What was the cause of the decline in remittances sent to Pakistan between 1982 and 2000? I am trying to find out what caused the 2-decade long decline in remittances as a % of GDP. I have spent an hour trying to search for explanations but haven't found anything. I know its a long shoot and thought it won't hurt to ask here to see if anyone can explain the cause

Perhaps more enlightening would be the reason why Remittances increased so much from 1976 to 1982, and then cooled off.
1977 was the year of a military coup in Pakistan (and the imposition of Martial Law), that was also, it appears, the beginning of deep structural socioeconomic changes. In such situation it is not uncommon to see a wave of emigration, among those that do not "fit well" in the new situation. But this rarely means that the emigrants severe all ties with the country back home, usually some family is left behind. Hence, increased Remittances.
In 1985 Martial Law was lifted and elections were held, and this could explain the downward trend.
So I would look into the emigration/repatrization flows in Pakistan during that era, coupled with the political situation and any economic reforms.


Why is the yen getting stronger even with negative interest rates? Checking this graph we can see that 1 Yen is worth increasingly more dollars this past week.

I wonder why is this, specially when the BoJ has imposed negative nominal interest rates.

It seems a bit strange...

Negative interest rates are not incompatible with appreciation of the local currency. As pointed out by the economist (Why investors buy bonds with negative yields), some investors buy bonds to place bets on currencies. Thus, it does not matter so much that the interest rate is negative.

Thus, the variation of the yen reflects other trends. It is very tricky to point out at one event or idea in particular, but here are a few possible drivers of the appreciation of the Yen:

The dollar is weakening, following the release of the minutes of the Fed meeting which showed that the central bank does not intend to raise interest rates in April.
Japan is running out of options to put downward pressure on the yen. The central bank already buys everything in sight, and thus would have difficulties to increase the money supply. The feeling that central banks are loosing grip is very tangible since a few months (if not years)
G20 countries recently agreed to not proceed to competitive devaluations of their currency. Therefore, investors might expect that Yen won't go down easily, and that the most logical path is unpward.
Japan's Prime Minister Shinzo Abe seems to hesitate to proceed to planned increase in sale tax. The first increase had a desastrous short-term effect on the economy, and most firms have a pessimistic outlook (latest PMI 49.1). Therefore, it becomes more and more likely that the government will delay the increase in sale tax, and potentially also try to stimulate the economy further.

These are all guesses. It might be that one or more of the above guesses actually moved the Yen. Or maybe it didn't and something else is happening. Maybe investors aren't as rational as we think they are and they just bet on the Yen because of their gut without logical reasons.


Firms Betas - Equity, Debt betas My question is related to the following equation:
$$\beta_{asset}=\frac{Equity}{Equity+Debt}\beta_{equity}+\frac{Debt}{Equity+Debt}\beta_{debt} $$

Why can the $\beta_{asset}$ be seen as if the firm had been financed only with equity?
We can measure the $\beta_{equity}$ by CAPM, but how can we measure $\beta_{debt}$?

Any help would be appreciated

$
\newcommand{\Cov}{\text{Cov}}
$

  Why can the $\beta_{asset}$ be seen as if the firm had been financed only with equity?

The general idea with regard to this question stems from a discussion about how equity is a residual claim. To go through this step-by-step, recall that the value of a firm is given by the discounted present value of its cash flows. Equity is a claim to whatever is left over after other financial claim-holders have been paid (e.g., debt).  In this way, equity can be viewed as a call option and debt can be viewed as a put option. (See here and here.)

So, if the firm was financed only by equity, then equity would be the claim to 100% of the cash flow. Thus, $\beta_{\text{asset}}$ in that case can be seen as the if the firm was only financed with equity.

  We can measure the $\beta_{equity}$ by CAPM, but how can we measure $\beta_{debt}$?

You say that you can measure $\beta_{\text{equity}}$ by CAPM. However, you can measure any cash-flow by CAPM---even debt. Since $V = D + E$, keep in mind that
$$
\Cov(X + Y, Z) = \Cov(X,Z) + \Cov(Y,Z).
$$
The problem, I guess, is that you need to know the distribution of debts cash flows. This depends on the face value of total debt and the distribution of the underlying cash flows. This can get especially complicated if you're thinking about considering a dynamic setting.

This question, I'm guessing, came from a discussion of the Modigliani-Miller theorem. Remember the idea behind Proposition 2. It's illustrated in the following graph:


What does the distribution of the savings rate in America look like? I know the average saving rate in the US is ~5%, but I'm curious about the distribution. An ideal answer would be a histogram with the data broken down by what proportion of population are saving at what percentage.

How much do people save?

Report on the Economic Well-Being of U.S. Households in 2014, Board of Governors of the Federal Reserve System, p. 22


Where does the extra money come from when a new country joins the Euro and converts its currency? Whenever a new country becomes a member of the Eurozone, they convert all their local currency into the Euro. What I don't understand is where does this huge new volume of Euros come from overnight? Does the European Central Bank simply print the extra money? If so, why doesn't this cause significant inflation?

Yes the European Cenral Bank issues the extra quantity of money (as for the actual printing there are factories that print euros in many member countries of the EU, under the control of the ECB).

Regarding why this does not cause inflation, it is because alongside the additional quantity of money comes the additional quantity of output of the new member, and the additional transactions related to this additional output that the additional quantity of money is called upon to facilitate.

Use the traditional "quantity theory of money"

$$PQ = VM$$

$M$ increases but $Q$ also increases, so $P$ does not have to increase.

Of course it is much more complex and complicated and gradual in a real world situation, but the fundamental idea is the above.


Question on consumption theory Question:

What my did is

I proceed this question until that point. But, I will be happy if help me to solve this question.

Thank you.

Consumer's Budget Constraint is

$$p_1x_1 + p_2x_2 + c\alpha x_1 = y$$

Holding $\alpha$ fixed, consumer's utility maximization problem is

\begin{eqnarray*} \max_{x_1, x_2} & \ (\alpha q + (1-\alpha))x_1 x_2 \\ \text{s.t.} & \ (p_1 + c\alpha)x_1 + p_2x_2  = y \end{eqnarray*}

Solving it we get the optimal bundle of goods as:
\begin{eqnarray*} (x_1, x_2) = \left(\dfrac{y}{2(p_1+c\alpha)},\dfrac{y}{2p_2}\right) \end{eqnarray*}

Corresponding utility as a function of $\alpha$ and other parameters is

\begin{eqnarray*} (\alpha q + (1-\alpha))\left(\dfrac{y^2}{4p_2(p_1+c\alpha)}\right)  \end{eqnarray*}

Now we find optimal value of $\alpha$ by solving
\begin{eqnarray*} \max_{0 \leq \alpha \leq 1} & \ (\alpha q + (1-\alpha))\left(\dfrac{y^2}{4p_2(p_1+c\alpha)}\right)  \end{eqnarray*}

Equivalently, we can find the optimal value of $\alpha$ by maximizing $\log$ of the objective
\begin{eqnarray*} \max_{0 \leq \alpha \leq 1} & \ \ln(\alpha q + (1-\alpha)) - \ln(p_1+c\alpha) + 2\ln y - \ln 4 - \ln p_2   \end{eqnarray*}

Differentiating the objective with respect to $\alpha$, we get
\begin{eqnarray*} \frac{p_1(q-1) - c}{(\alpha(q-1) + 1)(p_1+c\alpha)} \begin{cases} > 0 & \text{if } p_1(q-1) > c \\ = 0 & \text{if } p_1(q-1) = c  \\ < 0 & \text{if } p_1(q-1) < c \end{cases} \end{eqnarray*}

Therefore, optimal value of $\alpha$ is $1$ when $p_1(q-1) > c$, all values of $\alpha$ in the interval $[0, 1]$ are optimal when $p_1(q-1) = c$ and optimal value of $\alpha$ is $0$ when $p_1(q-1) < c$. In short, optimal value $\alpha^*$ of $\alpha$ satisfy

\begin{eqnarray*} \alpha^*  \in \begin{cases}  \{1\} & \text{if } p_1(q-1) > c \\  [0, 1] & \text{if } p_1(q-1) = c  \\  \{0\} & \text{if } p_1(q-1) < c \end{cases} \end{eqnarray*}

Consequently, final demand $(x_1^*, x_2^*)$ for $(x_1, x_2)$ satisfy
\begin{eqnarray*} (x_1^*, x_2^*, \alpha^*)  = \begin{cases}  \left(\dfrac{y}{2(p_1+c)},\dfrac{y}{2p_2}, 1\right) & \text{if } p_1(q-1) > c \\  \left(\dfrac{y}{2(p_1+c\alpha)},\dfrac{y}{2p_2}, \alpha\right) & \text{if } p_1(q-1) = c \text{ and } 0 \leq \alpha \leq 1 \\  \left(\dfrac{y}{2p_1},\dfrac{y}{2p_2}, 0\right) & \text{if } p_1(q-1) < c \end{cases} \end{eqnarray*}

Alternatively, we can write demand for $x_1$ as
\begin{eqnarray*} x_1^*  \in \begin{cases}  \left\{\dfrac{y}{2(p_1+c)}\right\} & \text{if } p_1 > \dfrac{c}{q-1} \\  \left[\dfrac{y}{2(p_1+c)}, \dfrac{y}{2p_1}\right] & \text{if } p_1= \dfrac{c}{q-1}  \\  \left\{\dfrac{y}{2p_1}\right\} & \text{if } p_1 < \dfrac{c}{q-1} \end{cases} \end{eqnarray*}

Here is the figure demonstrating the relationship between demand for $x_1$ and its price $p_1$, holding $q$, $y$ and $c$ fixed.

Now we consider Uno's revenue as a function of price $p_1$ :
\begin{eqnarray*} r(p_1) = \begin{cases} \dfrac{y}{2} & \text{if } p_1 \leq \dfrac{c}{q-1}  \\ \dfrac{yp_1}{2(p_1+c)} & \text{if }  \dfrac{c}{q-1} < p_1 \leq \overline{p}_1 \end{cases} \end{eqnarray*}

Consequently, profit as a function of price $p_1$ is
\begin{eqnarray*} \pi(p_1) = \begin{cases} \dfrac{y}{2} - \dfrac{ky}{2p_1} & \text{if } p_1 \leq \dfrac{c}{q-1}  \\ \dfrac{y(p_1-k)}{2(p_1+c)} & \text{if }  \dfrac{c}{q-1} < p_1 \leq \overline{p}_1 \end{cases} \end{eqnarray*}

Maximizing profit with respect to $p_1$, we get the optimal price as:

\begin{eqnarray*} p_1^* = \begin{cases} \dfrac{c}{q-1} & \text{if } 1 - \dfrac{k(q-1)}{c} \geq \dfrac{\overline{p}_1-k}{\overline{p}_1+c} \\ \overline{p}_1 & \text{if } 1 - \dfrac{k(q-1)}{c} < \dfrac{\overline{p}_1-k}{\overline{p}_1+c} \end{cases}\end{eqnarray*}

Now you can solve the remaining two parts in a similar way.


