best” means that it has “lowest variance”; on the other, unbiasedness refers to the expected value of the estimator being equivalent to the true value of the parameter (Wooldridge 102).

We now turn our attention to the Gauss Markov Theorem, which guarantees that the Ordinary Least Squares method under certain conditions. They are colloquially referred to as the Gauss Markov Assumptions. It is important to note that the first four ensure the unbiasedness of the linear estimator, while the last one preserves the lowest variance (Wooldridge 105).

  1. Linearity in Parameters
  2. Random Sampling
  3. No Perfect Collinearity
  4. Exogeneity
  5. Homoscedasticity

The first two assumptions are self-explanatory; the parameters we are estimating must be linear, and our sample data is to be collected through a randomized, probabilistic mechanism. The third condition, no perfect collinearity, ensures that the regressors are not perfectly correlated with one another. An example of this is including both outcomes of a binary variable into a model. Suppose we are interested in official language preferences: if we were to add English and French as regressors, the model would exhibit perfect collinearity because we know if someone prefers English, they do not prefer French at the exact same time. Mathematically, if they were both indicator variables, we would not be able to differentiate when an observation prefers English or French because one of them will always have a value of 1. Exogeneity means that the regressors cannot be correlated with the error term. The converse of this is endogeneity, and examples of this include omitted variable bias, reverse causality, and measurement error. The fifth and final assumption is homoscedasticity, which means the variance of the error term must be constant no matter what the value of regressors are.

Admittedly, no one will ever walk up to you and ask “What are the conditions for the Gauss Markov Theorem?”. However, as the first article alluded to a few weeks ago, we need to use econometric models with discretion. To put the importance of these assumptions into perspective, consider this analogy. The criminal code is in place so that the citizens of our country can function well together without harming one another. A police officer will never come up to you and ask you to recite the criminal code, but when you start violating the laws, you will likely find yourself in trouble. It is important for us to identify when we are breaking the law, and find methods to avoid doing so. The same can be said using OLS. By learning the five assumptions, we know of possible issues that we may run into when performing linear regression.

In summary, let’s end the discussion of OLS with more insights on the Gauss Markov Theorem.   If all of the conditions simultaneously hold, we know that OLS can is BLUE. In later articles, we will discuss specific ways to mitigate violations of these conditions. For example, when we have endogeneity present (the fourth assumption is violated), our OLS estimator will be biased. We will talk about methods to solve this issue like performing an Instrumental Variable Estimation to produce unbiased estimates.

 

REFERENCE

  1. Wooldridge, Jeffrey M. Introductory Econometrics: A Modern Approach. 5th ed. Mason, OH: South-Western Cengage Learning, 2013. Print.

Newsonomics: Trends in Competition and Bias in the News Industry

Allegedly the most empirical civilization of all time, our Information Age would no doubt serve its audience righteously in their attempts to obtain knowledge. But take a look at the N-gram, a Google search engine that charts the frequency of a word in printed sources over time, for the word epistemology:

Google N-gram Viewer of ‘epistemology’

As the study of ‘how we know’, epistemology distinguishes justified beliefs from opinion. Since the dawn of the Information Age in the 1990s and the advent of the Internet, the use of this word, and implicitly its application to our lives, has been in decline. But what does this trend mean for the news media industry in terms of how news firms compete?

Firstly, considering audience trends in the US, newspapers have decreased in circulation by 7%, while the average viewership for prime-time news has increased by 8% [1]. Competition in the Cable TV market has increased because of the reduction of regulatory controls during the 1980s, subsequently incentivizing news firms to enter this market [2]. This raised much appraise with academics and professionals in the field who hold that the ‘persuasion game’, between firms in the market who bout for news scoops and larger readerships, will always yield the truth. Given that at least one news source propagates the truth and consumers read all sources, the truth will be known by all readers as all firms eventually bend to the most empirical facts and information over time as presented in the truthful news source, since each firm’s reputation is on the line [3]. For example, a Democrat newspaper reveals a scandal concerning a Republican, and a Republican newspaper initially denies it. However, assuming the Democrat newspaper has the best facts, the Republican newspaper eventually concedes to some of the allegations because their reputation is at stake as their readership, who also reads the Democrat newspaper, begins to know of the truth.

Now, let’s complicate our ‘persuasion game’ by introducing a bias on the supply-side of the news market. Naturally, news firms are incentivized to be the first to find and publish ‘scoops’, news stories that are desirable to the public. However, a firm might be suppressed as a result of government intrusion. Consider the following variables: government bribe B, firm revenue for story circulation R, the number of firms N, and value to government of suppression V. The bribe must be B ≥ R. Further, B ≤ V/N, since the value of suppression will be distributed between the number of firms. Therefore, the suppression equilibrium is V/N ≥ R, which indicates that a greater number of firms, or increased competition, will decrease the likelihood that the story is suppressed. Additionally, as firms drop out and avoid a particular story, remaining firms have a growing incentive to publish as their potential audience grows. Human rights violations in Iraq’s Abu Ghraib prison and the leak of the ‘Pentagon Papers’ are examples of stories that were suppressed by government intrusion after their initial publication [3].