What does taxes less subsidies mean? What does 'taxes less subsidies' actually mean? It feels like it is grammatically incorrect. I have assumed it to just mean taxes minus subsidies.

You are correct, that it is taxes less subsidies = taxes - subsidies or in another word net tax for some particular product. For example, following OECD:

Taxes Less Subsidies On Products:
Net taxes on products (net indirect taxes) are the sum of product taxes less subsidies. Product taxes are those taxes payable by producers that relate to the production, sale, purchase or use of the goods and services. Subsidies are grants on the current account made by general government to private enterprises and unincorporated public enterprises. The grants may take the form of payments to ensure a guaranteed price or to enable maintenance of prices of goods and services below costs of production, and other forms of assistance to producers.

Of course, you can extend the definition outside taxes for just products I just wanted to showcase an example of more detailed definition.
As to its grammatical correctness, English is my 2nd language and this is economics site not site on English language - but you will commonly see 'taxes less subsidies' used all across academic literature. It might appear grammatically incorrect as it is part of the jargon, so of course this is not the way how laymen might discuss taxes.


Is it bad for the economy of a country if forreign firms buy companies? If a forreign firm buys a company. For example a Russian firm buys a British company. Is this good or bad or neutral for the British economy?

As I see it, the profits of the company will be going abroad so this seems bad.

Alternatively, there's nothing to say the people making profits if the company is British owned aren't spending their money abroad anyway.

Would it even matter if every British company was forreign owned?

If it doesn't matter. Why would the Chinese government be buying British firms? Surely to help their economy at the expense of the British economy? Yet, the British government seems to encourage this as "investment" in British industry. So who is getting the best deal here? Seems like Britain is getting a short term boost at the cost of long term profits.

It depends upon the circumstances and isn't necessarily bad.

Suppose a foreign firm A buys a British company from its current British owner B. A is gaining the right to whatever stream of profits the company may make in future. B is gaining the price paid for the company by A.  Whether that is a good deal for B will depend upon various considerations including:

The company's likely future stream of profits if it remains in B's ownership.
The sale price, and how this compares with the discounted present value of the above stream of profits.
Whether B's best use of the sale receipt is relatively advantageous, having regard to its preferences and attitude to risk (an entrepreneur who has taken risks in building up a company may in later years wish to hold their wealth in a safer form).

So it's quite possible for the sale to be good for B. Since B is likely, through their use of the sale receipts, to contribute to the British economy by spending (creating demand) and/or saving (providing capital for other firms), it could be good for Britain.

However, these possible advantages for Britain could in some circumstances be offset by other considerations:

A's plans for the company may involve a loss of British jobs.  This could be because capital equipment will be substituted for labour, or because the company will be scaled down (perhaps the motive for buying it is to reduce competition).
The company may operate in a sector within which foreign ownership is considered an unacceptable risk for strategic rather than economic reasons.  This might be argued in respect of firms supplying military equipment or essential infrastructure.


Even at the break-even inflation rate, isn't the YTM of a TIPS greater than that of a normal treasury bond? At a the break-even rate of inflation, the semi-annual interest payments from a TIPS and a normal government bond would be roughly equivalent. However, the principal amount originally invested in the TIPS continues to be compounded by the inflation rate while the principal amount invested in a normal government bond is nominally constant. Thus, assuming a positive break-even inflation rate throughout the holding period up till maturity (which includes both the semi-annual interest payments and the gains due to compounding of the principal by the annual inflation), the yield to maturity for a TIPS should be larger. Is my analysis correct?

Your analysis is incorrect.
The quoted market "breakeven inflation" is the spread between quoted yields. It is an approximation of the true economic breakeven from a total return perspective (possibly ignoring the par put on principal) to maturity, but under normal circumstances, it is not far off the economic breakeven. (Since the exact pattern of future CPI would matter, even the economic breakeven has technical calculation issues.)
Take an imaginary world with a 5% nominal par coupon, and a 3% inflation-linked par coupon (2% breakeven).

The conventional bond pays a 5% coupon.
The TIPS starts out with a 3% coupon, with the 3% of a par value that is expected to grow at 2% a year. It takes a long time for 3% to catch up to 5% at a 2% growth rate. (The principal future value increases by 2% per year, but that increase needs to be discounted by the nominal discount rate of 5%.)

The lower coupons are compensated by growth of the principal, keeping total returns equal.
(For an easier example, imagine a 2% nominal bond, and a 0% inflation-linked.)


Illustrating Karesh Kuhn Tucker with two non-nonnegativy constraints binding I'm teaching Karesh-Kuhn-Tucker, and looking for papers, ideally in the fields of development, agricultural or environmental economics, and ideally in good journals, that I can use to illustrate the situation where the KKT conditions are satisfied with two contraints (not nonnegativity) are binding.
The corner solution circled in blue illustrates what I mean.  Would anybody be able to suggest some?    Thanks very muich indeed.

Only two or three papers spontaneously come to my mind, they are not very recent (but quite seminal papers, useful to find further newest contributions):
Lee, Lung-Fei, and Mark M. Pitt, 1986, "Microeconometric Demand System with Binding Nonnegativity Constraints: The Dual Approach," Econometrica, 54, 1237–1242.
Lee, Lung-Fei and Mark M. Pitt, 1987, "Microeconometric models of rationing, imperfect markets, and non-negativity constraints," Journal of Econometrics, 36, 89-110.
Here is a more recent contribution:
Golan, Amos, et al. “Estimating a Demand System with Nonnegativity Constraints: Mexican Meat Demand,” The Review of Economics and Statistics, vol. 83, no. 3, 2001, pp. 541–550.


How to justify an instrumental variable? I am hoping for some tips on what I could do for a term paper in applied econometrics. We are running a 2sls where I want to use a firm's location as an IV. How can I go about justifying it is a valid instrument? More specifically, how would you suggest I can argue the exclusion restriction holds for my instrument. I am thinking of a verbal argument of about a page tops, since I have limited space left. Any suggestions would be greatly appreciated. Thank you.

PS: My endogenous variable is a dummy for whether the business owner is a member of a political party, and my outcome variable is a leverage ra

To motivate a good IV in a paper, you need a good story. For example: schools build in Indonesia as an instrument for education outcomes, quarter of birth as an instrument for income as a result of compulsory education, in their respective papers.

The IV has to be correlated to the characteristic you're trying to fix and uncorrelated to any of the other observable characteristics.

That way, the IV is only affecting the Y variable through the characteristic you're instrumenting. As far as statistically strong, you can look at examples from a few papers and see what kind of statistical scrutiny they used.


Correct Equation for Pooled OLS Regression (with Time Dummies and Interaction Terms) I have a question regarding a pooled OLS regression. Basically, I’m not sure I’m writing out the equation properly.

The data is on feature films released between 2006 and 2016 (11 years); box office revenue is the dependent variable. What I’m interested in is the coefficient of the variable CritSentiment and if it increases over time (CritSentiment is a binary variable that takes the value 1 if critical reception for a film is positive and 0 otherwise).

So aside from a bunch of film-specific controls (such as production budget), I’m including yearly time dummies to control for any trend-effects, as well as interaction terms between these time dummies and CritSentiment. The coefficients of these interaction terms should measure the estimated difference between the coefficient of CritSentiment in year t and the coefficient in the (omitted) base year.

$$\textit{Revenue}_{it} = \alpha + \beta_1 \textit{Budget}_{it} + \ ... \ + \beta_{15} CritSentiment_{it} \ + \sum_{t=1}^{11-1} \gamma_t Year_t \ + \sum_{t=1}^{11-1} \delta_{t} Year_{it} CritSentiment_{it} \ + \epsilon_{it}$$

What I’m unsure about is basically just whether the above equation correctly assigns the i and t subscripts, which I find a bit confusing (especially when it comes to the intercept and interaction terms).

Thanks a lot in advance.

I am not sure if I understand your research question correctly, but you may be trying to determine if the effect of critical reception on a film's revenue changes over time.  That means you only have one observation per film with its revenue and film-specific control variable values (including year of release and single critical reception value) saved in multiple variables.  In that case, this is the model equation you should have:

You should not have both i and t subscripts for any film-specific variables if you only have one set of values per film.  The i subscript is used on all film-related variables, including year of release.  I included t superscripts to make it clear that there are multiple Year variables.  And if you are not doing a fixed effects model (film fixed effects), there should not be any subscript on the intercept term.


What is an Economic Sector? I am of the understanding that an Economy is broken down as follows:

Traditional;
Command;
Market;
Mixed.

Each Economy being made up of Sectors, which in turn, are made up of Industries.

Simply put, what defines a Sector?  I understand that it is the broad categorisation of its associated Industries but is there some kind of universal criteria that need to be met for a term to be viewed as a Sector?

I say criteria, as I come across many interpretations of what a Sector is.  For example, some sources state that a Sector is made up as follows:

Primary;
Secondary;
Tertiary;
Quaternary;
Quinary.

Other sources then approach sectors from a sense of ownership as follows:

Public/State Sector;
Private Sector;
Voluntary Sector.

Then there are the other sources who look at Sectors from the view of a Broad Categorisation of Products/Services.  For example:

Financial;
Healthcare;
Hospitality.

As well as terms seemingly being used interchangeably, it also appears that some sources see Sectors as Industries and vice versa.

Any clarity, on the differentiation, would be greatly appreciated.

The division of the economy into sectors is arbitrary, meaning there is no universally accepted division of the economy. It is contextually dependent.


Is there any good textbook for theoretical economics mathematical modelling? I am currently reading some theoretical economics books and, of course, many mathematical expressions appear. I kind of guess their meaning, but it takes a lot of time and, after all, my guesses are assumptions rather than certainties. Many times I find myself lost even in the easiest questions like: why use an exponent instead of a multiplication in this particular case? And even if I kind of guess their meaning, I struggle to understand the creation process of a model. I have looked for mathematical modelling textbooks but all I kind find are introductions to models for processing big data or data analysis. I would like to read a textbook that is fully focused on theoretical models. Also, the books I find for mathematical economics and such are books that teach how to solve specific problems rather than how to formulate models. Does anyone know any good textbook for someone like me? Thank you.

Your question seems a bit broad. What kind of “theoretical economics” are your reading?

Nevertheless, I infer from what you write that you need to start from the beginning with maths for economcis (and maths in general), (this is because of your comment not knowing when to use an exponent  and when to multiply.