More often in our Information Age, a bias is introduced on the demand-side of the news market. Consumers have a preference for news sources that confirm their prior beliefs [4]. When the main source of news was newspapers, readers could pick up multiple papers with different biases to get an objective view of all sides of an issue, thus the success of the ‘persuasion game’ in yielding truth. However, with the rise of prime-TV news coverage, and readers turning to other sources on the Internet, like Facebook, it became simple and easy to appease your own bias. Given that consumers have a psychological urge to confirm and fall further in their beliefs [5] and that news quality is increasingly being associated with whether or not their belief is confirmed [3], it comes as no surprise that news firms cater to their audience by bias-targeting. Thus, considering the N-gram presented above, a decline in empiricism can be causally related to the advent of Internet news and the drinking of the Kool-Aid, en masse.

Bias-targeting is ever present in the strategy of prime-TV news firms who hope to satisfy their audience. With the Information Age, such a formula has unfurled itself farther as the news industry’s competition increases with evermore rapid forms of ingestion: Websites, mobile apps and social media posts. Just in case such conveniences weren’t courtly enough, Facebook’s news feed algorithm prioritizes what a user is likely to click on and browse through [6]. However, this may only reinforce false biases. Further, as a user’s online traffic becomes more prevalent, it paves the way for bias-targeting on a political level.

Cambridge Analytica is a Big Data company that worked for the ‘Brexit’ campaign in its primal stages and Trump’s Presidential campaign [7]. Their accurate modelling of people’s digital footprints gives particular persons an edge as they confirm those biases at that right place, at the right time, to the right people. And the irony that seeps through is that the populist movement, so unempirical and unscientific in their diatribes and nationalistic jargon, was thrust forth unto the steeple because of the modern work of statisticians and scientists of the day.

[1] http://www.journalism.org/2016/06/15/state-of-the-news-media-2016/
[2] Hamilton, James T. 2004. All the News that’s Fit to Sell. Princeton, NJ: Princeton University Press.
[3] https://web.stanford.edu/~gentzkow/research/jepmedia.pdf
[4] https://web.stanford.edu/~gentzkow/research/BiasReputation.pdf
[5] Nisbett, Richard, and Lee Ross. 1980. Human Inference: Strategies and Shortcomings of Social Judgment. Englewood Cliffs, NJ: Prentice-Hall, Inc.
[6] https://www.bloomberg.com/view/articles/2017-02-17/mark-zuckerberg-s-manifesto-for-facebook-offers-a-social-dystopia
[7] https://motherboard.vice.com/en_us/article/how-our-likes-helped-trump-win

 

Implications of a Strong USD

After Donald Trump’s surprise U.S. election victory and the Republicans’ full control of the Congress, the markets have reacted and the U.S. Dollar (dollar) has been continually surging – catching companies and investors off guard. The new U.S. administration seems to believe that this is a sign of “global confidence in Trumpism”, but there are many concerns for U.S. exporters towards an overly strong exchange rate [1].

A strong dollar is defined as one that can purchase more foreign currency relative to a weak dollar. This means that U.S. consumers will pay less for imports but foreign consumers will pay more for U.S. exports [4]. This is good for U.S. consumers as the appreciation of the dollar against other currencies makes foreign goods and foreign travel cheaper, both of which American consumers enjoy. However, this negatively affects tourism as the United States becomes a less affordable travel destination [3].  

A second consideration is the impact of a rising dollar on the earnings of U.S. companies with large foreign operations [5]. In 2012, for companies in the S&P 500 that provided foreign sales details, 47% of total sales came from abroad, mainly Europe and Asia. Clearly, a stronger dollar would have a negative effect on net exports produced domestically, thus creating a drag on potential earnings. Interestingly, one can consider that “truly global U.S. –based” companies involved in exports do not produce within the U.S., but rather internationally [6]. The effects of globalization in the past decades have allowed companies the ability to purchase materials and set up factories abroad, which means that the rising dollar does not have a huge negative relationship with production as initially understood [2]. The real issue is when the earnings in foreign currencies are converted back to the domestic currency, as companies will feel the full brunt of the reduced returns.

As an example, Apple, the world’s most valuable company and a company known for their international dominance, faces some of the greatest foreign exchange exposures with 22% of their sales from China and 23% from Europe [1]. In the past quarter, Apple reported its biggest hit to its margins in China, about 3% in revenue growth, due to the weakness of the Chinese RMB against the dollar. Luca Maestri, Apple’s finance chief, has suggested the company has been preparing for further dollar strength but has come to realize that “at some point, the strong dollar becomes the new normal and we need to work with that” [1].