Having said this, I would recommend:

“Essential Mathematics for Economic Analysis” by Hammond et al

This book starts at the basics and builds up mathematical tools to study economic ideas.

Having mastered this book, I would try

“The Structure of Economics” of Eugene Silberberg. This books is more advanced, but it is “economics with mathematics”, so having aquired the basic mathematical tools in the first book, this book focuses con economic models from a mathematical standpoint.


Producer Econometrics: Univariate modelling with missing data Im interested in forecasting revenue for 2018.

Year           Revenue
 2010        $22,306,000
 2011        $22,420,000
 2012        $23,010,000
 2013             NA
 2014        $25,430,000
 2015        $25,601,000
 2016        $25,267,000
 2017        $23,895,400

Im unable to identify the appropriate model (AR,MA,ARMA ect.) since the use ACF and the PACF is not possible since i lack data for 2013.

How would i deal with such an issue? (preferably using R)

Alternatively, you can use the mean of the period, or fit a linear trend and interpolate. These methods use more information than just two years, which has the benefit of accounting for possible idiosyncratic factors in 2012 or 2014, with the cost of perhaps adding idiosyncratic factors from years as far as 2017.

Here is the R code with the three methods (including Alecos's):

# Interpolate between 2012 and 2014
df = data.frame(year = 2010:2017, y = c(22306000,22420000,23010000,NA,25430000,25601000,25267000,23895400))
df$y[is.na(df$y)] = mean(df$y[df$year==2012 | df$year==2014], na.rm=TRUE)

# Replace with mean of period
df = data.frame(year = 2010:2017, y = c(22306000,22420000,23010000,NA,25430000,25601000,25267000,23895400))
df$y[is.na(df$y)] = mean(df$y, na.rm=TRUE)

# Regression interpolation
df = data.frame(year = 2010:2017, y = c(22306000,22420000,23010000,NA,25430000,25601000,25267000,23895400))
fit <- lm(y ~ year, data=df)
df$y[df$year==2013] <- predict(fit, newdata = data.frame(year = 2013))

The results with each method are 24220000, 23989914, and 23753107 respectively. They are different because the series does not follows a linear trend:

# Plot
df = data.frame(year = 2010:2017, y = c(22306000,22420000,23010000,NA,25430000,25601000,25267000,23895400))
plot(x=df$year,df$y, type="l",lwd = 2)

Thus, it seems Aleco's method might be the most appropriate in this case. (It is also possible to fit non-linear trends)


What caused the stagflation in the early 1970s USA? I am aware of the conventional reasons: demand push inflation due to much higher oil prices, and a continuation of a mild recession.

Looking for a clearer explanation than I have been able to find, especially wrt monetary policy (IE, printing money)

The 19702-73 inflation was a supply side shock, a negative supply shock to be specific. Because of the high oil prices, production cost of almost every rose sharply.

Since, this was the first time that such a shock was seen at such large scale it was mostly misunderstood and traditional short term policy tools i.e. easy monetary policy and fiscal stimulus were deployed. What had actually happened was since oil is such an essential part of production, not just the short term but the long term output or the potential output itself was affected and should have been revised. Because of the incorrect diagnosis and policy response, inflation got embedded into the long term expectations and hence it just went into a spiral.


CES production function estimation Introduction

There are different ways of estimating the parameters of a production function. For example, single-equation and system equation techniques are both possible. Another difference among methods is that estimable forms may either involve direct or indirect estimation of the parameters. For instance, rather than estimate the production function as is, one may instead estimate the derived demand functions or, say, use other relations such as factor shares. Also to be considered are the underlying economic assumptions; such possibilities being perfect competition, constant returns to scale, profit maximization, etc.

Question

Bearing the above in mind, my question is what is the standard (accepted?) method of estimating normalized CES (constant elasticity of substitution) production functions?

For information, a normalized CES  production function can be written as

$$
Y = Y_{0} \lbrace \pi_{0} K_{0}^{\frac{1-\sigma}{\sigma}}(K_{t}\cdot e^{\gamma_{K}(t-t_{0})})^{\frac{\sigma-1}{\sigma}} + (1-\pi_{0})N_{0}^{\frac{1-\sigma}{\sigma}}(N_{t}\cdot e^{\gamma_{N}(t-t_{0})})^{\frac{\sigma-1}{\sigma}}\rbrace
$$

following the notation found in Klump, McAdam, and Willman (2011, p.22).

Importantly, what data is required to estimate the parameters of this particular production function? And, what is the exact procedure involved? Demonstrations and references are most welcome!

Reference:

Rainer Klump, Peter McAdam, and Alpo Willman, The normalized nested
CES production function, theory and empirics, ECB Working Paper Series,
No. 1294. (Feb., 2011), 2011.

@GraemeWalsh, another option is to use nonlinear least squares to estimate the elasticitiy of substitution, $\sigma$. This is what you want to estimate. The rest is either assumption or data. If you assume the technology is directed i.e. induced, you should use Box-Cox transformation of technology growth so that factor augmenting technological change grows at varying rates over time.

Values of $\gamma$ depend on the average growth rate of output and how you want the technological progress to be augmented. If you think labour-augmentation was strong, then choose a value that is close to actual average rate of output growth for $\gamma_N$, something smaller for the growth rate of the capital augmenting tech growth rate $\gamma_K$.

$\pi$s are constant share parameter.I do not know much about normaisation except that it should be chosen with reference to a common time period. You could normalise all the variables and parameters using the first period, or any other. Alternatively, use non-linear methods of estimation. You could try using micEconCES package in R.


Which is more economical with resources, an e-tick or a paper ticket? I always get an e-ticket on my mobile, to save the environment and so on.

But then I thought well, am I really saving trees? I have to give my phone a full charge in order that it doesn't run out just when the conductor asks for my ticket. Which means that it needs electricity and a powerstation is burning some fosil fuels somewhere no doubt.

So that got me wondering, which would be better for the environment, if everyone got e-tickets on their phones. Or everyone got a paper ticket.

We shall assume:

We don't count manufacture of phone. (We assume we will have one
anyway).
When phone is not used for buying tickets it is not charged up.
One ticket per day.
Paper ticket is on A4 paper with ink.
E-ticket needs a full battery charge for the day.

My intuition is that an e-ticket is worse because to get the energy needed to power a phone a would think it wold require burning many hundreds of paper tickets. Is this intutition correct?

According to this study by the IATA, it costs \$1 to process an e-ticket, versus \$10 to process paper ticket. I assume this is only from the airline's point of view. You could argue that this is not the "environmental cost" you care about, but I just wanted to point it out.

I'm a bit confused by your phone charging assumptions, but according to this post, it costs close to 1 cent to charge a phone (10,000 mAh, at least). Also, you won't need your phone at full charge to use e-ticket.

On top of that, paper tickets also have a lot of costs associated with it, from the manufacturing process, logistics of getting the paper to your local store, getting it from the store to your home. Then we need to talk about recycling costs, etc.

So without the cost of the phone taken into account, I still think it's more efficient to use e-ticket.


What exactly is certainty equivalence in the context of DSGE models? I keep reading about certainty equivalence in the context of DSGE models.
I understand that it has something to do with "Getting rid of the expectation operator", but I'm not entirely sure? What exactly is "certainty equivalence" in the context of DSGE models?
Do we have certainty equivalence if the solution to a stochastic model $M_S$ is the same as the solution to the non-stochastic model $M_N$, if $M_N$ is obtained by taking the equations of $M_S$ and simply removing the expectation operator and the random shocks?

EDIT: I just read in the Dynare user manual, that a first order taylor approximation of a DSGE model has "certainty equivalence", because future shocks drop out when you take the expectation operator. Yet current shocks do not drop out, as we can see in the following equation:

Note the $u$ at the very end. This denotes the current-time shock.

So if this is a "certainty equivalent model", but we still have an exogenous shock, then what does certainty equivalence mean? Apparently it doesn't mean "the absence of uncertainty" since there is still an exogenous shock.

Intuitively, it means that the model has such characteristics that "the best we can say" about remaining uncertainty, is that it will be zero. From general experience, we know that it won't be zero, but the information we possess does not permit us to say anything else than that it will be zero. The even deeper assumption here is that the information and knowledge we possess make all things that remain unpredictable to average to zero.

In such a case, of course the actual realized path of the model is affected by these totally unpredictable shocks, but the decisions we take are based on a rule "as if" the future shocks will be zero (it is implied that we have to take decisions prior to observe the realization of the shock).

More technically, quoting from Lungqvist & Sargent's "Recursive Macroeconomic Theory" 2004, 2nd ed:

  a) p.113: "CERTAINTY EQUIVALENCE PRINCIPLE: The decision rule that
  solves the stochastic optimal linear regulator problem is identical
  with the decision rule for the corresponding nonstochastic linear
  optimal regulator problem.

  b) p.115: The certainty equivalence principle is a special property of
  the optimal linear regulator problem, and comes from the quadratic
  objective function. the linear transition equation, and the property
  that (future disturbances have zero mean conditional on the current
  state). Certainty equivalence does not characterize stochastic control
  problems generally.

Please read also this post, so that if you do further search, to make sure that you look for "certainty equivalence in macroeconomics".


What are good advanced textbooks to learn mathematics for economist? I am looking for books or other sources that focus on math that is above bachelor level (i.e. above just simple calculus). I am not looking for a specialized text for some field but just general mathematics at graduate level covering wide range of topic. My current math skills are very shaky after some simple univariate/multivariate calculus. If instead of textbook you know of good MOOC course that you could recommend it would help me as well. Thank you!

In my honest opinion the best book in this regard is fundamental methods of mathematical economics by Chiang and Wainwright.
It starts at the very basics and then goes all the way up to dynamic optimisation, also covering linear algebra, matrices, advanced calculus  topics such as implicit functions and equation solving at all levels.
Combined with a fine and clear step by step writing style and lots of examples and exercises I find it really a good book.


Intertemporal utility maximization through consumption I need help in solving this question from one of the entrance examination.

Q.Consider an economy where a representitive agent lives for three periods.
In the first period, she is young - this is the time when she gets
education. In the second period, she is middle-aged and with the level
of education acquired in the first period, she generates income. More
specifically, if she has $h$ units of education in the first period, she can
earn $wh$, in the second period, where $w$ is the exogenously given wage
rate.

The agent borrows funds for her education when she is young and
repays with interest when she is middle aged. If in the first period,
the agent borrows $e$, then the human capital $h$ at the beginning of the
second period becomes $h(e)$, where $$dh/de > 0$$$$d^2h/de^2 < 0$$

In the third period of her life, she consumes out of her savings made
in the second period, that is, when she was middle aged. Assume
that the exogenous rate of interest (gross) on saving or borrowing is
$R$. For simplicity, assume that an agent does not consume when she
is young and, thus, the life time utility is $u(c^m) + bu(c^o)$, where $c^m$ and $c^o$ are the level of consumption when they are middle-aged and
old respectively and $0<b<1$ is the discount factor.

1. Write down the utility maximization problem of the agent and the
first order conditions.

2.  How does the optimal level of education vary with the wage rate
and the rate of interest?

I cannot understand how to use the interest rate. Also I have got following answer to 1:-

maximizing$$U = u(c^m) + bu(c^o)$$ subjected to the constraint
$$c^o/(1+r) + c^m = wh(e) - (1+r)e$$
from which we can get Lagrange first order equations.

I cannot see how $R$ could be used. Also got a doubtful answer for 2.

Hint : You can write down your Lagrangian and simply take derivatives according to $c^{o}$ and $c^{m}$. So, you will mainly have two first order conditions with a lagrange multiplier. After, you will combine these two equation to eliminate your lagrange multiplier, which will give your intertemporal optimality condition (so-called Euler equation). I don't write the whole maximisation problem but only Euler condition.

$$bu^{'}\left(c^{o}\right)=\frac{u^{'}\left(c^{m}\right)}{1+r}$$

The role of interest rate is quite evident. If your interest rate increases, the marginal utiliy of consuming when old decreases, which means that it is optimal to consume more when old. Intuitively, it is plausible, if interest rate increases, the opportunity cost of consuming today increases.

For the second question, when you try to find optimal level of education, you should take the derivative according to $e$. So, the lagrange multiplier cancels out, which mean that you find a somewhat static problem. You will have ;

$$h^{'}(e)=\frac{1+r}{w}$$

If wage is higher, marginal utility of capital is less, which means that the level of education is higher. So, if wage is high, there are more incentives to invest on human capital. You can make the inverse similar interpretation for the interest rate.


Why is the fed forbidden from buying gov't debt directly from the treasury? I know it's forbidden in its charter.  But what is the economic rationale?

There is no direct economic rationale for this. This is done because there is a worry that if Fed will directly deal with government it will undermine its independence.
When it comes to the independence itself most economists would argue that independent central banks perform their duties better than ones that are not independent (the same way how for example independent courts usually rule more fairly than ones that are not). This is also how Fed itself justifies its independence as you can see at their page here. Also for gauging the consensus among economists on central bank independence you can see this IGM poll amongst the top US economists (the poll is about political appointments - but that is all part of the whole Fed independence issue).


How much does a public sector pay rise actually cost the UK government? This is something that's in the UK news at the moment. Public sector workers have experienced a 1% annual cap on pay increase since 2013.

Government ministers are appearing on TV saying that they don't have the multiple billions required to fund an increase to bring it in line with the private sector.

Despite the headline figure (let's call it £6 billion), how much does the pay increase actually cost the government?  I'm thinking that VAT receipts, income tax receipts and corporation tax receipts (from an increase in spending) would surely all go up?

Unison (2014) - Net cost

The Public sector trade union did an analysis of lifting the cap in 2014. The report is here. Unlike the IFS analysis presented above, Unison estimates the net cost of an increase in public pay by 3%, using a microsimulation model. They estimates are summarised in the table below:

The key here is that a gross increase in the cost by approx. £4 billion reduces to a net increase between £1.7 and £2 billion (or £2.2; see Table 6a). The difference between scenarios depends on the assumption of the fiscal multiplier, which can range between 0.34 (used by the Office of Budget Responsibility), and 1.02 (upper bound used by the IMF). Naturally, the larger the multiplier is the higher the benefit from the wage increase, and the lower the net cost.

Institute for Fiscal Studies (2017) - Gross cost

The Institute for Fiscal Studies provided an analysis of the 2017 general election Labour and Lib Dem manifiesto, which included a lift to the 1% public pay cap increase. As the report states:

  Our analysis of the Labour plan implies that, compared to the current government’s plans, by 2021–22 a Labour government would need to provide departments and local government with an additional £9.2 billion per year to pay for the higher costs of employing public sector workers. Of this, £2.9 billion would be for the NHS. Comparing the Liberal Democrats’ plans to the current Conservative government’s plans, it would necessitate an extra £5.3 billion per year, of which £1.6 billion would be for the NHS.

The table below summarises their conclusions:

The key difference between the two parties is that the Lib Dem suggested to increase pay in line with inflation, whereas the Labour party suggested to increase pay in line with the private sector (more precisely, based on the recommendations of Pay Review Bodies).

As the report states, any forecast is highly dependent on the state of the economy (uncertainty due to e.g. Brexit):

  These Figures are highly sensitive to the forecasts of the economy. For the Liberal Democrats, the cost will be higher if inflation is higher in 2018–19 and 2019–20 than is expected by the OBR currently, or lower if inflation is lower. Under Labour’s policy if private sector earnings growth performs less well over the coming years than is forecast by the OBR (it has consistently underperformed OBR forecasts in recent years), then it would cost less than is implied by Table 1. Conversely, if private sector earnings growth performs better than forecast, and public pay is increased faster too, then the cost to departments and local government of Labour’s policy would be higher too.

Notice that these figures are gross cost estimates. I.e. they do not include indirect costs or benefits associated with it. For example, further costs might arise due to how the spending is financed. Such increase in spending would certainly require (i) more taxation, and/or (ii) more borrowing (cuts also possible, but less likely, due to party manifestos). The former could change incentives to work or invest (affecting growth), whereas the latter means higher borrowing costs, which have to be paid too. Regarding the benefits, if you have some belief in the fiscal multiplier, you could expect that part of that increase might be offset by extra revenues (income, VAT, etc) due to higher GDP (e.g. via consumption) from public workers. If this is a permanent increase, then such change in consumption is likely to be higher (at least according to the permanent income hypothesis).


Selection bias - Will multiple regressions solve the problem? Now I have a data from an African country concerning (i) levels of corruption across public sectors and (ii) perceptions of service quality from households (bad, medium and high). The data consist two types of household: those who have used the public services and those who have NOT.

I have read several papers from some respected journals (World Development, Journal of Development Economics) that address the problem of selectivity bias: those who have not engaged in public services might do so because they knew they would have to bribe (corruption) or they had bad experience from the past, and they would end up feeling bad.

Authors from the papers, however, do not use Heckit models, that I have learned from my degree. Instead, they argue that by running two regressions: (i) using data on those who actually used the services and (ii) all households in the sample, regardless of the service usage. I feel this approach is not correct.

I wish to understand further how selection bias, particularly in this example, should be handled. Some problems with the data are that the data might be subjective, quite small (around 500 households), and prone to measurement errors. Do you have any suggestions on dealing with the problems?

Many thanks.

What you are referring to is two-stage least squares. This is an instrumental variable commonly applied to correct for endogeniety and selection bias. It is a pretty hot topic in economics at the moment and, when applied correctly, can be very useful and will remove the selection bias.

There are a few conditions and assumptions -
Suppose you want to estimate this equation

$y_i = \beta x_i +\epsilon_i$
where

$i$ indexes observations,
$y_i$ is the dependent variable,
$x_i$ is an independent variable,
$\epsilon_i$ is an unobserved error term representing all causes of $y_i$ other than $x_i$
$\beta$ is an unobserved scalar parameter.

we suspect $x_i$ is endogenous

($cov(x_i, \epsilon)\neq 0$)

but we have a variable $z_i$ which is correlated to $x_i$ but uncorrelated with $\epsilon$

($cov(z_i, x_i) \neq 0$ and $cov(z_i, \epsilon)=0$).

This is a candidate for 2SLS:

Stage one is to estimate $x_i$:

$\hat x_i= \hat \gamma z_i + \epsilon$

Stage 2 is to estimate $y_i$

$y_i= \beta \hat x_i+ \epsilon$

The difference between this and the first regression is that $\hat x_i$ is uncorrelated with the error term and this selection bias has been corrected for. There are lot's of different uses of this. In principle, the two-stage regression used in the paper could correct for some of the biases discussed in the paper.

Further Reading:

This ppt (Slide 20 onwards) descibes an excellent (and very famous) example of IV.

These notes are also pretty solid as well.

This question provides some textbooks which are also very helpful. My personal favourite is "Mostly Harmless Econometrics" by Angrist and Pischkes (Written by the guy who did that famous example example above) and "Econometric Analysis of Cross Section and Panel Data" by Wooldridge. It is worth noting that both of these are graduate level books.


Market Theory: Upper limit of capital/weatlth accumulation? Politicians often bicker about how big the government should be when it comes to redistributing wealth.

Question: My question is simple; would a laissez-faire approach to the market always result in inequality? Is there an upper-limit to capital/wealth accumulation? That is to say, if the governments never step in, are there any market mechanisms to counter-act a few people absorbing extreme levels of wealth?

Note: I want to focus on free markets as much as possible, but if we so choose to go down the rabbit hole of "equality of opportunity" and "equality of outcome" here are my two cents: "Equality of outcome" comes off as Orwellian and dystopian in that the economy is planned absolutely, but "equality of opportunity" implies winners and losers under a market where people are free to produce, consume and compete.

A market is an social institution with various attributes and works under complex conditions. Under some conditions a pure monopoly is the only known limit.

Markets are creations by human intelligence and will not exist if not used for merchand. The market mechanisms are used in our society to enable a complex, diverse, work-sharing economy. Not the other way around.

Side note: The question is not how big a government is. A small government can have a bigger impact on a market than big government.

  My question is simple; would a laissez-faire approach to the market always result in inequality?

The reason why markets are so useful, they lower the costs to synchronize the various supplies with the societal limitless demands (individual demands can be limited). Markets can react to  technological, cultural and knowledge changes in the societies. But they depend on the kind of economy wherein they function. When the economy prefers bigger enterprises than many small firms, markets can not change much on these structures. Nevertheless the answer to your question is no. When a market starts under the condition of fair distribution and some other factors like transactions costs, market entry costs, costs for research and development and others don't play an important role, markets can stabelize the fair distribution of wealth.


Yuan to be a reserve currency, IMF is considering If yuan becomes a reserve currency, can we expect the petrodollars to be swapped with petroyuans given china's ever increasing mammoth demand for energy resources?

Yuan will certainly appear in the reserves of oil exporting countries. The question is how much of it?