Unemployment Rate in the United States averaged 5.81 percent from 1948 until 2017. The unemployment rate is currently at 4.8% in January 2017.

On the positive side, a higher dollar effectively transfers demand from the U.S. economy to other economies around the world [5]. The U.S. unemployment rate is currently below its 50-year average and is showing signs that it will continually decrease. By contrast, other economies, notably in Japan and emerging Asia countries, would benefit greatly from a boost to their exports as a result of a higher dollar. In the long run, this will develop a stronger and more balanced global economy [5].

The strong dollar will remain a concern in the coming years as President Trump moves to revive domestic production. As it currently stands, having a stubborn stance for domestic development may harm the U.S. in the long run with reduced export potential; however, the strong exchange rate will be hugely favoured by American consumers. The rise of the dollar in 2016 will have impacts well into 2017, and those impacts should be considered positive on a global scale in the U.S. and around the world [5].


[1] https://www.ft.com/content/8399c6a2-aa82-11e6-ba7d-76378e4fef24
[2] http://fortune.com/2015/03/04/strong-dollar-effects/
[3] https://www.thestreet.com/story/13327355/1/3-impacts-of-a-strong-dollar-weigh-on-next-week-s-fed-meeting.html
[4] http://www.infoplease.com/cig/economics/dollar-us-economy.html
[5] http://www.barrons.com/articles/3-ways-a-strong-dollar-impacts-the-global-economy-1413236429
[6] https://hbr.org/2015/10/strong-dollar-weak-thinking

Pure vs. Mixed Strategies

The stadium lights are blinding, and the murmuring of the crowd in the stands is amplified into a deafening roar. Yet, your senses have never been more acute. The date is January 29, 2017, and are playing to win your fifth Australian Open championship title in tennis. Millions of people are watching your every movement from across the world. You are Roger Federer. Where do you place your serves across the net?

We are often unaware of the different dimensions that everyday games are comprised of. Something seemingly as simple as a serve in tennis can be dissected into many parts, both physical and mental. In this article, we are going to explore pure and mixed strategies in game theory, using tennis as an example.

What is a pure strategy?

A pure strategy is an unconditional, defined choice that a person makes in a situation or game. For example, in the game of Rock-Paper-Scissors,if a player would choose to only play scissors for each and every independent trial, regardless of the other player’s strategy, choosing scissors would be the player’s pure strategy. The probability for choosing scissors equal to 1 and all other options (paper and rock) is chosen with the probability of 0. The set of all options (i.e. rock, paper, and scissors) available in this game is known as the strategy set.

What is a mixed strategy?

A mixed strategy is an assignment of probability to all choices in the strategy set. Using the example of Rock-Paper-Scissors, if a person’s probability of employing each pure strategy is equal, then the probability distribution of the strategy set would be 1/3 for each option, or approximately 33%. In other words, a person using a mixed strategy incorporates more than one pure strategy into a game.

The definition of a mixed strategy does not rule out the possibility for an option(s)to never be chosen (eg. pscissors= 0.5, prock = 0.5, ppaper = 0). This means that in a way, a pure strategy can also be considered a mixed strategy at its extreme, with a binary probability assignment (setting one option to 1 and all others equal to 0). For this article, we shall say that pure strategies are not mixed strategies.

In the game of tennis, each point is a zero-sum game with two players (one being the server S, and the other being the returner R). In this scenario, assume each player has two strategies (forehand F, and backhand B). Observe the following hypothetical in the payoff matrix:

The strategies FS or BS are observed for the server when the ball is served to the side of the service box closest to the returner’s forehand or backhand, respectively. For the returner, the strategies FR and BR are observed when the returner moves to the forehand or backhand side to return the serve, respectively. This gives us the payoffs when the returner receives the serve correctly (FS,FR or BS,BR), or incorrectly (FS,BR or BS,FR). The payoffs to each player for every action are given in pure strategy payoffs, as each player is only guaranteed their payoff given the opponent’s strategy is employed 100% of the time. Given these pure strategy payoffs, we can calculate the mixed strategy payoffs by figuring out the probability each strategy is chosen by each player.

So you are Roger. It is apparent to you that a pure strategy would be exploitable. If you serve to the backhand 100% of the time, it would be easy for the opponent to catch on and return from the backhand side more often than the forehand, maximizing his expected payoff. Same goes for the serve to the forehand. But how often should you mix your strategy and serve to each side to minimize your opponent’s chances of winning? Calculating these probabilities would give us our mixed strategy Nash equilibria, or the probabilities that each strategy is used which would minimize the opponent’s expected payoff. In the following article, we will look at how to find mixed strategy Nash equilibria, and how to interpret them.