China still has many problems with its currency and a long way to go until it becomes as appealing as dollar or even Japanese yen. Whether countries include a currency in their reserve basket ultimately depends on how predictable and stable it is compare to other currencies. It is also preferred that the currency appreciates in the long term. Living in China myself and holding my savings in yuan, I try to keep an eye on factors and risks that may move it up or down in medium to long term. Here are the most important in my opinion:

Upside:

China is still a huge and rapidly growing economy, expanding at least 4% a year (~7% being the official figure). As long as it produces so much goods and services that can be bought with its national currency, yuan will be appealing to investors.
China's population is growing and with recent cancellation of a one-child policy, it will continue to grow even faster. Growing population generally leads to economic expansion.
There are still market reforms to be made that, if implemented, will make the currency even more appealing. For example allowing banks to set lending and deposit rates freely would send yuan sky high.
China's state owned enterprises (SOEs) have trillions of dollar-denominated debt on their balance sheets. If yuan were to depreciate considerably, they would go bust being unable to service debt. It limits the freedom of Chinese government to devalue yuan.

Downside:

China still has a lot of work to do before yuan becomes a full-fledged reserve currency. It is still not freely convertible, there are capital controls in place for Chinese citizens, the People's Bank of China (China's central bank) is not independent of China's government, etc.
China's economy is slowing and the reforms that are being done are not enough. To reach growth targets and maintain social stability, the Chinese government may continue the policy of devaluing yuan to boost exports. Chinese corporate sector is certainly betting on it: http://www.marketwatch.com/story/chinese-companies-are-betting-on-further-yuan-weakness-2015-11-18
China packs a lot of political risk. It is not a democratic state with thick censorship of every media outlet. If it starts the process of democratization, it may become politically unstable with disastrous consequences to the economy and its currency. If it continues the path of one-party rule with a tight grip on the economy, it may lead to prolonged stagnation and slow devaluation of yuan.


Is marketing a field of economics? I would argue that the marketing (or de-marketing as in the example of a recall) of goods and services is an implementation of knowledge and experience in microeconomics as it deals with the practical economic activity of single persons and/or entities.
Is marketing a field of economics?

Yes, marketing falls under the JEL code of M, specifically M31.


Can debt to GDP ratio be reduced transfering debt to local autorities? It is my understanding that not only government but also local authorities issue bonds.
This answer on Money and Finance Stack Exchange suggests that such debts are not accounted in the computation of the government debt  (At least for the US).

Questions:

Is there an estimate of the total municipal bond per countries?
Could a very indebted country try to reduce his debt to GDP ratio forcing local authorities to issue more bond and thus reducing the government spending? If yes, is there any country that attempted this strategy?

To answer your second question: a country could probably do that, but it would achieve not much more thereby than clean up that particular statistic. In Europe, the Treaty of Maastricht that specifies the maximum debt-to-gdp ratio a country can have pertains to the whole government sector, which is defined so as to include local authorities (see this explanation on the site of the Belgian government https://www.debtagency.be/en/datagovernmentdebtdebt).

I don't know the situation in the U.S., but I think it can be assumed that in general any state or international institution that wants to know about another state's debt levels will not only look at the debt-to-gdp ratio.

In an analogous case, most E.U. officials are aware that the United States unemployment rate is on average lower than the European version partly because of differences in labour force participation, which works 'behind the scenes' of the official statistic (http://bruegel.org/2017/09/employment-in-europe-and-the-us-the-eus-remarkable-strength/).


Constant to the power of t in steady state I am wondering how to get the steady-state for the following Euler equation. I know that we can get rid of time in subscripts. However, here I have a constant (a) to the power of $t$. Does anyone know if there is a way to get rid of $t$ in power? Or can I just consider $a^t$ a new constant, say $\bar{a}$?
$$ \frac{1}{c_{t}}=a^t \beta E_t \Big[(1+r_{t+1})\dfrac{1}{c_{t+1}}\Big] $$

If the variables are constant, everything in the equation is time-invariant, while $a^t$ will still grow or fall over time (unless $a=1$). This is a contradiction and no steady state exists, unless $a=1$.


Difference-in-differences with long time horizon and repeated treatments I have a high-frequency panel dataset on the order of $i=150$ and $t=5000$. I am interested in studying the causal impact of a treatment with the following characteristics:

The same unit can be treated several times
Different units can be treated at different times
The effect of the treatment does not spill over beyond the current time period

Here is an example of treatment over time (where black indicates treated, and the y axis contains a row for each unit $i$):

Here is an example of a treated unit (black) and a comparison unit (blue) when treatment is administered (red), where the $y$ axis is an outcome of interest:

Coming from the perspective of causal inference / program evaluation, it seems like the natural approach is to use some sort of difference-in-differences flavored model, where treated units act as controls for untreated units at different points in time. However, I am struggling to find an analogy in the literature.

Typically, in example diff-and-diff models I have seen, units are treated only once, control units are never treated, and the treatment persists into the future.
Also, with such a long time horizon autocorrelation seems problematic, and time-varying, individual-level seasonal fixed effects are likely necessary. Consequently, I expect that I need to make some modifications to the basic panel approach of including fixed effects for $i$ and $t$.

My question is:

Have people used diff-in-diff analyses with similar datasets? If so, could you point me to some sample papers?
Is there an alternative approach that would be be better suited to this setting? If so, are there relevant references? (e.g. from macro, finance, time series literature).

Thanks for any guidance you can provide.

This question is related to a post I addressed on CrossValidated. The "generalized" difference-in-differences (DiD) estimator is amenable to settings with multiple groups and multiple exposure periods. Take the following specification:
$$
y_{it} = \gamma_{i} + \lambda_{t} + \delta T_{it} + \epsilon_{it},
$$
where $\gamma_{i}$ and $\lambda_{t}$ denote unit (i.e., individual, entity, county, state, etc.) and time (i.e., day, month, year, etc.) fixed effects, respectively. You may also see this referenced as a ‘two-way’ fixed effects estimator. The variable $T_{it}$ is a treatment dummy, indexing the $i$ units affected by the policy/intervention during periods $t$, 0 otherwise. In practice, $T_{it}$ can take on any pattern. Thus, it can more than handle intermittent exposure periods.
Your main policy dummy $T_{it}$ is your interaction term, but you must instantiate it manually to account for the different entities moving into and out of a treated status across time. Thus, $T_{it}$ 'turns on' (i.e., equals 1) if two conditions are met: (1) the entity is in the treatment group and it is in the post-treatment period. Be careful because $T_{it}$ does not demarcate a precise treatment group. Rather, it a discrete indictor for adopter entities and only during those adopter periods. Any 'off' period of treatment should be coded 0.
The problem in your setting is you have a large number of treated units with staggered adoption periods, making it exceedingly difficult to demonstrate a common trend across groups. Centering all units on their adoption date is insufficient as a subset of treated units have multiple treatment regimes. I wonder if you could work on subsets of your data where most treated entities enter into the treatment epoch at more or less the same time. However, this might be difficult with repeated, transient post-exposure periods. Pre-trends might also be violated in settings with irregular exposure periods and heterogeneous treatment effects, a point noted in a recent working paper. In sum, while the "generalized" DiD estimator will work in your setting, you must be cognizant of the downsides of using this approach.
I have previously evaluated policies that were introduced and repealed on several occasions over time. The only difference is the policy dummy turned 'on' and 'off' at the same time for all units. While a different subset of entities were treated in each iteration of the policy, the exposure period was standardized. Thus, I was able to focus on subsets of my panel and assess trend equivalence before each adoption period. I would be happy to share this research if it offers any further insight.
You might also find this working paper an interesting read.


Why does Walmart (SYMBOL:WMT) have its Q1 2015 end April 30 instead of March 30 The Walmart 10-Q form covers the period for the three months ending April 30th while other companies post their first quarter reports for the three months ending March 30th. Why does Walmart end one month earlier than other companies? How are companies regulated in this regard?

A December fiscal year end, which gives a first quarter of three months ending March 30, aligns the fiscal and the tax year. This can be very convenient and in the United States is sometimes required. In addition, some regulated firms like banks are required to prepare documents on calendar quarters regardless of the month of their fiscal year end, and it is often cheaper and easier to have them be synchronized rather than close the books additionally for regulators.

Firms may be motivated to alter their fiscal years so that they can better serve their customers or investors. For example, some banks have a fiscal year end not in December so that customers needing to do financial transactions at the end of their year could do so without the bank simultaneously having to close their own books. For many years Morgan Stanley did this. Walmart may be doing this because December is the Christmas shopping season in the United States and management wants to focus on that critical shopping period without the distraction of accounting issues. Additionally, if some shopping comes in after the holiday (say if Hanukkah comes late or because of a rash of belated Festivus shopping), it might split a single shopping season into different fiscal years which could be undesirable for investors trying to compare retailer performance.

I don't want to lean too hard on any of these explanations for Walmart's timing. If I recall correctly from looking in Compustat a few years ago more than 80 percent of US listed firms have a December FYE and this didn't vary a huge amount across industries.

UPDATE:
I went into Compustat and I redid the table of retail, banking, and other firms showing the months of fiscal year end the last 12 months (8/2014-7/2015).
I was surprised to see that retail was indeed vastly (>20 times) more likely to have a January FYE than a typical publicly listed firm in 2015.  The results appear in the figure below.

Source: Compustat

This gives credence to the hypothesis that as a retailer with significant holiday sales, Walmart may have a January FYE to highlight those results.


Adverse Selection: Positive Selection of Worker Types (Mas-Collel) I'm reviewing some question from Mas-Collel and I am stuck on a chapter 13 question related to adverse selection.
Consider a model of positive selection in which there are workers of two possible productivity types, $\theta_H$ and $\theta_L$, with $\infty > \theta_H > \theta_L > 0$ and $\lambda = Prob(\theta=\theta_H)  \in (0,1)$.
A worker of type $\theta_i$ can produce $\theta_i$ for a firm in exchange for a wage $w$ or work at home and gain $r(\theta_i)$.
r(.) is strictly decreasing and r$(\theta_H) < \theta_H$ and that $r(\theta_L)>\theta_L$. Show that the highest-wage competitive equilibrium need not be a constrained Pareto optimum. [13.B.9]
If the equilibrium is not a constrained Pareto optimal, then it could be a Pareto optimal, this occurs where all types are full employed when $w = \theta$, i.e. the condition that $\Theta^* = \{\theta:r(\theta) \leq w^*\}$.

In PO, you want all types with opportunity cost $r(\theta)\leq \theta$ to trade, because the firm gets more productivity than the worker has to give up on home productivity ("opportunity cost").
By your assumptions $r(\theta_H) < \theta_H$ and $r(\theta_L)>\theta_L$ such that in PO, L shall stay at home and H shall work. However, you need to offer H a wage of at least $w\geq r(\theta_H)$.
The highest wage a firm would offer is the expected $\theta$ of a worker who is willing to accept this wage. Suppose that $\mathbb E[\theta]=\lambda \theta_H + (1-\lambda)\theta_L >r(\theta_H)$ and, by definition,  $\theta_L<\mathbb E[\theta]<\theta_H$.
Now, it could be that $w=E[\theta] > r(\theta_L)$ such that L would also want to accept this wage, but this is inefficient as
$$w > r(\theta_L) > \theta_L.$$
Low types should not work, but because there are so few of them ($\lambda$ is large), the firms would still profit if they also accepted $w$.
An uniformed third party could Pareto improve the allocation by changing the wage to $w' \in (r(\theta_H),r(\theta_L))$ such that L types would reject $w'$.


Difference between 'ideal variety' and 'love of variety' - International trade What really is the difference between the "ideal variety" (Lancaster) of a differentiated product approach and the "love of variety" (Dixit and Stiglitz) approach?

Basically, the difference is that in the love of variety approach the entry of new varieties in the market does not "crowd" variety space. So, differentiated varieties may exhibit a high or low degree of substitutability, but this is invariant to the number of products in the market. Hence, consumers "love" variety, in the sense that increased variety improves welfare.

In the Lancaster ideal variety approach, entry of new varieties causes "crowding". Goods become more substitutable as more varieties enter the market. So, the marginal utility of new varieties falls as the market size grows.

These two approaches have different implications for welfare of small and large countries as discussed in Hummels and Lugovskyy.


How does a division of a company spinning off from it's 'parent' company change it from a cost center to a profit center? Reading an article about how many IT divisions of big companies in Japan, became seperate companies. The motivation is apparently to turn them in profit centers. Can anyone explain how becoming a seperate company would be profitable for the original company?

Extract from article:

"Software development is a critically important part of the Japanese IT sector.  The software developers can be categorized into three groups – Maker, User, and Independent System Integrator (so-called SIer). The Maker group consists of computer manufacturers and their subsidiary companies which provide total system solutions including software development and support as well as hardware. Representative companies are Fujitsu, NEC, Hitachi and IBM.  Companies in the User group are former IT divisions which were spun off from parent “user” companies in order to transform themselves into profit centers from cost centers. Most of the large players in financial, manufacturing, and trading sectors keep vertical relationships with their IT subsidiary companies. "

Source: Evaluating The Strategic Implications
Of Japanese IT Offshore Outsourcing
In China And India

The parent company pays (roughly) the same amount for IT services as it did before, but those payments are now counted as income for the spinoff company.  It's mostly an accounting trick, although as Aidan O'Gara pointed out, the new spinoff may take on other clients and start to generate additional income that way.

Note that some companies use a form of internal currency to track inter-departmental services.  In such situations, departments providing critical infrastructure (such as IT) can often build up a hefty surplus of this internal currency, which can sometimes be spent by managers on internal "perks" for employees (free meals in the company cafeteria, free transportation home from work in a company limo, etc.)  I enjoyed such perks (working in a software support department as an otherwise low-paid intern) at a Wall Street firm in the 1990s.  However, if such internal accounting is denominated in actual currency — as it was when I worked at a public university — then it can lead to flawed apples-to-oranges comparisons by some departments, in which they (incorrectly) believe it is cheaper to use an outside vendor rather than the institution's internal department, due to local optimization that ignores economies of scale or the needs of other departments.


Does a private company that is 100% financed by a bank loan have a WACC equal to the interest rate? When estimating a company's Cost of Debt for a Weighted Average Cost of Capital (WACC) calculation we normally look into its bond yield. But for a private company with 100% debt capital structure, will the cost of debt be simply equal to the interest rate? If not why?

Thanks.

Let's address your question in a canonical manner. Say that:

the required rate of return of (private) investors is denoted by $r$.
the interest rate or the cost of debt is denoted by $r_D$ (naturally $r_D < r$)
the share of debt in the capital structure of the company is denoted by $X\%$
the corporate tax rate is denoted by $T_c$

It follows that the average cost of capital (average over equity and debt), $r'$, is such that

$r' = X\% r_D (1-T_c) + (1-X\%) r$

In your case, $X\% = 100\% = 1$, then $r' = r_D(1-T_c)$.

  [...] will the cost of debt be simply equal to the interest rate? If not why?

No. Because of $T_c$, the corporate tax rate being potentially non-zero.


$a\geq 0$, $x\sim y$ implies $x+a\sim y+a$ so the preference is linear? $\succsim$ is a countinuous and convex weak order.

$x,y,a$ are vectors in $\mathbb R^n$

We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero.

We want to prove (or disprove by counterexample) that:

Suppose $x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R^n$,

Then the preference is linear.

One definition of linear preference is that $x\sim y$ implies $x+a\sim y+a$ for any $x,y,a$.

This is not true.

Let $n=1$ and define $u(x)=\min{\{x,0\}}$. Let $\succsim$ be the preference relation represented by $u$. This preference relation is continuous and convex. We also have $x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R$. But let $x=0$, $y=1$, and $a=-1$. Then $x\sim y$, but $y+a=0\succ -1=x+a$, thus $x+a\nsim y+a$ and $\succsim$ is not linear.


The effect of Monetary Policy on Asset Price Inflation My macroeconomics professor told the following:
A decrease in interest rate causes that consumers rather spend their money on investments (stocks, houses) than put the money on the bank, and the increase in demand for stocks and houses causes asset price inflation in return.

However, if I try to search for a scholarly source saying the same thing, I cannot find anything. Is the above reasoning a solid one?

Thank you very much in advance!

My understanding of the effect of easing monetary policy on asset prices is that it can work through a more direct channel.

If markets are efficient and risk neutral then generally the value of an asset $i$ is equal to the net present value of the expected cash flows generated by that project:
$$ P_i = NPV(i) = \sum_{\tau=0}^{\infty} \frac{E[C_\tau]}{\Pi_{\ell=0}^{\tau}(1+r_{\ell})} $$
Monetary policy directly lowers the denominator of the the fraction in the sum, so it raises the value of the sum. In English, by reducing the rate at which we discount future investment the present value of the asset's cash flows become more valuable. If monetary policy can also improve the economy more generally, it can also increase the expected size of the cash flows, further increasing the value of the asset (it also raises the numerator).


Mixed Cournot/Bertrand Duopoly I am learning basic Oligopoly models.

I know that :

In Cournot model firms set output - output is the strategic variable.
In Bertrand model firms set prices - price is the strategic variable.

Simple problems I see are usually given demand/cost fucntion for a differentiated duopoly and let us determine the Bertrand or Cournot equilibrium.

Here however is a mixed market:

Assume the following duopoly (firms are denoted by 1 and 2) with the following demand functions:

$$P_1=100-0.5Q_1-0.4Q_2 \\
P_2=100-0.5Q_2-0.4Q_1$$

Firm 1 plays Cournot while firm 2 plays Bertrand. Assuming that there are no costs, find the optimal Nash quantity-price solution.

How can I solve for the equilibrium?

Each player seeks to maximize his or her revenue. As you said, in the Cournot model, the player varies the output. In the Bertrand model, the player varies the price.

So we first solve for $Q_{2}$ as a function of $P_{2}$:

$$Q_{2} = 200 - 2P_{2} - 0.8Q_{1}$$

We then substitute $Q_{2}$ into $P_{1}$ to get:

$$P_{1} = 100 - 0.5Q_{1} - 0.4 (200 - 2P_{2} - 0.8Q_{1}) = 50 - 0.18Q_{1} + 0.8P_{2}$$

Player $1$'s maximization problem is:

$$\max_{Q_{1}} 50Q_{1} - 0.18Q_{1}^{2} + 0.8P_{2}Q_{1}$$

Which yields the first order conditions:

$$0.36Q_{1} = 50 + 0.8P_{2} \implies Q_{1}^{*} = \frac{1250}{9} + \frac{20}{9}P_{2}$$

Now we can substitute $Q_{1}^{*}$ into $Q_{2}$ to get:

$$Q_{2} = 200 - 2P_{2} - \frac{4}{5}(\frac{1250}{9} + \frac{20}{9}P_{2})$$

Now maximize $Q_{2}$ with respect to $P_{2}$. Can you take it from here?


Infinite Horizon Transversality Condition This question is an extension of Endogenous Growth: Balanced Growth Path with CRRA Utility

however, this question asks about a specific concept used in that question, and I think it would be helpful to have a question dedicated to this concept.

We will use the model in this question:

  $\textbf{Model:}$
  $$K_t=\frac{1}{n}\sum_{t=1}^nk_t$$
  In this model, $k_t$ is chosen by agents, and $K_t=\bar{k}_t$ (the average of all $k_t$).

  Now, agents want to dynamically maximize utility (under certain constraints) and they have CRRA (constant relative risk aversion) utility, so the maximization looks like:
  $$\sum_{t=0}^\infty\beta^t\bigg(\frac{c_t^{1-\gamma}}{1-\gamma}\bigg)$$
  $$s.t.\;Y_t=k_t^\alpha(E_tL)^{1-\alpha}$$
  $$c_t+i_t=Y_t$$
  $$k_{t+1}=(1-\delta)k_t+i_t$$
  $$c_t,i_t\geq0$$

  $E_tL$ is effective labor and the rest of the variables are typical  (I can give their definitions if requested).

  One last addition to the model is that there are two equilibrium constraints:
  $$E_t=\frac{K_t}{L}$$
  $$k_t=K_t$$

In the answers section, I was instructed to use transversality conditions and inada conditions in order to show that a balanced growth path is optimal. Below is my derivation of the transversality condition:

First, we must derive the finite horizon transversality condition. We do this by solving:
$$\underset{\{k_t\}_{t=0}^{T+1}}{max}\;\sum_{t=0}^{T}\beta^tU(\frac{}{})$$
$$s.t.\;k_{T+1}\geq0$$
With our model that means:
$$\underset{\{k_t\}_{t=0}^{T+1}}{max}\;\sum_{t=0}^{T}\beta^t\bigg(\frac{((1+1-\delta)k_t-k_{t+1})^{1-\gamma}}{1-\gamma}\bigg)$$
$$s.t.\;k_{T+1}\geq0$$

Our Lagrangian is:
$$\ell(\frac{}{})=\sum_{t=0}^{T}\beta^t\bigg(\frac{((1+1-\delta)k_t-k_{t+1})^{1-\gamma}}{1-\gamma}\bigg)+\lambda k_{T+1}$$

In order to get the transversality condition, we differentiate with respect to $k_{T+1}$ and use the constraint.

FOC:
$$\frac{\beta^T}{((1+(1-\delta))k_T-k_{T+1})^\gamma}=\lambda \qquad (1)$$
$$\lambda k_{T+1}=0 \qquad (2)$$
$$\lambda , k_{T+1}\geq 0 \qquad (3)$$
Solving this system, we get $\textbf{the finite horizon transversality condition is:}$
$$\bigg(\frac{\beta^T}{((1+(1-\delta))k_T-k_{T+1})^\gamma}\bigg)k_{T+1}=0$$
Now, in order to get the infinite horizon transversality condition, we maximize the discounted utility function again, but we set the limit of finite horizon transversality condition as $T\rightarrow \infty$ equal to 0 as the constraint.

This means that we have to solve:
$$\underset{\{k_t\}_{t=0}^\infty}{max}\;\sum_{t=0}^\infty\beta^t\bigg(\frac{((1+(1-\delta))k_t-k_{t+1})^{1-\gamma}}{1-\gamma}\bigg)$$
$$s.t.\; \underset{T\rightarrow\infty}{lim}\;\bigg[\bigg(\frac{\beta^T}{((1+(1-\delta))k_T-k_{T+1})^\gamma}\bigg)k_{T+1}\bigg]=0$$

This is where my question comes. How do we solve this? Can we use a lagrangian? If so, how do we take first order conditions in the presence of the limit? Any help would be greatly appreciated!

Your confusion comes from the fact that you treat the Transversality condition as a constraint, while it is a condition for optimality. So the formulation at the end of your question is wrong. What you do is you solve your model as usual, and then check if the solution (here the balanced growth path) satisfies the Transversality condition.

The Transversality condition (TVC) is

$$\lim_{t \rightarrow \infty} \beta^t u'(c_t)k_{t+1} =0$$

In your model, $u'(c_t) = c_t^{-\gamma}$ and $c_t = (2-\delta)k_t - k_{t+1}$

So the TVC becomes indeed

$$\lim_{t \rightarrow \infty} \frac {\beta^tk_{t+1}}{[(2-\delta)k_t - k_{t+1}]^{\gamma}} =0$$

What we want is to check whether the (unique) balanced growth path satisfies the Transversality condition. On the balanced growth path we have $k_{t+1} = (1+g)k_t$ where $g$ is a constant determined by the exogenous parameters of the model and the optimizing conditions. So when on the balanced growth path, the TVC becomes

$$\lim_{t \rightarrow \infty} \frac {\beta^t(1+g)k_t}{[(2-\delta)k_t - (1+g)k_t]^{\gamma}} = \lim_{t \rightarrow \infty}\frac {(1+g)}{(1-\delta-g)^{\gamma}}\beta^t k_t^{1-\gamma}=0$$

The constants are unimportant, so we want that

$$\lim_{t \rightarrow \infty}\beta^t k_t^{1-\gamma}=0$$

holds. Note that if $\gamma \geq 1$ (which is the consensus in the literature) the condition does hold, since capital goes in the denominator, and we're done.

For the case $\gamma <1$, we want the expression to hold at the limit only, i.e. eventually . "Eventually" implies that, if $k^*_s$ is the level of capital at time $s<t$ when the economy arrives at the balanced growth path, we will have $k_t = k_s^*\cdot (1+g)^{t-s}$. Then the TVC becomes

$$\lim_{t \rightarrow \infty}\beta^t \big[k_s^*\cdot (1+g)^{t-s}\big]^{1-\gamma}=0$$

Again, shed things that do not depend on $t$, to get

$$\lim_{t \rightarrow \infty}\beta^t (1+g)^{(1-\gamma)t}=0 \implies \lim_{t \rightarrow \infty}\big[\beta (1+g)^{(1-\gamma)}\big]^t=0$$

So the TVC will hold if and only if

$$\beta (1+g)^{(1-\gamma)} <1$$

In the other question the OP has obtained

$$1+g = [\beta(\alpha+1-\delta)]^{\frac{1}{\gamma}}$$

Substituting, we want

$$\beta \Big([\beta(\alpha+1-\delta)]^{1/\gamma}\Big)^{(1-\gamma)} <1$$

This can be simplified a bit, and it is a restriction on the parameters that must hold in order for the balanced growth path to satisfy the Transversality condition (when $\gamma <1$). For baseline values of the other parameters one can see that the condition is not likely to be satisfied.


A few questions in paper Chong 2007 I think it is hard to derive Eq(5) in paper Chong (2007).
 (http://www.bgu.ac.il/~grade/inst_ineq.pdf) Could anyone share any ideas on its derivations or intuitions behind it? Let's discuss it in more details to help us understand more about this paper. Thank you a lot.

Could you help me derive Eq(5) in paper Chong (2007)?

My initial derivations were wrong because I misread Eq(1) as $y_{i,t}=c_{i,t}+r_{i,t}$. It was until I read the answer posted by @AlecosPapadopoulos that I realized that the paper actually uses $y_{i,t}=c_{i,t}+r_{i,t+1}$.

However, apropos of the latest edit of OP's inquiry (now to discuss the intuitions behind [the paper]), I still posit that the paper is a subtle promotion of socialism premised on flawed or impractical notions.

The paper makes the point (and Alecos' answer presents a clear derivation of Eqs(5)) that the optimal value of rent seeking $r_{i,t+1}$ is $0$ for strong institutions, which are denoted by $w=0$. This means that no household should pursue rent seeking. Or equivalently (see Eq(2)), that no household should seek to appropriate a larger share of the resource (page 6). Regardless of the model's time horizon (generations instead of shorter periods), that differs very little (if at all) from socialism.

Additionally, since $y_{i,t}=c_{i,t}+r_{i,t+1}$, the optimal choice in strong institutions would be $y_{i,t}=c_{i,t}$. That is, the household should allocate its entire income to consumption. Obviously, that generalized policy renders a real-life economy highly vulnerable to contingencies and structural changes. That vulnerability inherently contradicts any notion of "strong" institution.

Furthermore, substituting $w=0$ and "optimal" $r_{i,t+1}=0$ in Eq(2) gives $a_{i,t+1}=A\frac{0^0}{\int^1_0{0^0di}}$. What are we supposed to do with that?

Another problem is the model's inter-generational framework. I appreciate Alecos' emphasis/clarification that different values of $t$ for a same household $i$ allude to different generations of that household.

But that modeling horizon is hardly realistic because each household experiences too many or too profound transformations (oftentimes just from one generation to the next one) to be still considered a single, continued entity. Indeed, households go through marriages, divorces, remarriages, child bearing in each marriage, emigration, bankruptcy, and so forth.

It is not necessarily realistic to assume that $w$ is constant throughout generations either, as the paper subsequently assumes.


Christiano Fitzgerald filtering process I'm trying to compare the results of Christiano Fitzgerald bandpass filter with wavelets. I'm familiar with wavelet decompositions in general, but I'm rather new with Christiano Fitzgerald (CF).

So far, I have understood that CF is able to decompose the series to trend and cycles and it is also able to decompose the signal in specific time frames as wavelets do. However wavelets operate with a pyramid algorithm where the first level decomposes the signal to mother and father and it finds the 2-4 frequency and the trend. Then, it picks these results and it decomposes them again to find 4-8 and so on.

The documentation of mFilter in R states the following for CF:

  Arguments:

  type: the filter type, "asymmetric", asymmetric Christiano-Fitzgerald
  filter (default), "symmetric", symmetric Christiano-Fitzgerald
  filter "fixed", fixed length Christiano Fitzgerald filter,
  "baxter-king", Baxter-King fixed length symmetric filter,
  "trigonometric", trigonometric regression filter.
  pl: minimum period of oscillation of desired component $(pl<=2)$.
  pu: maximum period of oscillation of desired component $(2<=pl<pu<infinity)$.
  root: logical, FALSE if no unit root in time series (default), TRUE if unit root in time series. The root option has no
  effect if
  type is "baxter-king" or "trigonometric".
  drift: logical, FALSE if no drift in time series (default), TRUE if drift in time series.
  nfix: sets fixed lead/lag length or order of the filter with "baxter-king" and "fixed". The nfix option sets the order of the
  filter by $2*nfix+1$. The default is $nfix=1$.
  theta: moving average coefficients for time series model: $x(t) = mu + root*x(t-1) + theta(1)*e(t) + theta(2)*e(t-1) + . . .$ ,
  where $e(t)$ is a white noise.

Are the arguments pl and pu responsible for the level of decomposition? For example, if I pick $pl = 2$ and $pu = 4$, it will go for 2-4 days/weeks etc and if I go for $pl = 32$ and $pu = 64$ it will decomposes for 32-64 days/weeks/months etc or am I missing something?

Thank you in advance

If you pick pl=2 and pu = 4 and your data is daily, then indeed you filter out the trend that has frequency up to 4 days. So, your trend line is a sum of trigonometric functions with the aforementioned periodicity. The cycle comprises all the other remaining frequences.


Proof: Risk averse; Certainty Equivalent smaller than expected value I would like to show for a randomly distributed variable $x$ with CDF $F(\cdot)$ , given a Bernoulli utility function $u(x)$ the following property holds:

The certainty equivalent, $CE(\cdot)$, is smaller than the expected value, $\mathbb E(\cdot)$, if and only if the decision maker is risk-averse.

$$CE(F,u) \leq \int_{-\infty}^{\infty} x dF(x) \quad  \forall F(\cdot)$$

By Jensens Inequality for risk-averse agents we have:
$$\int_{-\infty}^{\infty} u(x) f(x)dx \leq u(\int_{-\infty}^{\infty} x f(x) dx)$$

I know that the CE is defined as:
$u(CE) = \mathbb E(U(X)) = \int_{-\infty}^{\infty} f(x)u(x)\,dx$

Hence,

$$u(CE)  \leq u(\int_{-\infty}^{\infty} x f(x) dx)$$

and

$$CE \leq \int_{-\infty}^{\infty} x f(x) dx$$

Is it possible to kind of invert the u() function is we assume it is strictly increasing?

I also thought about rearranging it to:

$$u(CE) = \int_{-\infty}^{\infty} f(x) dx * \int_{-\infty}^{\infty} u(x) dx$$

but I fail to see how that helps.

I thought perhaps showing that the risk premium is positive for risk-averse agents is equivalent but I could not get started either.

I would be glad for a hint to work out the solution myself.

You basically have the proof, just remember that for any function $f(x)$ strictly increasing, then $f(a)\leq f(b)$ if and only if $a\leq b$. It is also true that for any strictly increasing function its inverse exists, but there is probably no need for that.


Difference(s) between Rational Expectations Equilibrium and Nash equilibium What is the major difference between the notion of rational expectations equilibrium and Nash equilibium? And why do we, only, have a rational expectation about the first moment (the price) in the former one? Do they coincide or they constitute a completely different framework? They seem so similar to me in some articles, that I can not distinguish their features if they are any!

Hi: They are pretty close to completely different. I don't know the least thing about game theory but a nash equilibrium describes what happens in a game when two or more people have a certain type of expectation. RE is one type of expectation but if you google for RE you'll see that it's a field in itself. It happens to have an application in game theory but it's a seperate field developed by macro-economists in the early 70's. RE founder could be viewed as Lucas or John Muth depending on who you ask. Muth came up with the concept in 1961. Lucas applied it to macro-economics in the early 70's and it took off from there.


Why are property price-to-rent ratios relatively low in the US? I am looking at the data here (for 2015). There are data for 489 cities from around the world, of which 82 are in the US.

Using the measure "Price To Rent Ratio Outside Of City Centre", 69 of the 82 US cities are in the bottom 125 of all cities (roughly the bottom quartile) and the highest-ranked US city is Santa Barbara, CA at #206.
Using the measure "Price To Rent Ratio City Centre", 67 of the 82 US cities are in the bottom 125 of all cities and the highest-ranked US city is again Santa Barbara, CA at #147.

What might explain why the property price-to-rent ratio in the US is relatively low, when compared to the rest of the world?

Reviewing their methodology, they make a number of assumptions that will affect their results. They don't provide the sources of the data they use as inputs, so it's impossible to fully evaluate their methodology, but it is worth noting their description:

  Price to Rent Ratio - is the average cost of ownership divided by the
  received rent income (if buying to let) or the estimated rent that
  would be paid if renting (if buying to reside). Our formula to
  estimate rent per square meter assumes 1 bedroom apt has 50 square
  meters and 3 bedroom apartment has 110 square meters. It doesn't take
  into account taxes or maintenance fees.

Given the relatively simple assumptions, lack of transparency regarding input data, and reliance on assumed homogeneity in housing stock both internationally and intra-city, I wouldn't rely on these data to arrive at any conclusions, let alone the conclusion that price-to-rent ratios are particularly low in the US.


LM-Curve formula question An LM Curve can be described as following
$M^d(Y,i) = M_0 + M_1Y – M_2i$
$M^d = M/P$
M and P are exogen
I know that $i$ is interest rate, and Y is GDP.
Why is $M_1$ and $M_2$ positive? And what does $M_0$ represent?
I can't quite wrap my head around it

Here;
$M^d(Y,i)$ is the demand for money.
$M_0$ is the ‘autonomous’ demand for money, i.e. demand for money that would not depend on income or interest rate.
$M_1$ is the effect that real income/output has on demand for money. It will be positive because ceteris paribus when there is more goods and services around people demand more money for carrying out transactions.
$M_2$ is the effect nominal interest rate has on money demand. It is actually negative not positive, and the reason why it is negative is that if interest rate is higher people demand less money both because it is more expensive to get (borrow) money and because with higher interest rate people prefer to save more and postpone their purchases to the future so they need less money.


World bank data - GDP per capita current US\$ vs constant 2005 US\$ I'm looking at two charts from world bank on GDP per capita for Croatia and Russia - and this is what I get:

Now, from what I gathered, the first chart should represent nominal gdp and the second one real gdp (in 2005 US$).

Shouldn't the charts look similar, only with different absolute values? I thought that, for example, you could get 2014 real values simply by adjusting nominal values for total inflation between 2005 and 2014. If that inflation was 25%, then 2014 real = 2014 nominal / 1.25 (in 2005 US$).

How come that in the first chart GDP per capita is almost the same in 2014, and in the second one Croatia's GDP per capita is more than 50% larger?

The two charts are consistent in the basic sense that the 2005 values are the same in both, with Croatia about $\$10200$ and Russia about $\$5300$. What happens in other years depends on exchange rates and inflation in the three countries concerned (Croatia, Russia and the United States).

The current USD-based figures are calculated much as you would expect: take the GDP per capita in local currency (kuna in Croatia, rubles in Russia) and covert these to dollars at the exchange rates applying in the different years.

Your question would make sense if the constant USD-based figures were calculated by taking the current USD-based figures and deflating them for price changes in the US since 2005. So the Croatian and Russian numbers current USD-based figures would have been deflated by the same ratios, and if they were to meet in a particular year in one series then they would meet in the same year in the other series.

But they were not calculated that way.

Instead the constant USD-based figures were calculated by taking the GDP per capita in local currency each year, and were deflated by price changes locally since 2005 to give GDP per capita in constant local currency units, and then converted to dollars using the 2005 exchange rates. Because exchange rates did not match varying relative local price changes in Croatia and Russia compared with the United States, this produces a different result.

There is a way to approach this question to reduce the problem, but that would involve purchasing power parities (PPP) looking at what money can actually buy in different countries rather than market exchange rates, and the statistical invention of the international dollar (not an actual currency) to handle price changes year-to-year. It results in different data again and can lead to different rankings between countries (famously, China would appear to be relatively much richer). Here it would suggest Russia having significantly higher GDP per capita than Croatia since 2011 on a PPP basis, the opposite of your second chart due to the the ruble seeming to have been undervalued in the market exchange rates compared with the kuna in terms of what it can apparently buy locally.


What makes a company too big to fail? I have read the too big to fail Wikipedia and as far as I understand, a company is too big to fail (and thus will receive government bail-outs) if it's failure has a significant impact on an important industry or the economy as a whole. Is my understanding correct? For example, a company such as Snapchat would not be bailed out because while it is worth a lot of money, its failure does not hurt the United State's infrastructure or the economy as much as GM's failure.

In economics Too Big To Fail (TBTF) can have slightly different meaning depending on what research you are looking at but generally speaking literature seems to agree that what matters is how interconnected or systemically important firm is (e.g. see Bernanke 2010;  Zhou, 2009).
Systemically important firms are such that other firms critically depend on them. In fact in recent literature you will often see people arguing that TBTF is a misnomer and better terms would be “too complex to fail” or  “too interconnected to fail” (see Kaufman, 2014), because really TBTF has much less to do with actual size than interconnectedness of a firm.
This is the reason why you usually hear the term TBTF being applied to banks or financial institutions. Financial, institutions are an economic equivalent of infrastructure as they help to allocate capital to its most efficient uses and many other firms depend on them (see Mishkin & Eakins Financial Markets and Institutions).
Consequently, whether General Motors or Snapchat are TBTF depends on how interconnected are with the rest of an economy. If there would be significantly many  'influencers' and 'content creators' that they would become significant part of an economy snapchat might be TBTF. This being said although I was not able to find specific papers on examining how interconnected GM or Snapchat are I am going on a limb to say that probably neither of them are TBTF. As argued by Strahan (2013) TBTF in most cases really applies mainly to financial sector due to reasons already mention above.
In fact Strahan specifically argues in that paper that non-financial firms, using General Motors as an example of non-financial firm that would not be TBTF, can only be TBTF in rare cases. Although the paper makes just analytical argument for this and draws only on general literature without actually examining networks of General Motors specifically (importantly note just because firm is bailed out that does not mean it was TBTF - every company has incentive to argue its TBTF to get bailout and policymakers often cannot examine networks in real time so they have to make an educated guesses about whether firm is actually TBTF or not - if a non-financial firm claims to be TBTF its good to be skeptical given literature but I would not dismiss it out of hand either).


How to interpret "desired significance level"? I was studying threats to internal validity from Stock and Watson's Introduction to Econometrics 2nd edition, chapter 14 Assessing studies based on multiple regression.

The textbook says "hypothesis tests should have the desired significance level (the actual rejection rate of the test under the null hypothesis should equal its desired significance level). and confidence intervals should have the desired confidence level.

How should I interpret this short paragraph?

What I think it means is that the hypothesis tests should have appropriate/not-too-off-tract significance level. But what is desired confidence level? And why does these conditions have to do with threats to internal validity?

Pardon my poor understanding...

Thanks in advance for your help!

I am not sure what you mean by "appropriate significance level."

Basically how sure you want to be is your choice. A frequently used analogy is the presumption of innocence. You are considered guilty only if this is proven beyond reasonable doubt. But what exactly is reasonable?
This is for you to decide. If you require very strong evidence then the probability of making a false positive conclusion (Type I error) decreases. But this will increase the probability of making a false negative conclusion (Type II error).
In the presumption of innocence analogy: If you change the law in a way that will require more evidence for a conviction, you will send fewer innocent people to jail (Type I), but you will also let more guilty ones go (Type II).

The significance level is the probability of a Type I error occuring.

In some situations you can perform a cost benefit analysis. In quality control you may be able to determine the cost of the damage caused by a malfunctioning part and then compare this to the cost of throwing away a properly functioning part. Using these you can actually calculate a cost minimizing significance level. However in other situations this is not feasible, or sometimes not even desirable. Then you have to make your own decision about the significance level.

In econometrics the most frequently used significance levels are 0.1%, 1% and 5%. My understanding is that this is a rule of thumb and there is actually no calculation behind it. (I could be wrong.)
Given some data you might say that "the findings are significant on the 5% level but not on the 1% level," or you can simply give the p-value, this is what is usually done.


What is the difference between "Social Choice Theory", "Public Choice Theory", and "Collective decision-making? I need to know the difference between Social Choice, Public Choice and collective decision-making. Also, Is public choice, social choice the same as collective choice? Thank you

Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in some sense.1

A social choice is related to a collective decision. Many different opinions, preferences and interests are taken into account to form a decision which is acceptable by everyone who is involved. Opinions, preferences and interests don't just have a personal background, but a social one, too. The society around you influences your thinking and doing by socializing. Hence the name: Social choice theory.

Group decision-making (also known as collaborative decision-making) is a situation faced when individuals collectively make a choice from the alternatives before them. The decision is then no longer attributable to any single individual who is a member of the group.2

Collective decision-making refers to a group of people who are committed to make a decision. Collective means that the decision isn't made upon the ideas of one person but of several. Responsibility is shared among these people. One alone can't be held responsible for the decision as several people agreed to it.

A. What is Public Choice? Public choice is the study of political decision making.
i. It attempts to understand how public policies come to be adopted using economic models of the impacts of policies on individuals,
ii. and models of individual political behavior under a variety of political institutions.
iii. It tends to use rational choice models to do so, which is largely what distinguishes it from mainstream and classical political economy.3
[...] iii. (Roughly speaking, public choice, and/or rational politics, is the application of
economic models of human action to politics.)

The theory of Public choice believes that every politician is rational and economically (self-)interested. The goal of Public choice is to analyze and predict the behaviour of politicians and bureaucrats - analyzing their public choice.
Social choice theory and group decision-making are somewhat related to each other. However, a social choice doesn't need to be made by several people, it just has to represent several people. By considering a lot of interests and preferences, one or more make a decision to achieve the best.
Public choice is more like a field of research. Hence, it's related to both Social choice and group decision-making. As it's the application of economic models of human action to politics, you research the advantages and disadvantages of doing public decisions.
Long story short: Social choices and group decision-making are actions, Public choice is a field of study which researches political behaviour out of a economic view. All three are related to each other but still are independent approaches for making a decision.

1 Wikipedia: Social choice theory
2 Wikipedia: Group decision-making
3 http://rdc1.net/class/BayreuthU/PUBCL1.pdf